Quantum-Critical transport at a semimetal-to-insulator transition on the honeycomb lattice

TL;DR

This paper investigates the universal transport properties at the quantum critical point of a semimetal-to-insulator transition on the honeycomb lattice, combining theoretical models and experimental relevance.

Contribution

It provides a detailed analysis of quantum-critical conductivity using renormalization group and large-N methods, revealing universal behavior and crossover phenomena.

Findings

Quantum-critical conductivity is temperature independent at low temperatures.

Logarithmic temperature dependence due to Coulomb interactions masks the universal behavior.

Results align well with recent experimental data on gap formation in honeycomb lattice systems.

Abstract

In this paper we study transport properties of electrons on the two-dimensional honeycomb lattice. We consider a half-filled system in the vicinity of a symmetry-breaking transition from a semimetallic phase towards an insulating phase with either charge density or spin density wave order. The effect of either order is to break the sublattice inversion symmetry which induces a finite gap for the electronic single-particle excitations. Phenomenologically, such a scenario is described in the framework of a Gross-Neveu theory. We analyze two related formulations of the model by means of (i) a controlled renormalization group calculation and (ii) the large-N method, both of which in combination with a Boltzmann transport equation. We determine the quantum-critical conductivity and also discuss crossover behavior from quantum critical behavior into the insulating and/or the semimetallic phases. We find that at asymptotically low temperatures the quantum-critical conductivity is given by a temperature independent universal number. Over a large temperature window the temperature independent quantum critical conductivity is masked by a logarithmically temperature dependent contribution due to the marginally irrelevant long-range Coulomb interaction. We discuss possible origins of this peculiarity in the two complementary formulations of the model. Furthermore, we consider possible relations of our findings to recent experiments, with a special emphasis on the quantum-critical-to-insulator crossover. We find that our results are in remarkably good qualitative and quantitative agreement with a recent analysis of the data sets under the hypothesis of an underlying gap in the single-particle spectrum.