Fluctuation-dissipation theorem for chiral systems in non-equilibrium steady states

Abstract

We consider a three-terminal system with a chiral edge channel connecting the source and drain terminals. Charge can tunnel between the chiral edge and a third terminal. The third terminal is maintained at a different temperature and voltage than the source and drain. We prove a general relation for the current noises detected in the drain and third terminal. It has the same structure as an equilibrium fluctuation-dissipation relation with the nonlinear response in place of the linear conductance. The result applies to a general chiral system and can be useful for detecting "upstream" modes on quantum Hall edges.

detailed proof

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• Edge Probes of Topological Order
• Chirality, causality, and fluctuation-dissipation theorems in non-equilibrium steady states
• Observation of the scaling dimension of fractional quantum Hall anyons
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• Different fractional charges from auto- and cross-correlation noise in quantum Hall states without upstream modes
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• Anyonic analogue of optical Mach-Zehnder interferometer