Two-parameter scaling theory of transport near a spectral node

TL;DR

This paper develops a two-parameter scaling theory for the conductivity of 2D Dirac electron gases, revealing fixed points and explaining experimental and numerical observations, including metal-insulator transitions.

Contribution

It introduces a novel two-parameter scaling framework for transport near spectral nodes, extending to include spectral gaps and metal-insulator transitions.

Findings

Finite-size scaling flow toward a finite fixed point representing minimal conductivity.

Unstable fixed points with higher conductivities depending on boundary conditions.

Extension of the model to describe metal-insulator transitions with spectral gaps.

Abstract

We investigate the finite-size scaling behavior of the conductivity in a two-dimensional Dirac electron gas within a chiral sigma model. Based on the fact that the conductivity is a function of system size times scattering rate, we obtain a two-parameter scaling flow toward a finite fixed point. The latter is the minimal conductivity of the infinite system. Depending on boundary conditions, we also observe unstable fixed points with conductivities much larger than the experimentally observed values, which may account for results found in some numerical simulations. By including a spectral gap we extend our scaling approach to describe a metal-insulator transition.