Limits of Thermal Conductance Quantization in Chiral Topological Josephson Junctions

TL;DR

This paper explores the limits of thermal conductance quantization in chiral topological Josephson junctions, revealing conditions for robust quantization and the influence of topology, geometry, and parameters on thermal transport.

Contribution

It provides new criteria for detecting chiral Majorana modes and analyzes how topology and sample specifics affect thermal conductance quantization.

Findings

Half-quantized thermal conductance occurs near phase difference π.

Quantization is limited to low doping and specific junction lengths.

Thermal response varies with Zeeman field and topology.

Abstract

We investigate thermal and non-local electrical transport in four-terminal Josephson junctions formed by a normal region coupled to two transverse chiral superconducting leads, supporting phases characterized by Chern numbers ${\cal C}=0,\,1$\,and\,2. We identify the conditions under which a single chiral Majorana mode (${\cal C}=1$) produces a robust half-quantized thermal conductance, while non-local electrical conductance remains strongly suppressed by particle-hole symmetry. Thermal conductance quantization occurs near a superconducting phase difference $\pi$, but only in the low-doping regime of the central region and in the intermediate- to long-junction limits. At finite Zeeman fields, the thermal response broadly follows the topology of the isolated superconducting leads for the $C=1$ phase while, in the ${\cal C}=2$ phase, the thermal conductance generally deviates from quantization, depending on the momentum-space location of the Majorana modes. Our results establish clear criteria for probing chiral Majorana modes in Josephson junctions and highlight the essential role of momentum-space structure, finite-size geometry, and sample parameters in thermal transport.