Relation between chiral anomaly and electric transport in $1D$ Dirac semimetal

TL;DR

This work analyzes how the chiral anomaly influences electric transport in a 1D Dirac semimetal realized by the SSH model, casting the problem in a lattice Wilson-fermion framework and treating dissipation via a finite rate ε within the nonequilibrium Keldysh formalism. By computing both the axial charge density ρ_5 and the current j to linear order in an external electric field E, the authors demonstrate that, at μ=0, ρ_5 and j coincide and scale as E/(2π ε), highlighting an anomaly-driven transport channel regulated by dissipation. The analysis via both Kubo (A) and Keldysh (B) approaches shows the same anomaly signature: a nonconservation of chiral charge proportional to E, arising from spectral flow across the Fermi point in the lattice model. The results connect anomaly physics to tight-binding Dirac systems, quantify the anomaly’s contribution to conductivity as σ = τ/π with τ = 1/(2ε), and suggest extensions to higher dimensions and more complex Dirac semimetals.

Abstract

We investigate the interplay of chiral anomaly and dissipation in one - dimensional Dirac semimetal. For definiteness we consider the Su Schrieffer Heeger (SSH) model, which on the language of lattice field theory represents 1 D Wilson fermions. We employ the non-equilibrium Keldysh Green function formalism, and calculate the chiral imbalance and electric conductivity in the presence of energy dissipation, revealing how these observables are connected to the chiral anomaly. By systematically incorporating dissipation effects into the Keldysh framework, we demonstrate how the anomaly-induced contributions manifest in both axial charge density and electric current.

Figures (1)

• Figure 1: $E_{1,2}$ as a function of $p$