Interaction effects on two-dimensional fermions with random hopping

Abstract

We study the effects of generic short-ranged interactions on a system of 2D Dirac fermions subject to a special kind of static disorder, often referred to as "chiral." The non-interacting system is a member of the disorder class BDI [M. R. Zirnbauer, J. Math. Phys. 37, 4986 (1996)]. It emerges, for example, as a low-energy description of a time-reversal invariant tight-binding model of spinless fermions on a honeycomb lattice, subject to random hopping, and possessing particle-hole symmetry. It is known that, in the absence of interactions, this disordered system is special in that it does not localize in 2D, but possesses extended states and a finite conductivity at zero energy, as well as a strongly divergent low-energy density of states. In the context of the hopping model, the short-range interactions that we consider are particle-hole symmetric density-density interactions. Using a perturbative one-loop renormalization group analysis, we show that the same mechanism responsible for the divergence of the density of states in the non-interacting system leads to an instability, in which the interactions are driven strongly relevant by the disorder. This result should be contrasted with the limit of clean Dirac fermions in 2D, which is stable against the inclusion of weak short-ranged interactions. Our work suggests a novel mechanism wherein a clean system, initially insensitive to interaction effects, can be made unstable to interactions upon the inclusion of weak static disorder. We dub this mechanism a "disorder-driven Mott transition." Our result for 2D fermions also contrasts sharply with known results in 1D, where a similar delocalized phase has been shown to be robust against the inclusion of weak interaction effects.

Negative Quantum Capacitance Induced by Midgap States in Single-layer Graphene

“…In previous theoretical studies, it has been suggested that midgap states enhance the Coulomb interactions and the correction term induced by midgap states has a negative sign, leading to the reduction of κ ~1 . The expression of κ −1 affected by midgap states is represented as1323334 where c is a positive numerical constant, Δ is a positive dimensionless number characterizing the strength of midgap states and is a high momentum cutoff of the order of the inverse of the lattice constant. Note that the second term in the bracket arising from the midgap states correction is negative and becomes significant if wave vector k is very small.…”

Criticality and entanglement in random quantum systems

“…[22], and especially by several groups [29,30,31]. While we concentrate mostly on disordered systems in 1d, Sec.…”

Single-particle Green’s functions and interacting topological insulators

“…(10), (11), and (12). In the rest of this section, we show that when properly generalized to the presence of interactions, the symmetries of the Hamiltonian lead to exactly the same constraints on the Green's functions as in the absence of interactions 15 . We first need to clarify what we mean by the interacting Hamiltonian and the interacting Green's function.…”