  We introduce carbon Kagome nanotubes (CKNTs) -- a new allotrope of carbon
formed by rolling up sheets of Kagome graphene, and investigate the properties
of this material using first principles calculations. Based on the direction of
rolling, we identify two principal varieties of CKNTs -- armchair and zigzag,
and find that the bending stiffness associated with rolling Kagome graphene
into either type of CKNT is about a third of that associated with rolling
conventional graphene into carbon nanotubes (CNTs). Ab initio molecular
dynamics simulations indicate that both types of CKNTs are likely to exist as
stable structures at room temperature. Each CKNT explored here is metallic and
features dispersionless states (i.e., flat bands) throughout its Brillouin
zone, along with an associated singular peak in the electronic density of
states, close to the Fermi level. We calculate the mechanical and electronic
response of CKNTs to torsional and axial strains and compare against
conventional CNTs. We show in particular, that upon twisting, degenerate
dispersionless electronic states in CKNTs split, Dirac points and partially
flat bands emerge from the quadratic band crossing point at the Fermi level,
and that these features can be explained using a relatively simple
tight-binding model.
  Overall, CKNTs appear to be unique and striking examples of realistic
elemental quasi-one-dimensional (1D) materials that can potentially display
fascinating collective material properties arising from the presence of
strongly correlated electrons. Additionally, distorted CKNTs may provide an
interesting material platform where flat band physics and chirality induced
anomalous transport effects may be studied together.
