  Searching for high-performance thermoelectric (TE) materials in the paradigm
of narrow-bandgap semiconductors has lasted for nearly 70 years and is
obviously hampered by a bottleneck of research now. Here we report on the
discovery of a few metallic compounds, TiFexCu2x-1Sb and TiFe1.33Sb, showing
the thermopower exceeding many TE semiconductors and the dimensionless figure
of merits comparable with the state-of-the-art TE materials. A quasi-linear
temperature (T) dependence of electrical resistivity in 2 K - 700 K and the
logarithmic T-dependent electronic specific heat at low temperature are also
observed to coexist with the high thermopower, highlighting the strong
intercoupling of the non-Fermi-liquid (NFL) quantum critical behavior of
electrons with TE transports. Electronic structure analysis reveals the
existence of fluctuating Fe-eg-related local magnetic moments, Fe-Fe
antiferromagnetic (AFM) interaction at the nearest 4c-4d sites, and two-fold
degenerate eg orbitals antiferromagnetically coupled with the dual-type
itinerant electrons close to the Fermi level, all of which infer to a
competition between the AFM ordering and Kondo-like spin compensation as well
as a parallel two-channel Kondo effect. These effects are both strongly
meditated by the structural disorder due to the random filling of Fe/Cu at the
equivalent 4c/4d sites of the Heusler crystal lattice. The magnetic
susceptibility deviates from ideal antiferromagnetism but can be fitted well by
x(T) = 1/({\theta} + BT{\alpha}), seemingly being consistent with the quantum
critical scenario of strong local correlation as discussed before. Our work not
only breaks the dilemma that the promising TE materials should be heavily-doped
semiconductors, but also demonstrates the correlation among high TE
performance, NFL quantum criticality, and magnetic fluctuation, which opens up
new directions for future research.
