Geometric phase for a dimerized disordered continuum: Topological shot noise

TL;DR

This paper explores how a topological geometric phase shift in a disordered electron system leads to quantized values and causes statistical fluctuations in conductance, termed topological shot noise.

Contribution

It demonstrates that the geometric phase in a disordered continuum is topologically invariant and links phase discontinuities to conductance fluctuations.

Findings

Phase shift is 0 or ±π depending on the circuit topology.

The phase shift's discontinuity causes spectral and conductance fluctuations.

Introduces the concept of topological shot noise as a consequence of phase quantization.

Abstract

Geometric phase shift associated with an electron propagating through a dimerized-disordered continuum is shown to be 0, or $\pm \pi$ (modulo 2$\pi$), according as the associated circuit traversed in the two-dimensional parameter space excludes, or encircles a certain singularity. This phase-shift is a topological invariant. Its discontinuous dependence on the electron energy and disorder implies a statistical spectral and conductance fluctuation in a corresponding mesoscopic system. Inasmuch as the fluctuation derives from the discreteness of the phase shift, it may aptly be called a topological shot-noise.