Majorana tunneling entropy

TL;DR

This paper explores how coupling a quantum dot to Majorana modes in topological superconductors can lead to non-integer entropy plateaus and unique thermodynamic signatures, challenging traditional thermodynamic principles.

Contribution

It demonstrates that Majorana bound states can induce non-integer entropy plateaus and alter thermodynamic behavior in quantum dots, revealing new physical phenomena.

Findings

Entropy can have non-integer plateaus due to Majorana states.

Specific heat exhibits low-temperature Majorana peaks.

Transport properties are fundamentally affected by Majorana coupling.

Abstract

In thermodynamics a macroscopic state of a system results from a number of its microscopic states. This number is given by the exponent of the system's entropy $\exp(S)$. In non-interacting systems with discrete energy spectra, such as large scale quantum dots, $S$ as a function of the temperature has usually a plateau shape with integer values of $\exp(S)$ on these plateaus. Plateaus with non-integer values of $\exp(S)$ are fundamentally forbidden and would be thermodynamically infeasible. Here we investigate the entropy of a non-interacting quantum dot coupled via tunneling to normal metals with continuum spectra as well as to topological superconductors. We show that the entropy may have non-integer plateaus if the topological superconductors support weakly overlapping Majorana bound states. This brings a fundamental change in the thermodynamics of the quantum dot whose specific heat $c_V$ acquires low temperature Majorana peaks which should be absent according to the conventional thermodynamics. We also provide a fundamental thermodynamic understanding of the transport properties, such as the linear conductance. In general our results show that the thermodynamics of systems coupled to Majorana modes represents a fundamental physical interest with diverse applications depending on versatility of possible coupling mechanisms.