Experimental Evidence of Fractional Entropy in Critical Kondo Systems

TL;DR

This study provides experimental thermodynamic evidence for fractional entropy associated with non-Abelian anyons in quantum-critical states, confirming their exotic quantum nature.

Contribution

It demonstrates a novel entropy measurement approach to identify non-Abelian anyons in engineered quantum-critical systems, advancing topological quantum computing research.

Findings

Measured fractional entropy consistent with Majorana zero modes and Fibonacci anyons.

Established entropy as a tool for characterizing non-Abelian quantum states.

Validated theoretical predictions of scaling dimensions for critical anyons.

Abstract

Unconventional quantum states defying the ubiquitous Fermi-liquid paradigm can emerge in the presence of strong electronic correlations. Among these, non-Abelian anyons - such as Majorana zero modes and Fibonacci anyons - are of particular interest for topological quantum computing due to their non-integer quantum dimensions d>1, which allows for protected non-local encoding and processing of quantum information. However, despite considerable efforts, the unambiguous characterisation of such anyons via transport measurements has proved challenging. Instead, here we provide experimental evidence for the low-temperature fractional entropy Delta S associated with a single anyon, which directly implies its non-Abelian character through the relation Delta S = kB ln(d). This thermodynamic signature is measured in metal-semiconductor quantum circuits engineered to realize quantum-critical states from frustrated interactions. Using a micrometre-scale metallic island coupled to two or three electronic leads, we tune the system to two-channel and three-channel Kondo critical points. By measuring the island charge and exploiting a thermodynamic Maxwell relation, we estimate the entropy associated with the anyons that emerge in these critical states. Our observations reveal fractional values, exposing non-Abelian anyons. The corresponding scaling dimensions are consistent with theoretical predictions for a Majorana zero mode Delta S = kB ln(sqrt(2)) and a Fibonacci anyon Delta S = kB ln(1 +sqrt(5))/2 for two and three channels. These findings establish entropy measurements as a powerful tool for characterizing exotic quantum states.