Diverging dc conductivity due to a flat band in a disordered system of pseudospin-1 Dirac-Weyl fermions

Abstract

Several lattices, such as the dice or the Lieb lattice, possess Dirac cones and a flat band crossing the Dirac point, whose effective model is the pseudospin-1 Dirac-Weyl equation. We investigate the fate of the flat band in the presence of disorder by focusing on the density of states (DOS) and dc conductivity. While the central hub site does not reveal the presence of the flat band, the sublattice resolved DOS on the noncentral sites exhibits a narrow peak with height ∼1/ √ g with g the dimensionless disorder variance. Although the group velocity is zero on the flat band, the dc conductivity diverges as ln(1/g) with decreasing disorder due to interband transitions around the band touching point between the propagating and the flat band. Generalizations to higher pseudospin are given.

Magnetic field independent shape of the zero-energy landau levels in a disordered T3 model

“…Recently, there is a growing interest in studying the T 3 model [23][24][25][26][27][28][29][30][31][32][33]. Experimentally, the lattice can be realized in a trilayer structure of the face-centered cubic lattice, such as SrTiO 3 /SrIrO 3 /SrTiO 3 heterostructures [34,35].…”

Revival resonant scattering, perfect caustics, and isotropic transport of pseudospin-1 particles

“…For convenience, we call such systems pseudospin-1 Dirac cone systems. Comparing with the conventional Dirac cone systems with massless pseudospin/spin-1/2 quasiparticles (i.e., systems without a flat band), pseudospin-1 systems can exhibit quite unusual physics such as superKlein tunneling for the two conical (linear dispersive) bands 23,32,40,41 , diffraction-free wave propagation and novel conical diffraction [24][25][26][27] , flat band rendering divergent dc conductivity with a tunable short-range disorder 42 , unconventional Anderson localization 43,44 , flat band ferromagnetism 28,45,46 , and peculiar topological phases under external gauge fields or spin-orbit coupling 35,[47][48][49] . Especially, the topological phases arise due to the flat band that permits a number of degenerate localized states with a topological origin (i.e., "caging" of carriers) 50 .…”

Flat-band conductivity properties at long-range Coulomb interactions

“…of clean systems at zero temperature diverges [13] and is then due to sliding of the hexagonal crystal as a whole [14]. Its Drude weight D = e 2 n/m is determined by carrier density n and particle masses m, just as in the absence of interactions [15]; in this work we do not con- sider crystalline disorder.…”

“…In quantum Hall systems, when kinetic energy is quenched, they cause Wigner crystallization at fillings ν < 1 /5 [10] (in graphene at ν < 0.28 [11]) while without magnetic field crystallization appears when the Coulomb energy E C exceeds the kinetic energy E K by a sufficiently big factor [12], E C /E K > 37 . The longitudinal conductivityof clean systems at zero temperature diverges [13] and is then due to sliding of the hexagonal crystal as a whole [14]. Its Drude weight D = e 2 n/m is determined by carrier density n and particle masses m, just as in the absence of interactions [15]; in this work we do not con- sider crystalline disorder.…”

“…which for T 3 resembles the relativistic expression for the operator j of graphene [13,23]. In T 3 , spin matrices…”