Zero-bias anomaly in disordered wires

Abstract

We calculate the low-energy tunneling density of states $ν(ε, T)$ of an $N$-channel disordered wire, taking into account the electron-electron interaction non-perturbatively. The finite scattering rate $1/τ$ results in a crossover from the Luttinger liquid behavior at higher energies, $ν\proptoε^α$, to the exponential dependence $ν(ε, T=0)\propto \exp{(-ε^*/ε)}$ at low energies, where $ε^*\propto 1/(N τ)$. At finite temperature $T$, the tunneling density of states depends on the energy through the dimensionless variable $ε/\sqrt{ε^* T}$. At the Fermi level $ν(ε=0,T) \propto \exp (-\sqrt{ε^*/T})$.