Half-integer thermal conductance in the absence of Majorana mode

TL;DR

This paper demonstrates that half-integer thermal conductance can occur in Abelian quantum Hall states due to equilibration effects, challenging the belief that it indicates non-Abelian Majorana modes.

Contribution

The study presents a theoretical and experimental framework showing half-integer thermal conductance in Abelian phases, not necessarily linked to Majorana modes.

Findings

Half-integer thermal conductance observed in Abelian phases.

Equilibration dynamics can produce non-integer thermal conductance values.

Proposed setup uses bilayer graphene with quantum Hall states.

Abstract

Considering a range of candidate quantum phases of matter, half-integer thermal conductance ($\kappa_{\text{th}}$) is believed to be an unambiguous evidence of non-Abelian states. It has been long known that such half-integer values arise due to the presence of Majorana edge modes, representing a significant step towards topological quantum computing platforms. Here, we challenge this prevailing notion by presenting a comprehensive theoretical and experimental study where half-integer two-terminal thermal conductance plateau is realized employing Abelian phases. Our proposed setup features a confined geometry of bilayer graphene, interfacing distinct particle-like and hole-like integer quantum Hall states. Each segment of the device exhibits full charge and thermal equilibration. Our approach is amenable to generalization to other quantum Hall platforms, and may give rise to other values of fractional (electrical and thermal) quantized transport. Our study demonstrates that the observation of robust non-integer values of thermal conductance can arise as a manifestation of mundane equilibration dynamics as opposed to underlying non-trivial topology.