Zero-bias anomaly in disordered wires

Abstract

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

5 pages, 1 figure