The conductance of a multi-mode ballistic ring: beyond Landauer and Kubo

TL;DR

This paper explores the conductance of multi-mode ballistic rings, revealing that it behaves differently from traditional Landauer and Kubo predictions due to energy-space percolation effects and matrix sparsity.

Contribution

It introduces a novel perspective on mesoscopic conductance by analyzing energy-space percolation, extending beyond Landauer and Kubo frameworks.

Findings

Conductance in rings can be unbounded, unlike in open systems.

Energy-space percolation critically influences conductance.

Non-universal structures affect mesoscopic transport.

Abstract

The Landauer conductance of a two terminal device equals to the number of open modes in the weak scattering limit. What is the corresponding result if we close the system into a ring? Is it still bounded by the number of open modes? Or is it unbounded as in the semi-classical (Drude) analysis? It turns out that the calculation of the mesoscopic conductance is similar to solving a percolation problem. The "percolation" is in energy space rather than in real space. The non-universal structures and the sparsity of the perturbation matrix cannot be ignored.