Shreyas Pulle

Upload folder using huggingface_hub

096dd06 verified about 1 month ago

63.5 kB

metadata

tags:
  - sentence-transformers
  - sentence-similarity
  - feature-extraction
  - dense
  - generated_from_trainer
  - dataset_size:4091
  - loss:MultipleNegativesRankingLoss
base_model: sentence-transformers/all-MiniLM-L6-v2
widget:
  - source_sentence: magnetic order superconductor
    sentences:
      - "arXiv:0802.4093v2 [cond-mat.str-el] 27 Feb 2009 Meissner eﬀect without superconductivity from a chiral d-density wave P. Kotetes∗and G. Varelogiannis† Department of Physics, National Technical University of Athens, GR-15780 Athens, Greece We demonstrate that the formation of a chiral d-density wave (CDDW) state generates a Topolo- gical Meissner eﬀect (TME) in the absence of any kind of superconductivity. The TME is identical to the usual superconducting Meissner eﬀect but it appears only for magnetic ﬁelds perpendicular to the plane while it is absent for in plane ﬁelds. The observed enhanced diamagnetic signals in the non-superconducting pseudogap regime of the cuprates may ﬁnd an alternative interpretation in terms of a TME, originating from a chiral d-density wave pseudogap. PACS numbers: 75.20.-g, 71.27.+a, 74.72.-h The Meissner eﬀect is considered to be the most direct signature of superconductivity [1]. However, the surpris- ing observations of such enhanced diamagnetic signals [2] well above the superconducting transition tempera- ture in the pseudogap regime of the cuprates [3], con- stitute a fascinating puzzle. There are two proposals for the nature of this regime that appear to dominate. The ﬁrst, associates the pseudogap with a dx2−y2 density wave (DDW) [4, 5], also called orbital antiferromagnet [6, 7], which normally competes with superconductivity. The second associates the pseudogap with spontaneous vortex-antivortex unbinding leading to incoherent super- conductivity [8] that should persist well above the su- perconducting Tc. This theory is reminiscent of the well known Kosterlitz-Thouless transition [9]. The available ARPES [10] and STM [11] experiments cannot diﬀerentiate a SC from a density wave (DW) gap, and therefore appear somehow incapable in settling di- rectly the issue. On the other hand, the unusual Nernst eﬀect and most importantly, the enhanced diamagnetic signal that accompanies it for a very large temperature region above the SC critical temperature [2], has been considered as a major argument in favor of the incoher- ent SC scenario. In fact, the enhanced diamagnetism is viewed as a signature of the usual Meissner eﬀect associ- ated solely with the SC state, and would therefore contra- dict the dx2−y2 density wave scenario since no Meissner eﬀect was expected in that case [7]. In this letter we put forward the Topological Meissner eﬀect (TME), that results from a chiral dxy + idx2−y2 density wave (CDDW) state. In fact, the Nernst region of the pseudogap regime may well be associated with a CDDW. The most intriguing property of a CDDW is that parity (P) and time-reversal (T ) violation induces Chern-Simons terms in the eﬀective action of the elec- tromagnetic ﬁeld, providing the possibility of the TME and the Spontaneous Quantum Hall eﬀect (SQHE) ear- lier discussed [12, 13, 14, 15, 16, 17, 18]. As we shall demonstrate, the TME is described by the same equa- tion we ﬁnd in the usual Meissner eﬀect of a supercon- ∗Electronic address: [email protected] †Electronic address: [email protected] ductor. Though, its origin is radically diﬀerent. In our system we encounter the realization of Parity Anomaly [13, 19], with the emerging Chern-Simons terms provi- ding a topological mass to the electromagnetic ﬁeld, in a gauge invariant manner [20, 21]. Moreover, the pos- session of chirality perpendicular to the plane, implies that the TME is strongly anisotropic. Particularly, it takes place for magnetic ﬁelds perpendicular to the plane while it is absent for in plane ﬁelds, in accordance with the experimental observations [2]. Note ﬁnally that a chi- ral d-density wave state has also been shown recently [22] to explain the experimental results concerning the Polar Kerr eﬀect in YBCO [23]. In order to demonstrate how the TME arises, we shall consider the following BCS hamiltonian for the CDDW HCDDW = 1 2 X k \x10 ∆kc† kck+Q + ∆∗ kc† k+Qck \x11 , (1) which describes a dxy+idx2−y2 state characterized by the wave-vector Q = (π, π), which is commensurate to the lattice (k + 2Q = k). Since spin degrees of freedom do not get involved we have considered spinless electrons, so that all our results will refer to one spin component. Fur- thermore, we use gµν = (1, −1, −1), ki = k = (kx, ky), kµ = k = (ω, k), qµ = q = (q0, q), µ = 0, 1, 2, i = 1, 2, e > 0, ℏ= 1 and we assume that repeated indices are summed. In the derivation of the Chern-Simons terms we shall restrict ourselves to the zero temperature case while necessary extensions to ﬁnite temperatures will be afterwards performed. In addition, the summation in k−space is all over the whole 1st Brillouin zone rather than the reduced Brillouin zone. This implies that the operators ck and ck+Q do not describe independent de- grees of freedom. In Eq.(1) we have introduced the CDDW order param- eter ∆k = η∆sin kx sin ky+i∆ \0cos kx −cos ky \x01 , where ∆ is the modulus of the idx2−y2 order parameter, η deﬁnes the relative magnitude of the two components and also determines the direction of the chirality of the state. The chiral character of the state implies the existence of an intrinsic angular momentum in k−space, perpendicular to the plane, originating from P −T violation. Speciﬁ- cally, the dx2−y2 component violates T as it is imaginary, 2 while the dxy component is odd under P in two dimen- sions, which is deﬁned as (kx, ky) →(kx, −ky). In order to obtain the total electronic Hamiltonian H, we have to add the corresponding kinetic part Hkin. For the kinetic part we keep only the nearest neighbors hop- ping term ǫk = −t \0cos kx + cos ky \x01 satisfying the nest- ing condition ǫk+Q = −ǫk, while we also set the chem- ical potential equal to zero. Our approximation can be justiﬁed by considering that our system is close to half- ﬁlling. Under these conditions the excitation spectrum consists of two bands which are fully gapped leading to the topological quantization of the Hall conductance [12, 13, 14, 15, 16, 17, 18], which is the coeﬃcient of the Chern-Simons terms. Omitting the next nearest neigh- bors hopping term δk = t′ cos kx cos ky does not alter qualitatively the occurrence of the TME. However, its inclusion would destroy the quantization of the Hall con- ductance, as in this case, the system is not fully gapped. Similar eﬀects would arise in the presence of disorder or by including the z-axis hopping term. Under this conditions, the total Hamiltonian of the system becomes H = 1 2 P k h ǫk \x10 c† kck −c† k+Qck+Q \x11 + \x10 ∆kc† kck+Q + h.c. \x11i . We obtain a compact representa- tion of H by introducing the spinor Ψ† k = 1 √ 2(c† k c† k+Q), the isospin Pauli matrices τ and the vector gk ≡ (Re∆k, −Im∆k, ǫk). This yields H = P k Ψ† k gk · τ Ψk. The latter indicates that the ground state of the sys- tem depends on the orientation of the g vector in isospin space. As a result, this hamiltonian supports skyrmion solutions which imply the presence of a Chern-Simons action (see e.g. [18]). To reveal the emerging Chern-Simons terms, we have to take into account the ﬂuctuations of the U(1) gauge ﬁeld Aµ. We add to the Hamiltonian the term Hem = R d2q (2π)2 P k Ψ† k+qΓµ k+q,kAµ(q)Ψk − R d2q (2π)2 P k Ψ† k+q e2 2mAi(−q)Ai(q)Ψk, which describes the interaction of the gauge ﬁeld with the electrons. We have introduced the paramagnetic interaction vertex Γµ k+q,k = −(e , e ∂ ∂ki gk · τ), where µ = 0, 1, 2 and i = 1, 2. At one-loop level, the eﬀective action Sem is given by the relation Sem = 1 2 R d3q (2π)3 Aµ(−q)Πµν(q)Aν(q), with the Polarization tensor Πµν, deﬁned as Πµν(q) = i 2 R k T r \x10 GkΓµ k,k+qGk+qΓν k+q,k \x11 −e2 m ρeδi,j. ρe is the two- dimensional electronic density (without including spin), T r denotes trace over isospin indices, Gk is the CDDW fermionic propagator and we have used the abbreviation R k = R dω 2π P k. Computing Πµν up to linear order in q, yields the Chern-Simons action SCS = Z d3x σxy 4 εµνλAµF νλ, (2) with Fµν = ∂µAν −∂νAµ. The coeﬃcient of the Chern- Simons action is the Hall conductance σxy. It can be shown that it is a topological invariant, reﬂecting the existence of a topologically non trivial, P −T violating ground state (see e.g. [18]). Using Eq.(2) we obtain σxy = i 2!ε0ji ∂Π0i ∂qj = e2 4π b N = e2 2π , (3) where we have introduced the winding number of the unit vector ˆgk = gk/| gk |, b N = 1 4π Z d2k ˆgk · ∂ˆgk ∂kx × ∂ˆgk ∂ky ! , (4) which is equal to 2, because the order parameter com- ponents are eigenfunctions of the angular momentum in k−space with eigenvalue l = 2. In the case of a perfect gap, the Hall conductance origi- nates only from the chirality b N of the lower energy band, E− k = −|gk|, which is fully occupied. In the same time, the upper band, E+ k = +|gk|, is totally empty while it is characterized by opposite chirality. Apparently, if both bands were equally occupied then σxy would be equal to zero. In the general case, the two bands, have diﬀerent occupation numbers n−and n+, yielding a non-quantized Hall conductance σxy = e2 2π(n−−n+). Deviations from nesting, disorder or a chemical potential generally lead to such an eﬀect. It is desirable to comprehend, even crudely, the eﬀect of these parameters on the Hall con- ductance and the TME. For this purpose we consider that a ﬁnite chemical po- tential is added to the system. We shall consider that its magnitude is of the order of min|gk|. This minimum is realized at the points k0 = (± π 2 , ± π 2 ), when η << 1. In this case, we may linearize the spectrum about these points so to obtain an approximate analytical solution. The two energy bands are described by the dispersions E± k = −µ± p m2 + (v0 · δk)2, with m = min|gk| = |gk0|, v0 the velocity at these points and δk = k−k0. If |µ| ≥m and µ < 0, hole-pockets arise in the lower band decreas- ing the full occupancy from n−= 1 to n−= 1−nex, with nex the portion of the empty states. On the other hand, if µ ≥m, electron pockets emerge in the upper band ris- ing its occupancy from zero. However, if we take into consideration that the two bands have opposite chirality, it is evident that in both cases, the eﬀect is the same. Consequently, σxy(µ) = σxy(1 −nex). The portion of the empty states will be determined by the area of the el- lipses deﬁned by the four hole-pockets. Straightforward calculations yield the simple relation nex = (µ2 −m2)/2πt∆. (5) We observe that for small values of |µ|, compared to t and ∆, the eﬀect of doping is negligible. We are now in position to obtain the equations of mo- tion of the gauge ﬁeld which will allow us to discuss the TME in a Hall bar geometry setup. We consider that the 3 FIG. 1: (Color online) (a) Inﬂuence of doping on the Topo- logical Meissner eﬀect. The relative change of magnetization hardly reaches 1% in the presence of a small chemical po- tential (∆= 20meV , t = 500meV ). (b) The magnetic ﬁeld screening as a function of the position on the Hall bar extend- ing from −lx to +lx, for diﬀerent values of the penetration depth λ over lx. The magnetic ﬁeld is totally expelled from the sample when lx/λ >> 1 exactly as in the superconducting case. Hall bar has dimensions Lx = 2lx, Ly >> Lx extending from −lx to lx on the x-axis. The relation Ly >> Lx in- dicates that there is negligible y-dependence of the"
      - >-
        QCage - A New Microwave-cavity Sample Holder for High-fidelity Qubit
        Measurements | In this video, you will learn about a new sample holder
        system, targeted at superconducting quantum processors with tens of
        qubits.


        The QCage is a sample holder system for microwave resonator-based
        quantum devices that encloses the sample chip in an all-surrounding
        microwave cavity, with a total number of 24 coplanar transmission lines
        optimized for frequencies up to 18 GHz. The QCage is designed to hold
        the chip suspended inside the cavity, supported only by four corner
        pedestals and clamped d
      - >-
        Elastic neutron scattering simultaneously probes both the crystal
        structure

        and magnetic order in a material. Inelastic neutron scattering measures
        phonons

        and magnetic excitations. Here, we review the average composition,
        crystal

        structure and magnetic order in the 245 family of Fe-based
        superconductors and

        in related insulating compounds from neutron diffraction works. A

        three-dimensional phase-diagram summarizes various structural, magnetic
        and

        electronic properties as a function of the sample composition. A high
        pressure

        phase diagram for the superconductor is also provided. Magnetic
        excitations and

        the theoretic Heisenberg Hamiltonian are provided for the
        superconductor.

        Issues for future works are discussed.
  - source_sentence: superconductivity
    sentences:
      - >-
        Unveiling the Enigma: 'Demon' Particle Found in Superconductor Offers
        Clues to Their Operation | A breakthrough discovery of a particle known
        as Pines's demon within a superconducting crystal could hold the key to
        unraveling the mysteries behind these remarkable superconductor
        materials.
      - >-
        et al., Phys. Rev. Lett. 62, 1532 (1989). 52. F. Creuzet et al.,
        Synthetic Metals 19, 289 (1987). 53. B. Gotschy et al., J. Phys. I
        (France) 2, 677 (1992). 54. J. Pouget et al., Mol. Cryst. Liq. Cryst.
        79, 129 (1982). 55. P. Foury-Leylekian et al., Phys. Rev. B 70,
        180405(R) (2004). 56. M. Dumm et al., Phys. Rev. B 61, 511 (2000). 57.
        C. Bourbonnais and B. Dumoulin, J. Phys. I (France) 6, 1727 (1996). 58.
        L. G. Caron, C. Bourbonnais, F. Creuzet, and D. Jerome, Synthetic Metals
        19, 69 (1987). 59. J. Riera and D. Poilblanc, Phys. Rev. B 62, R16243
        (2000). 60. J. P. Pouget, in Low Dimensional Conductors and
        Superconductors, edited by D. J´erome and L. G. Caron (Plenum Press, New
        York, 1987), p. 17. 61. D. Chow et al., Phys. Rev. Lett. 81, 3984
        (1998). 62. F. Zamborszky et al., Phys. Rev. B 66, 081103(R) (2002). 63.
        V. Ilakovac et al., Phys. Rev. B 50, 7136 (1994). 64. D. S. Chow et al.,
        Phys. Rev. Lett. 85, 1698 (2000). 65. L. G. Caron et al., Synthetic
        Metals 27B, 123 (1988). 66. J. P. Pouget et al., Phys. Rev. Lett. 37,
        437 (1976). 67. L. G. Caron and C. Bourbonnais, Phys. Rev. B 29, 4230
        (1984). 68. L. G. Caron and S. Moukouri, Phys. Rev. Lett 76, 4050
        (1996). 69. H. Bakrim and C. Bourbonnais (unpublished). 70. For a more
        details about the charge ordered state in the (TMTTF)2X series, see the
        contributions of P. Monceau et al.; S. B. Brown and P. M. Chaikin; and
        S. Brazovskii. 71. F. Nad, P. Monceau, C. Carcel, and J. M. Fabre, Phys.
        Rev. B 62, 1753 (2000). 54 C. Bourbonnais and D. J´erome 72. F. Nad, P.
        Monceau, C. Carcel, and J. M. Fabre, J. Phys.: Condens. Matter 12, L435
        (2000). 73. P. Monceau, F. Nad, and S. Brazovskii, Phys. Rev. Lett 86,
        4080 (2001). 74. C. Coulon, S. S. P. Parkin, and R. Laversanne, Phys.
        Rev. B 31, 3583 (1985). 75. R. Laversanne et al., J. Phys. (Paris) Lett.
        45, L393 (1984). 76. W. Yu et al., Phys. Rev. B 70, R121101 (2004). 77.
        H. Yoshioka, M. Tsuchiizu, and Y. Suzumura, J. Phys. Soc. Jpn. 70, 762
        (2001). 78. J. Riera and D. Poilblanc, Phys. Rev. B 63, R241102 (2001).
        79. H. Seo and H. Fukuyama, J. Phys. Soc. Jpn. 66, 1249 (1997). 80. R.
        T. Clay, S. Mazumdar, and D. K. Campbell, Phys. Rev. B 67, 115121
        (2003). 81. J. P. Pouget and S. Ravy, Synthetic Metals 85, 1523 (1997).
        82. B. J. Klemme et al., Phys. Rev. Lett. 75, 2408 (1995). 83. S. E.
        Brown et al., Synthetic Metals 86, 1937 (1997). 84. P. Auban et al., J.
        Phys. (France) 50, 2727 (1989). 85. P. Auban, D. J´erome, I. Johannsen,
        and K. Bechgaard, Synthetic Metals 41, 2285 (1991). 86. C. Bourbonnais
        and D. J´erome, Science 281, 1156 (1998). 87. K. Bechgaard et al., Solid
        State Comm. 33, 1119 (1980). 88. S. Tomic et al., J. Phys. I (France) 1,
        1603 (1991). 89. C. Bourbonnais and D. J´erome, in Advances in Synthetic
        Metals, Twenty Years of Progress in Science and Technology, edited by P.
        Bernier, S. Lefrant, and G. Bidan (Elsevier, New York, 1999), pp.
        206–261, arXiv:cond- mat/9903101. 90. A. Schwartz et al., Phys. Rev. B
        58, 1261 (1998). 91. C. Jacobsen, in Low Dimensional Conductors and
        Superconductors, edited by D. J´erome and L. Caron (Plenum Press, New
        York, 1987), p. 253. 92. T. Timusk, in Low Dimensional Conductors and
        Superconductors, edited by D. J´erome and L. Caron (Plenum Press, New
        York, 1987), p. 275. 93. K. Kikuchi et al., Solid State Comm. 42, 433
        (1982). 94. K. Bechgaard, M. Carneiro, M. Olsen, and F. Rasmussen, Phys.
        Rev. Lett. 46, 852 (1981). 95. H. Ng, T. Timusk, D. J´erome, and K.
        Bechgaard, Phys. Rev. B. 32, 8041 (1985). 96. H. Ng, T. Timusk, and K.
        Bechgaard, J. Physique 44, C3 (1983). 97. N. Joo et al., Eur. Phys. J. B
        40, 43 (2004). 98. K. Heuz´e et al., Adv. Materials 15, 1251 (2003). 99.
        T. Itou et al., Phys. Rev. Lett. 93, 216408 (2004). 100. E. B. Lopes et
        al., Eur. Phys. J. B 29, 27 (2002). 101. D. J´erome, A. Mazaud, M.
        Ribault, and K. Bechgaard, J. Phys. (Paris) Lett. 41, L95 (1980). 102.
        R. Brusetti, M. Ribault, D. Jerome, and K.Bechgaard, J. Phys. (Paris)
        43, 801 (1982). 103. K. Mortensen, Y. Tomkiewiez, T. D. Schultz, and E.
        M. Engler, Phys. Rev. Lett. 46, 1234 (1982). 104. A. Andrieux, D.
        J´erome, and K. Bechgaard, J. Phys. (Paris) Lett. 42, L87 (1981). 105.
        T. Adachi et al., J. Am. Chem. Soc. 122, 3238 (2000). 1 Interacting
        electrons in quasi-one-dimensional organic superconductors 55 106. L.
        Balicas et al., J. Phys. I (France) 4, 1539 (1994). 107. P.
        Auban-Senzier et al., Synthetic Metals 133-134, 11 (2003). 108. C. S.
        Jacobsen, D. Tanner, and K. Bechgaard, Phys. Rev. Lett. 46, 1142 (1981).
        109. V. Vescoli et al., Science 281, 1181 (1998). 110. T. Takahashi, Y.
        Maniwa, H. Kawamura, and G. Saito, Physica 143B, 417 (1986). 111. G.
        Montambaux, Phys. Rev. B 38, 4788 (1988). 112. L. Gor’kov, J. Phys. I
        (France) 6, 1697 (1996). 113. C. Seidel and V. N. Prigodin, J. Phys.
        (Paris) Lett. 44, L403 (1983). 114. R. Duprat and C. Bourbonnais, Eur.
        Phys. J. B 21, 219 (2001). 115. D. J´erome and H. Schulz, Adv. in
        Physics 31, 299 (1982). 116. T. Vuletic et al., Eur. Phys. J. B 25, 319
        (2002). 117. Y. Hasegawa and H. Fukuyama, J. Phys. Soc. Jpn. 55, 3978
        (1986). 118. J. F. Kwak et al., Phys. Rev. Lett. 56, 972 (1986). 119. J.
        P. Pouget and S. Ravy, J. Phys. I (France) 6, 1501 (1996). 120. S.
        Kagoshima et al., Solid State Comm. 110, 479 (1999). 121. H. K. Ng, T.
        Timusk, and K. Bechgaard, Phys. Rev. B 30, 5842 (1984). 122. N. Cao, T.
        Timusk, and K. Bechgaard, J. Phys. I (France) 6, 1719 (1996). 123. S.
        Mazumdar, R. Ramasesha, R. T. Clay, and D. K. Campbell, Phys. Rev. Lett.
        82, 1522 (1999). 124. M. Kobayashi, M. Ogata, and K. Yonemitsu, J. Phys.
        Soc. Jpn. 67, 1098 (1998). 125. J. C. Nickel, R. Duprat, C. Bourbonnais,
        and N. Dupuis, Phys. Rev. Lett. 95, 247001 (2005). 126. M. Ribault, G.
        Benedek, D. J´erome, and K. Bechgaard, J. Phys. Lett. Paris 41, L
        (1980). 127. K. Andres et al., Phys. Rev. Lett. 45, 1449 (1980). 128. P.
        Garoche, R. Brusetti, and K. Bechgaard, Phys. Rev. Lett. 49, 1346
        (1982). 129. R. Brusetti, P. Garoche, and K. Bechgaard, J. Phys. C 16,
        2495 (1983). 130. S. Belin and K. Behnia, Phys. Rev. Lett. 79, 2125
        (1997). 131. J. Bardeen, G. Rickaysen, and L. Teword, Phys. Rev. 113,
        982 (1959). 132. M. Takigawa, H. Yasuoka, and G. Saito, J. Phys. Soc.
        Jpn 56, 873 (1987). 133. Y. Hasegawa and H. Fukuyama, J. Phys. Soc. Jpn.
        56, 877 (1987). 134. I. J. Lee et al., Phys. Rev. Lett. 88, 17004
        (2002). 135. L. P. Le et al., Phys.Rev.B. 48, 7284 (1993). 136. G.
        M.Luke et al., Physica B326, 378 (2003). 137. G. M. Luke et al., Nature
        394, 558 (1998). 138. D. U. Gubser et al., Mol. Cryst. Liq. Cryst. 79,
        225 (1982). 139. R. L. Greene et al., Mol. Cryst. Liq. Cryst. 79, 183
        (1982). 140. K. Murata et al., Mol. Cryst. Liq. Cryst. 79, 283 (1982).
        141. K. Murata et al., Japanese Journal of Applied Physics 26, 1367
        (1987). 142. N. Joo, to be published (2006). 143. L. P. Gorkov and D.
        J´erome, J. Phys. Lett. 46, L643 (1985). 144. I. J. Lee, P. M. Chaikin,
        and M. J. Naughton, Phys. Rev. B 62, R14669 (2000). 145. J. I. Oh and M.
        J. Naughton, Phys. Rev. Lett. 92, 067001 (2004). 146. H. Wilhelm (2004),
        unpublished data and private communication. 147. H. J. Schulz et al., J.
        Physique. Lett 42, L (1981). 148. L. Jennings and C. Swenson, Phys. Rev
        112, 31 (1958). 56 C. Bourbonnais and D. J´erome 149. D. Mailly, Ph.D.
        thesis, Thesis Universit´e d’Orsay, 1983. 150. F. Creuzet, D. J´erome,
        and A. Moradpour, Mol. Cryst. Liq. Cryst. 119, 297 (1985). 151. K.
        Murata et al., Mol. Cryst. Liq. Cryst. 119, 245 (1985). 152. F. Guo et
        al., J. Phys. Soc. Jpn. 67, 3000 (1998). 153. W. Kang, S. Hannahs, and
        P. Chaikin, Phys. Rev. Lett. 70, 3091 (1993). 154. I. J. Lee et al.,
        Phys. Rev. Lett. 94, 197001 (2005). 155. R. L. Greene and E. M. Engler,
        Phys. Rev. Lett. 45, 1587 (1980). 156. M. H´eritier, G. Montambaux, and
        P. Lederer, J. Phys. (Paris) Lett. 45, L943 (1984). 157. L. P. Gorkov
        and P. D. Grigoriev, Europhys. Lett. 71, 425 (2005). 158. P.
        Auban-Senzier, (2006), to be published. 159. C. Colin and P.
        Auban-Senzier and C. R. Pasquier and K. Bechgaard, preprint (2006). 160.
        S. Bouﬀard et al., J. Phys. C 15, 295 (1982). 161. M.-Y. Choi et al.,
        Phys. Rev. B 25, 6208 (1982). 162. A. A. Abrikosov, J. Low Temp. Phys
        53, 359 (1983). 163. L. Zuppirolli, in Low Dimensional Conductors and
        Superconductors, edited by D. J´erome and L. G. Caron (Plenum Press, New
        York, 1987), p. 307. 164. M. Sanquer and S. Bouﬀard, Mol. Cryst. Liq.
        Cryst. 119, 147 (1985). 165. I. Johannsen et al., Mol. Cryst. Liq.
        Cryst. 119, 277 (1985). 166. K. Mortensen and E. M. Engler, Phys. Rev. B
        29, 842 (1984). 167. S. Tomic, J´erome, P. Monod, and K. Bechgaard, J.
        de Phys. (Paris) Lett. 43, L839 (1982). 168. B. Korin-Hamzi´c, L.
        Forr´o, J. R. Cooper, and K. Bechgaard, Phys. Rev. B 38, 11177 (1988).
        169. S. Ravy, R. Moret, J. P. Pouget, and R. Com`es, Physica 143 B, 542
        (1986). 170. N. Joo et al., Europhys. Lett. 72, 645 (2005). 171. K.
        Maki, H. Won, and S. Haas, Phys. Rev. B 69, 012502 (2004). 172. A. I.
        Larkin, Sov. Phys. JETP 21, 153 (1965). 173. A. G. Lebed, JETP Lett. 44,
        114 (1986). 174. N. Dupuis, G. Montambaux, and C. A. R. S. de Melo,
        Phys. Rev. Lett. 70, 2613 (1993). 175. The claim for triplet
        superconducting pairing in (TM)2X is based essentially on NMR
        investigations (77Se Knight shift and spin-lattice relaxation time T1)
        performed on (TMTSF)2PF6 under pressure [134]. A major diﬃculty regard-
        ing this experiment is the actual control of the temperature of the
        electron spins during the time of the NMR pulse and acquisition. It is
        not unlikely that the electron spins can reach a temperature above Tc
        for the experiment leading to the determination of the Knight shift, see
        also recent data obtained by Shinagawa et-al on (TMTSF)2ClO4(Proceedings
        of ISCOM 05). 176. H. Mayaﬀre et al., Phys. Rev. Lett 75, 4951 (1995).
        177. K. Kanoda, K. Miyagawa, A. Kawamoto, and Y. Nakazawa, Phys. Rev. B.
        54, 76 (1996). 178. S. Kamiya et al., Phys. Rev. B 65, 134510 (2002).
        179. F. Zuo et al., Phys. Rev. B . 61, 750 (2000). 180. D. J´erome and
        C. R. Pasquier, in One Dimensional Organic Superconductors, edited by A.
        V. Narlikar (Springer Verlag, Berlin, 2005). 181. N. Dupuis, C.
        Bourbonnais, and J. C. Nickel, Fiz. Nizk. Temp. 32, 505 (2006),
        arXiv:cond-mat/0510544. 1 Interacting electrons in quasi-one-dimensional
        organic superconductors 57 182. V. J. Emery, J. Phys. (Paris) Coll. 44,
        977 (1983). 183. W. Kang, S. T. Hannahs, and P. M. Chaikin, Phys. Rev.
        Lett. 70, 3091 (1993). 184. T. Takahashi, J´erome, and K. Bechgaard, J.
        de Phys. (Paris) Lett. 43, L565 (1982). 185. H. Schwenk, K. Andres, and
        F. Wudl, Phys. Rev. B 29, 500 (1984). 186. W. Wu et al., Phys. Rev.
        Lett. 94, 097004 (2005). 187. W. Kohn and J. M. Luttinger, Phys. Rev.
        Lett. 15, 524 (1965). 188. V. J. Emery, Synthetic Metals 13, 21 (1986).
        189. M. T. B´eal-Monod, C. Bourbonnais, and V. J. Emery, Phys. Rev. B
        34, 7716 (1986). 190. L. G. Caron and C. Bourbonnais, Physica 143B, 453
        (1986). 191. D. J. Scalapino, E. Loh, and J. E. Hirsch, Phys. Rev. B 34,
      - >-
        By periodically driving a single bosonic Josephson junction (BJJ) with
        an

        impurity, a synthetic gauge field is generated in the Fock space of the
        system.

        At a critical synthetic gauge flux the ground state undergoes a quantum
        phase

        transition which is analogous to the Meissner-Abrikosov-vortex
        transition found

        in type-II superconductors with an applied magnetic field. A second
        quantum

        phase transition involving attractive interactions between the bosons of
        the

        BJJ is shown to enhance the sensitivity of the system to the

        Meissner-Abrikosov-vortex transition.
  - source_sentence: superconductivity
    sentences:
      - >-
        Room-Temperature Superconductor LK-99 Revolutionary Science |
        Room-Temperature Superconductor LK-99 Revolutionary Science.

        Dive deep into the groundbreaking discovery of LK-99, a room-temperature
        superconductor that's challenging our understanding of physics. From its
        origins to its potential applications, we explore how this scientific
        marvel could reshape industries and redefine the future of technology.
        Join us as we unravel the mysteries of superconductivity, the
        controversies surrounding it, and the potential it holds for a brighter,
        more efficient fu
      - "3. Results\nIn the following calculations, we set ∆= 1 meV as the en-\nergy unit. The superconducting coherence length is ξ = ℏvF/∆≈\n360 nm, which is set as the length unit.\n3.1. Josephson junction with out-of-plane spin polarization\nThe Josephson junction with the out-of-plane spin polariza-\ntion is schematically shown in Fig. 1(a), where the spin polar-\nization in the left superconducting region is along the z axis and\nthe spin polarization in the right superconducting region lies in\nthe y −z plane with the polar angle θm. The Andreev-like trans-\nfer matrices at the NS interfaces are given by\nSν =\n1\ncos θν cos ϕν + i sin ϕν\n×\n sin θν cos ϕν + cos γ\n−i sin γ\ni sin γ\nsin θν cos ϕν −cos γ\n!\n,\n(13)\nwhere ν = + (−) for the right (left) interface, θ+ = θm, θ−= 0,\nand ϕ± = ±ϕs/2. The Andreev-like bound states can be found\nfrom the same determinant in Eq. (12), which are given by\ndet\n\x10\n1 −M−1S−1\n+ MS−\n\x11\n= 0,\n(14)\nleading to the Andreev-like levels\n\f\f\f\f\f\nE±\n∆\n\f\f\f\f\f =\ns\nY2 −2XZ ±\np\nY2 −4Y2Z (X + Z)\n2 \0X2 + Y2\x01\n,\n(15)\nX = 2 sin2 α −(3 + cos 2α) cos(2kL),\nY = −4 cos α sin(2kL),\nZ = cos2 α\0 cos ϕs + cos θm cos ϕs\n+ cos θm + 2 cos(2kL) −1\x01.\nWith the help of Eq. (12), the spin Josephson current density\nat T = 0 K can be obtained by the ϕs-dependent Andreev-like\nlevels\nj(ϕs) = −\nX\nℓ=±\nZ\nµW\n2πℏvF\ndEℓ\ndϕs\ncos αdα,\n(16)\nwhere Eℓis the positive root of Eq. (15) and W is the width of\nthe junction.\nThe supercurrent-phase relations at different θm are shown\nin Fig. 2(a) for kFL = 0.1. The spin Josephson current de-\ncreases with the increasing of θm, and drops to zero when the\nspin polarizations in the left and right superconducting regions\nare antiparallel, i.e., θm = π. In this antiparallel configuration,\nthe spin polarizations of the spin-triplet electron-hole condensa-\ntions in the left and right spin superconductors are opposite, the\nAndreev-like process between two NS interfaces can not form\na closed loop. Consequently, the ϕs-dependent Andreev-like\nlevels are abesnt, leading to the zero supercurrent.\nFor kFL = 2, the supercurrent is reversed and the π-state\nJosephson junction appears, as shown in Fig. 2(b). This 0 −π\nphase transition is attributed to the Fermi-momentum splitting\nAndreev-like reflections at the NS interfaces. At the Fermi sur-\nface, the right-propagating spin-up electron with the wave vec-\ntor kF is converted into a left-propagating spin-down electron\nwith the wave vector −kF due to the Andreev-like reflection,\nleading to the wave vector difference ∆k = 2kF. An additional\nphase shift 2kFL is accumulated in a closed Andreev loop. The\ntotal scattering phase acquired by the electrons in this closed\nAndreev loop is 2kFL ± ϕs −2 arccos(E/∆) [26], which should\n3\n−2\n0\n−3\n0\n3\n2\nkF L = 0.1\nϕm = 0\nπ\nφs/π\nj/j0\n(a)\n−2\n0\n−3\n0\n3\n2\nkF L = 2\nϕm = 0\nπ\nφs/π\nj/j0\n(b)\n0\n5\n10\n15\n0\n1\n2\nL/ξ\njc/j0\n(c)\nϕm = 0.3π\nϕm = 0.8π\n−1\n0\n0\n1\n2\n1\nϕm/π\njc/j0\n(d)\nL = 0.1ξ\nL = 1.5ξ\nFigure 3: (a, b) The current-phase relation for the Josephson junctions with the in-plane spin polarization. The red arrows indicate the curves with the increasing\ndeviation of the relative angles φm, which change from 0 to π with a step of π/4. (c) The critical spin Josephson current density jc as a function of L for φm = 0.3π\n(solid) and φm = 0.8π (dashed). The Fermi level is µ = 0.5∆. (d) The critical spin Josephson current density jc as a function of θm for L = 0.1ξ (solid) and L = 1.5ξ\n(dashed). Both j and jc are renormalized by j0 = µ∆W/2πℏvF.\nbe quantized according to the quasiclassical Bohr-Sommerfeld\nquantization condition [27, 28], i.e., 2kFL±ϕs−2 arccos(E/∆) =\n2πn (n ∈Z). Consequently, the state of the junction can be con-\ntrolled by the phase factor cos(kFL). The spin supercurrent can\nbe expressed as j ∝cos(kFL) sin ϕs. For 2nπ + π/2 < kFL <\n2nπ + 3π/2, the spin supercurrent is reversed.\nThe critical current defined by jc = max | j(ϕs)| as a function\nof the junction length L is shown in Fig. 2(c). Due to the addi-\ntional phase kFL, the critical current is proportional to cos(kFL),\nwhich exhibits an oscillation behavior as the the junction length\nincreases. For µ = 0.5∆in Fig. 2(c), the oscillation period can\nbe estimated as TL = π/kF = 2πξ. The critical current as a\nfunction of the polar angle θm is shown in Fig. 2(d). The θm-\ndependent critical current is symmetric due to the rotation sym-\nmetry, i.e., jc(θm) = jc(−θm). The critical current reaches its\nmaximum value at θm = 0 and becomes zero at θm = ±π.\n3.2. Josephson junction with in-plane spin polarization\nThe Josephson junction with in-plane spin polarization is\nschematically shown in Fig. 1(b), where the spin polarization in\nthe left superconducting region is along the x axis and the spin\npolarization in the right superconducting region lies in the x −y\nplane with the azimuthal angle φm. The Andreev-like transfer\nmatrices are given by\nSν =\n−ieiφν\nsin(φν + ϕν)×\n cos (φν + ϕν) + cos γ\n−i sin γ\ni sin γ\ncos (φν + ϕν) −cos γ\n!\n,\n(17)\nwhere ν = + (−) for the right (left) interface, φ+ = φm, φ−= 0,\nand ϕ± = ±ϕs/2. The Andreev-like levels are given by\n\f\f\f\f\f\nE±\n∆\n\f\f\f\f\f =\nv\nu\nu\nu\nu\nt ¯Y2 −2 ¯X ¯Z ±\nq\n¯Y2 −4 ¯Y2 ¯Z\n\x10 ¯X + ¯Z\n\x11\n2\n\x10 ¯X2 + ¯Y2\x11\n,\n(18)\n¯X = 8(3 cos(2kL) + 2 cos 2α cos2(kL) −1),\n¯Y = 32 cos α sin(2kL),\n¯Z = −4 cos2 α\02 cos φm −cos 2φm + cos ϕs\n+2 cos(φm + ϕs) + cos(2φm + ϕs) + 4 cos(2kL) −1\x01.\nThe zero-temperature Josephson current obtained by Eq.\n(16) is shown in Fig. 3(a) at kFL = 0.1. Due to the spin ro-\ntation symmetry, the supercurrent for the Josephson junctions\nwith parallel in-plane spin polarization (φm = 0) is the same as\nthat for the Josephson junctions with parallel out-of-plane spin\npolarization (θm = 0). For the antiparallel in-plane polarization\n(φm = π), the Josephson current is absent due to the absence of\nthe ϕs-dependent Andreev-like levels.\nFor φm , 0 and φm , π, the anomalous Josephson current\nj|ϕs=0 appears, as shown in Fig. 3(a). For simplicity, we present\nthe spin Josephson current for the one-dimensional (1D) case\nwith ky = 0:\nj1D ∝cos (kFL) cos2 \x12φm\n2\n\x13\nsin (ϕs + φm) ,\n(19)\nwhich can imply the qualitative properties of the two-dimensional\nJosephson junctions. Eq. (19) shows that the anomalous Joseph-\nson current at ϕs = 0 is proportional to cos(kFL) cos2(φm/2) sin φm.\nThe Josephson current can be reversed by the additional phase\nfactor cos(kFL). For kFL = 2, the reversed Josephson current\nobtained from Eq. (16) is shown in Fig. 3(b).\nThe critical currents jc as a function of the junction length\nL and the azimuthal angle φm are shown in Figs. 3(c) and 3(d),\nrespectively. The L-dependent oscillation is determined by the\nadditional phase factor cos(kFL) due to the Fermi-moment split-\nting. For a fixed L, the φm-resolved jc is symmetric, as shown\nin Fig. 3(d).\n4\nThe anomalous Josephson current j|ϕs=0 as a function of L\nis shown in Fig. 4(a). For φm = 0 and φm = π, the anomalous\nJosephson effect is absent. For φm , 0 and φm , π, j|ϕs=0\noscillates with the increasing of L and has the same oscillation\nperiod as jc. For µ = ∆in Fig. 4(a), the oscillation period is\nabout πξ. j|ϕs=0 as a function of φm is shown in Fig. 4(b). The\nφm-resolved anomalous Josephson current is asymmetric and\nsatisfies the relation\nj|ϕs=0(φm) = −j|ϕs=0(−φm),\n(20)\ndue to the symmetry of the BdG Hamiltonian, which is ex-\nplained in detail in Sec. 3.3.\n3.3. Symmetry analysis\nThe Hamiltonian of the spin superconductor with out-of-\nplane spin polarization can be written as\nHη\nS = hη(k) + H′(ϕs, θm),\n(21)\nwhere η = ± is the valley index, the k-dependent term hη(k) =\nℏvF(kxτx + ηkyτy) is the Hamiltonian of the pristine graphene\nfor the η valley and the k-independent term is given by\nH′(ϕs, θm) =M cos θmσzτ0 + M sin θmσxτ0\n+ ∆cos θm cos ϕsσxτz + ∆sin θm cos ϕsσzτz\n−∆sin ϕsσyτz.\n(22)\nUnder the time-reversal transformation, the Hamiltonian of the\npristine graphene remains unchanged\nhη(k) →T h¯η(−k)T −1\n= ℏvF(kxτx + ηkyτy)\n= hη(k),\n(23)\nwhere ¯η = −η, T = iσyτzC is the time-reversal operator with C\nbeing the complex conjugation. For the k-independent Hamilto-\nnian H′(ϕs, θm), considering the combined symmetry P = σyT\nwith σy being the spin rotation symmetry and T being the time-\nreversal symmetry, one finds that\nPH′(ϕs, θm)P−1 = H′(−ϕs, θm).\n(24)\n0\n5\n10\n15\n−1\n0\n1\nL/ξ\nj|φs=0/j0\n(a)\nϕm = 0.5π\nϕm = 0, π\n−1\n0\n−1\n0\n1\n1\nϕm/π\nj|φs=0/j0\n(b)\nL = 0.1ξ\nL = 1.5ξ\nFigure 4: (a) The anomalous spin Josephson current density j|ϕs=0 as a function\nof L for φm = 0.5π (solid) and φm = 0, π (dashed). The Fermi level is µ = ∆. (b)\nThe anomalous spin Josephson current j|ϕs=0 as a function of φm for Lm = 0.1ξ\n(solid) and L = 1.5ξ (dashed). j|ϕs=0 is renormalized by j0 = µ∆W/2πℏvF.\nDue to the spin degeneracy in pristine graphene, hη(k) remains\nunchanged under P. Consequently, with the help of Eq. (6), the\nBdG Hamiltonian for the Josephson junctions with the out-of-\nplane spin polarization holds the relation\nPHBdG(ϕs, θm)P−1 = HBdG(−ϕs, θm).\n(25)\nThe spin Josephson current density can be obtained via the ther-\nmodynamic relation [29, 30]\nj(ϕs) = −kBT∂ϕs ln Tr[e−HBdG(ϕs)/kBT].\n(26)\nBy substituting Eq. (25) into Eq. (26), one finds that the spin\nJosephson current holds the relation\nj(ϕs, θm) = −j(−ϕs, θm).\n(27)\nleading to the absence of the anomalous spin Josephson current,\ni.e., j|ϕs=0 = 0.\nFor the spin superconductor with in-plane spin polarization,\nthe Hamiltonian can be written as\nHη\nS = hη(k) + H′′(ϕs, φm),\n(28)\nwith\nH′′(ϕs, φm) =M cos φmσxτ0 + M sin φmσyτ0\n−∆sin(φm + ϕs) cos φmσyτz\n+ ∆sin(φm + ϕs) sin φmσxτz\n−∆cos(φm + ϕs)σzτz.\n(29)\nThe symmetry P is broken and the BdG Hamiltonian holds the\nrelation\nPHBdG(ϕs, φm)P−1 = HBdG(−ϕs, −φm).\n(30)\nWith the help of Eq. (26), one finds that the spin Josephson\ncurrent holds the relation\nj(ϕs, φm) = −j(−ϕs, −φm),\n(31)\nleading to the presence of the anomalous spin Josephson cur-\nrent. The anomalous Josephson current is an odd function of φm\nsatisfying j|ϕs=0(φm) = −j|ϕs=0(−φm), as shown in Fig. (4)(b).\nIn fact, the anomalous Josephson effect is possible when\nthe symmetries T , D and P are all broken [31, 32], where\nD = σyRxzT is another combined symmetry with Rxz being the\nmirror reflection about the x −z plane. We note that the sym-\nmetries T and D are always broken in our model for both the\nout-of-plane spin polarization and the in-plane spin polariza-\ntion. The combined symmetry P plays a key role in our model:\nFor the Josephson junction with out-of-plane spin polarization,\nthe absence of the anomalous Josephson current ( j|ϕs=0 = 0)\nis protected by P. For the Josephson junction with in-plane\nspin polarization, the breaking of P leads to the presence of the\nanomalous spin Josephson current.\n5"
      - >-
        A brief course on Superconductivity [Introduction Video] | Course Name:
        A brief course on Superconductivity


        Prof. Saurabh Basu

        Department of Physics

        Indian Institute of Technology Guwahati
  - source_sentence: how operate
    sentences:
      - >-
        The recently discovered universal scaling relation between the

        superconducting density and the transition temperature in
        high-temperature

        superconductors appears to indicate that those normal state carriers
        that are

        undergoing a superconducting transition at T = Tc, are experiencing
        critical

        dissipation and acting as preformed pairs.
      - >-
        The discovery of nickelate superconductivity provided the first example
        of a

        non-copper-based material with superconductivity strongly analogous to
        the

        cuprates, but recent findings raise questions and inconsistencies around
        the

        electron counts and doping phase diagrams. We show using superconducting

        La$_4$Ni$_3$O$_{10}$ that there are unconventional interlayer and
        interorbital

        intrinsic doping effects that render the $d_{x^2-y^2}$ orbital
        occupation

        similar to the cuprates. The results enable a consistent framework for

        nickelate superconductivity, while maintaining the connection between
        cuprate

        and nickelate superconductors.
      - >-
        How To: Operate Jeep JL Wrangler Four Wheel Drive 4wd 4x4 Command Trac
        Rock Trac| Kentucky Ohio IN | Easy operation for JL Jeep Wrangler Four
        Wheel Drive System 4wd 4x4. Need to know how to operate your Jeep's Four
        Wheel Drive System? 2018 Jeep JL Wrangler Unlimited 4 Door Sport,
        Rubicon, Sahara, Moab Edition, Gladiator. 4 Wheel High. Watch this video
        in Louisville Kentucky. We are close to Ohio, Indiana, St Louis,
        Indianapolis, Nashville, Tennessee, West Virginia, Missouri. Aev Dealer.
        American Expedition Vehicles. Montana. Detroit. New Albany. Dana 44. 

        https://www.crossjeepchrysler.com/ 

        htt
  - source_sentence: superconductivity
    sentences:
      - >-
        Quantum Levitation With YBCO SUPERCONDUCTOR! | Patreon:
        https://www.patreon.com/Thoisoi?ty=h

        Facebook: https://www.facebook.com/thoisoi2

        Music: http://audiomicro.com

        Hello everyone. Today I want to tell you about one unusual subject - the
        superconductor.

        A superconductor or a high-temperature superconducting ceramics is an
        alloy of oxides of yttrium, barium and copper in proportions (which you
        see on the screen) YBa2Cu3O7-x and abbreviated as YBCO.

        The ceramics was first made in the University of Alabama, USA in 1987.
        The uniqueness of this 
      - >-
        Non-invasive magnetic field sensing using optically - detected magnetic

        resonance of nitrogen-vacancy (NV) centers in diamond was used to study
        spatial

        distribution of the magnetic induction upon penetration and expulsion of
        weak

        magnetic fields in several representative superconductors. Vector
        magnetic

        fields were measured on the surface of conventional, Pb and Nb, and

        unconventional, LuNi$_2$B$_2$C, Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$,

        Ba(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$, and CaKFe$_4$As$_4$,
        superconductors,

        with diffraction - limited spatial resolution using variable -
        temperature

        confocal system. Magnetic induction profiles across the crystal edges
        were

        measured in zero-field-cooled (ZFC) and field-cooled (FC) conditions.
        While all

        superconductors show nearly perfect screening of magnetic fields applied
        after

        cooling to temperatures well below the superconducting transition,
        $T_c$, a

        range of very different behaviors was observed for Meissner expulsion
        upon

        cooling in static magnetic field from above $T_c$. Substantial
        conventional

        Meissner expulsion is found in LuNi$_2$B$_2$C, paramagnetic Meissner
        effect

        (PME) is found in Nb, and virtually no expulsion is observed in
        iron-based

        superconductors. In all cases, good correlation with macroscopic
        measurements

        of total magnetic moment is found. Our measurements of the spatial
        distribution

        of magnetic induction provide insight into microscopic physics of the
        Meissner

        effect.
      - >-
        We highlight the reproducibility and level of control over the
        electrical

        properties of YBa$_2$Cu$_3$O$_7$ Josephson junctions fabricated with

        irradiation from a focused helium ion beam. Specifically, we show the
        results

        of electrical transport properties for several junctions fabricated
        using a

        large range of irradiation doses. At the lower end of this range,
        junctions

        exhibit superconductor-normal metal-superconductor (SNS) Josephson
        junction

        properties. However, as dose increases there is a transition to
        electrical

        characteristics consistent with superconductor-insulator-superconductor
        (SIS)

        junctions. To investigate the uniformity of large numbers of helium ion

        Josephson junctions we fabricate arrays of both SNS and SIS Josephson
        junctions

        containing 20 connected in series. Electrical transport properties for
        these

        arrays reveal very uniform junctions with no appreciable spread in
        critical

        current or resistance.
pipeline_tag: sentence-similarity
library_name: sentence-transformers
metrics:
  - cosine_accuracy@1
  - cosine_accuracy@3
  - cosine_accuracy@5
  - cosine_accuracy@10
  - cosine_precision@1
  - cosine_precision@3
  - cosine_precision@5
  - cosine_precision@10
  - cosine_recall@1
  - cosine_recall@3
  - cosine_recall@5
  - cosine_recall@10
  - cosine_ndcg@10
  - cosine_mrr@10
  - cosine_map@100
model-index:
  - name: SentenceTransformer based on sentence-transformers/all-MiniLM-L6-v2
    results:
      - task:
          type: information-retrieval
          name: Information Retrieval
        dataset:
          name: superconductor eval
          type: superconductor-eval
        metrics:
          - type: cosine_accuracy@1
            value: 0.7
            name: Cosine Accuracy@1
          - type: cosine_accuracy@3
            value: 0.8
            name: Cosine Accuracy@3
          - type: cosine_accuracy@5
            value: 0.9
            name: Cosine Accuracy@5
          - type: cosine_accuracy@10
            value: 1
            name: Cosine Accuracy@10
          - type: cosine_precision@1
            value: 0.7
            name: Cosine Precision@1
          - type: cosine_precision@3
            value: 0.36666666666666664
            name: Cosine Precision@3
          - type: cosine_precision@5
            value: 0.24000000000000005
            name: Cosine Precision@5
          - type: cosine_precision@10
            value: 0.13000000000000003
            name: Cosine Precision@10
          - type: cosine_recall@1
            value: 0.5
            name: Cosine Recall@1
          - type: cosine_recall@3
            value: 0.7
            name: Cosine Recall@3
          - type: cosine_recall@5
            value: 0.8
            name: Cosine Recall@5
          - type: cosine_recall@10
            value: 0.9
            name: Cosine Recall@10
          - type: cosine_ndcg@10
            value: 0.7651427342885562
            name: Cosine Ndcg@10
          - type: cosine_mrr@10
            value: 0.7861111111111111
            name: Cosine Mrr@10
          - type: cosine_map@100
            value: 0.7098290598290597
            name: Cosine Map@100

SentenceTransformer based on sentence-transformers/all-MiniLM-L6-v2

This is a sentence-transformers model finetuned from sentence-transformers/all-MiniLM-L6-v2. It maps sentences & paragraphs to a 384-dimensional dense vector space and can be used for semantic textual similarity, semantic search, paraphrase mining, text classification, clustering, and more.

Model Details

Model Description

Model Type: Sentence Transformer
Base model: sentence-transformers/all-MiniLM-L6-v2
Maximum Sequence Length: 256 tokens
Output Dimensionality: 384 dimensions
Similarity Function: Cosine Similarity

Model Sources

Documentation: Sentence Transformers Documentation
Repository: Sentence Transformers on GitHub
Hugging Face: Sentence Transformers on Hugging Face

Full Model Architecture

SentenceTransformer(
  (0): Transformer({'max_seq_length': 256, 'do_lower_case': False, 'architecture': 'BertModel'})
  (1): Pooling({'word_embedding_dimension': 384, 'pooling_mode_cls_token': False, 'pooling_mode_mean_tokens': True, 'pooling_mode_max_tokens': False, 'pooling_mode_mean_sqrt_len_tokens': False, 'pooling_mode_weightedmean_tokens': False, 'pooling_mode_lasttoken': False, 'include_prompt': True})
  (2): Normalize()
)

Usage

Direct Usage (Sentence Transformers)

First install the Sentence Transformers library:

pip install -U sentence-transformers

Then you can load this model and run inference.

from sentence_transformers import SentenceTransformer

# Download from the 🤗 Hub
model = SentenceTransformer("sentence_transformers_model_id")
# Run inference
sentences = [
    'superconductivity',
    'We highlight the reproducibility and level of control over the electrical\nproperties of YBa$_2$Cu$_3$O$_7$ Josephson junctions fabricated with\nirradiation from a focused helium ion beam. Specifically, we show the results\nof electrical transport properties for several junctions fabricated using a\nlarge range of irradiation doses. At the lower end of this range, junctions\nexhibit superconductor-normal metal-superconductor (SNS) Josephson junction\nproperties. However, as dose increases there is a transition to electrical\ncharacteristics consistent with superconductor-insulator-superconductor (SIS)\njunctions. To investigate the uniformity of large numbers of helium ion\nJosephson junctions we fabricate arrays of both SNS and SIS Josephson junctions\ncontaining 20 connected in series. Electrical transport properties for these\narrays reveal very uniform junctions with no appreciable spread in critical\ncurrent or resistance.',
    'Non-invasive magnetic field sensing using optically - detected magnetic\nresonance of nitrogen-vacancy (NV) centers in diamond was used to study spatial\ndistribution of the magnetic induction upon penetration and expulsion of weak\nmagnetic fields in several representative superconductors. Vector magnetic\nfields were measured on the surface of conventional, Pb and Nb, and\nunconventional, LuNi$_2$B$_2$C, Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$,\nBa(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$, and CaKFe$_4$As$_4$, superconductors,\nwith diffraction - limited spatial resolution using variable - temperature\nconfocal system. Magnetic induction profiles across the crystal edges were\nmeasured in zero-field-cooled (ZFC) and field-cooled (FC) conditions. While all\nsuperconductors show nearly perfect screening of magnetic fields applied after\ncooling to temperatures well below the superconducting transition, $T_c$, a\nrange of very different behaviors was observed for Meissner expulsion upon\ncooling in static magnetic field from above $T_c$. Substantial conventional\nMeissner expulsion is found in LuNi$_2$B$_2$C, paramagnetic Meissner effect\n(PME) is found in Nb, and virtually no expulsion is observed in iron-based\nsuperconductors. In all cases, good correlation with macroscopic measurements\nof total magnetic moment is found. Our measurements of the spatial distribution\nof magnetic induction provide insight into microscopic physics of the Meissner\neffect.',
]
embeddings = model.encode(sentences)
print(embeddings.shape)
# [3, 384]

# Get the similarity scores for the embeddings
similarities = model.similarity(embeddings, embeddings)
print(similarities)
# tensor([[1.0000, 0.3505, 0.3544],
#         [0.3505, 1.0000, 0.6777],
#         [0.3544, 0.6777, 1.0000]])

Evaluation

Metrics

Information Retrieval

Dataset: superconductor-eval
Evaluated with InformationRetrievalEvaluator

Metric	Value
cosine_accuracy@1	0.7
cosine_accuracy@3	0.8
cosine_accuracy@5	0.9
cosine_accuracy@10	1.0
cosine_precision@1	0.7
cosine_precision@3	0.3667
cosine_precision@5	0.24
cosine_precision@10	0.13
cosine_recall@1	0.5
cosine_recall@3	0.7
cosine_recall@5	0.8
cosine_recall@10	0.9
cosine_ndcg@10	0.7651
cosine_mrr@10	0.7861
cosine_map@100	0.7098

Training Details

Training Dataset

Unnamed Dataset

Size: 4,091 training samples
Columns: sentence_0 and sentence_1
Approximate statistics based on the first 1000 samples:
sentence_0 sentence_1
type string string
details
min: 3 tokens
mean: 7.98 tokens
max: 41 tokens

min: 8 tokens
mean: 160.85 tokens
max: 256 tokens

	sentence_0	sentence_1
type	string	string
details	min: 3 tokens mean: 7.98 tokens max: 41 tokens	min: 8 tokens mean: 160.85 tokens max: 256 tokens

Samples:

sentence_0	sentence_1
`codimension two lump solutions in string field theory and ta`	`We present some solutions for lumps in two dimensions in level-expanded string field theory, as well as in two tachyonic theories: pure tachyonic string field theory and pure $\phi^3$ theory. Much easier to handle, these theories might be used to help understanding solitonic features of string field theory. We compare lump solutions between these theories and we discuss some convergence issues.`
`superconductivity explained`	`We review the current understanding of superconductivity in the quasi-one-dimensional organic conductors of the Bechgaard and Fabre salt families. We discuss the interplay between superconductivity, antiferromagnetism, and charge-density-wave fluctuations. The connection to recent experimental observations supporting unconventional pairing and the possibility of a triplet-spin order parameter for the superconducting phase is also presented.`
`erez berg`	Erez Berg- Theory of Strange Metals \| Understanding "strange metal" phenomena - metallic behavior that deviates from that expected of an ordinary Fermi liquid down to the lowest measurable temperatures - is among the most puzzling open problems in condensed matter physics. Such phenomena are observed across many different strongly correlated materials. They seem tied to other interesting phenomena, such as quantum criticality and unconventional superconductivity. I will describe theoretical advances in understanding the possible or

Loss: MultipleNegativesRankingLoss with these parameters:

{
    "scale": 20.0,
    "similarity_fct": "cos_sim",
    "gather_across_devices": false
}

Training Hyperparameters

Non-Default Hyperparameters

eval_strategy: steps
per_device_train_batch_size: 16
per_device_eval_batch_size: 16
num_train_epochs: 4
multi_dataset_batch_sampler: round_robin

All Hyperparameters

Click to expand

overwrite_output_dir: False
do_predict: False
eval_strategy: steps
prediction_loss_only: True
per_device_train_batch_size: 16
per_device_eval_batch_size: 16
per_gpu_train_batch_size: None
per_gpu_eval_batch_size: None
gradient_accumulation_steps: 1
eval_accumulation_steps: None
torch_empty_cache_steps: None
learning_rate: 5e-05
weight_decay: 0.0
adam_beta1: 0.9
adam_beta2: 0.999
adam_epsilon: 1e-08
max_grad_norm: 1
num_train_epochs: 4
max_steps: -1
lr_scheduler_type: linear
lr_scheduler_kwargs: {}
warmup_ratio: 0.0
warmup_steps: 0
log_level: passive
log_level_replica: warning
log_on_each_node: True
logging_nan_inf_filter: True
save_safetensors: True
save_on_each_node: False
save_only_model: False
restore_callback_states_from_checkpoint: False
no_cuda: False
use_cpu: False
use_mps_device: False
seed: 42
data_seed: None
jit_mode_eval: False
bf16: False
fp16: False
fp16_opt_level: O1
half_precision_backend: auto
bf16_full_eval: False
fp16_full_eval: False
tf32: None
local_rank: 0
ddp_backend: None
tpu_num_cores: None
tpu_metrics_debug: False
debug: []
dataloader_drop_last: False
dataloader_num_workers: 0
dataloader_prefetch_factor: None
past_index: -1
disable_tqdm: False
remove_unused_columns: True
label_names: None
load_best_model_at_end: False
ignore_data_skip: False
fsdp: []
fsdp_min_num_params: 0
fsdp_config: {'min_num_params': 0, 'xla': False, 'xla_fsdp_v2': False, 'xla_fsdp_grad_ckpt': False}
fsdp_transformer_layer_cls_to_wrap: None
accelerator_config: {'split_batches': False, 'dispatch_batches': None, 'even_batches': True, 'use_seedable_sampler': True, 'non_blocking': False, 'gradient_accumulation_kwargs': None}
parallelism_config: None
deepspeed: None
label_smoothing_factor: 0.0
optim: adamw_torch_fused
optim_args: None
adafactor: False
group_by_length: False
length_column_name: length
project: huggingface
trackio_space_id: trackio
ddp_find_unused_parameters: None
ddp_bucket_cap_mb: None
ddp_broadcast_buffers: False
dataloader_pin_memory: True
dataloader_persistent_workers: False
skip_memory_metrics: True
use_legacy_prediction_loop: False
push_to_hub: False
resume_from_checkpoint: None
hub_model_id: None
hub_strategy: every_save
hub_private_repo: None
hub_always_push: False
hub_revision: None
gradient_checkpointing: False
gradient_checkpointing_kwargs: None
include_inputs_for_metrics: False
include_for_metrics: []
eval_do_concat_batches: True
fp16_backend: auto
push_to_hub_model_id: None
push_to_hub_organization: None
mp_parameters:
auto_find_batch_size: False
full_determinism: False
torchdynamo: None
ray_scope: last
ddp_timeout: 1800
torch_compile: False
torch_compile_backend: None
torch_compile_mode: None
include_tokens_per_second: False
include_num_input_tokens_seen: no
neftune_noise_alpha: None
optim_target_modules: None
batch_eval_metrics: False
eval_on_start: False
use_liger_kernel: False
liger_kernel_config: None
eval_use_gather_object: False
average_tokens_across_devices: True
prompts: None
batch_sampler: batch_sampler
multi_dataset_batch_sampler: round_robin
router_mapping: {}
learning_rate_mapping: {}

Training Logs

Epoch	Step	superconductor-eval_cosine_ndcg@10
1.0	256	0.7651

Framework Versions

Python: 3.9.6
Sentence Transformers: 5.1.2
Transformers: 4.57.1
PyTorch: 2.8.0
Accelerate: 1.10.1
Datasets: 4.3.0
Tokenizers: 0.22.1

Citation

BibTeX

Sentence Transformers

@inproceedings{reimers-2019-sentence-bert,
    title = "Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks",
    author = "Reimers, Nils and Gurevych, Iryna",
    booktitle = "Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing",
    month = "11",
    year = "2019",
    publisher = "Association for Computational Linguistics",
    url = "https://arxiv.org/abs/1908.10084",
}

MultipleNegativesRankingLoss

@misc{henderson2017efficient,
    title={Efficient Natural Language Response Suggestion for Smart Reply},
    author={Matthew Henderson and Rami Al-Rfou and Brian Strope and Yun-hsuan Sung and Laszlo Lukacs and Ruiqi Guo and Sanjiv Kumar and Balint Miklos and Ray Kurzweil},
    year={2017},
    eprint={1705.00652},
    archivePrefix={arXiv},
    primaryClass={cs.CL}
}