Role of coherence in resistance quantization

TL;DR

This paper compares different types of resistance quantization, highlighting that some require only local coherence while others need global phase coherence, revealing fundamental differences in quantum transport phenomena.

Contribution

It clarifies the coherence requirements for various resistance quantizations, emphasizing the unique role of global phase coherence in charge relaxation resistance.

Findings

Quantum Hall and quantum point contact resistances need only local coherence.

Charge relaxation resistance remains quantized with arbitrary backscattering.

Global phase coherence is essential for charge relaxation resistance quantization.

Abstract

The quantization of resistances in the quantum Hall effect and ballistic transport through quantum point contacts is compared with the quantization of the charge relaxation resistance of a coherent mesoscopic capacitor. While the former two require the existence of a perfectly transmitting channel, the charge relaxation resistance remains quantized for arbitrary backscattering. The quantum Hall effect and the quantum point contact require only local phase coherence. In contrast quantization of the charge relaxation resistance requires global phase coherence.