Fermi edge singularity in a non-equilibrium system

TL;DR

This paper provides exact analytical results for the Fermi Edge Singularity in the absorption spectrum of a non-equilibrium tunnel junction, revealing how out-of-equilibrium conditions alter spectral lineshapes and thresholds.

Contribution

It introduces a novel exact solution for the Fermi Edge Singularity in non-equilibrium systems, accounting for complex scattering matrix effects.

Findings

Spectrum extends below the original threshold due to external power source.

Lineshape depends on phase differences of reflection amplitudes, not just total phase shift.

Results simplify to known equilibrium cases with complex scattering matrix elements.

Abstract

We report exact results for the Fermi Edge Singularity in the absorption spectrum of an out-of-equilibrium tunnel junction. We consider two metals with chemical potential difference V separated by a tunneling barrier containing a defect, which exists in one of two states. When it is in its excited state, tunneling through the otherwise impermeable barrier is possible. We find that the lineshape not only depends on the total scattering phase shift as in the equilibrium case but also on the difference in the phase of the reflection amplitudes on the two sides of the barrier. The out-of-equilibrium spectrum extends below the original threshold as energy can be provided by the power source driving current across the barrier. Our results have a surprisingly simple interpretation in terms of known results for the equilibrium case but with (in general complex-valued) combinations of elements of the scattering matrix replacing the equilibrium phase shifts.