Microscopic origin of collective exponentially small resistance states

TL;DR

This paper explains the microscopic origin of exponentially small resistance states in high mobility 2DES under magnetic fields and microwave radiation, linking the energy gap to a quantum model involving the Prime Number Theorem.

Contribution

It introduces a novel quantum model that explains the energy gap responsible for zero resistance states using number theory concepts.

Findings

The energy gap Δ is derived from a microscopic quantum model.

The model connects the resistance states to prime number distributions.

This approach provides a new theoretical understanding of ESRS in 2DES.

Abstract

The formation of "zero" (exponentially small) resistance states (ESRS) in high mobility two-dimensional electron systems (2DES) in a static magnetic field B and subjected to strong microwave (MW) radiation has attracted great theoretical interest. These states appear to be associated with a new kind of energy gap $\Delta$. Here I show that the energy gap $\Delta$ is explained by a microscopic quantum model that involves the Prime Number Theorem, hitherto reserved for only mathematical contexts.