Thermoelectric current in a graphene Cooper pair splitter

Z B Tan,N S Kirsanov,V M Vinokur,A Galda,G B Lesovik,P J Hakonen,D S Golubev,A Savin,A Laitinen,M Haque

doi:10.1038/s41467-020-20476-7

Abstract

Generation of electric voltage in a conductor by applying a temperature gradient is a fundamental phenomenon called the Seebeck effect. This effect and its inverse is widely exploited in diverse applications ranging from thermoelectric power generators to temperature sensing. Recently, a possibility of thermoelectricity arising from the interplay of the non-local Cooper pair splitting and the elastic co-tunneling in the hybrid normal metal-superconductor-normal metal structures was predicted. Here, we report the observation of the non-local Seebeck effect in a graphene-based Cooper pair splitting device comprising two quantum dots connected to an aluminum superconductor and present a theoretical description of this phenomenon. The observed non-local Seebeck effect offers an efficient tool for producing entangled electrons.

Highlights

Background subtractionThe direct experimental measurement allows to obtain the total electric current through the left dot, IL(R), constituting the sum of local, I loc LðRÞ, and non-local, ΔInLðl RÞ, contributions.Note that, in theory, while the non-local contribution depends on both gate voltages, the local one is determined only by the gate voltage on the corresponding dot
We present the experimental observation of the non-local thermoelectric current generated by imposing thermal gradient across a quantum dot–superconductor–quantum dot (QD-S-QD) splitter. We find that both Cooper pair splitting (CPS) and elastic co-tunneling (EC) processes contribute to the non-local thermoelectric current and that their relative contributions can be tuned by the gate potentials
Taking that the non-local transport is primarily coherent and that the electron energies are smaller than the superconducting gap, ∣E∣ < Δ, we find, see Supplementary Note 4, that the EC, τEC(E), and CPS, τCPS(E), probabilities are given by the expressions τEC 1⁄4 τLðEÞτSτRðEÞ; τCPS 1⁄4 τLðEÞτSτRðÀEÞ: ð1Þ

Summary

Introduction

In theory, while the non-local contribution depends on both gate voltages, the local one is determined only by the gate voltage on the corresponding dot. This suggests that the local current through the left (right) dot is nothing but the total current IL(R). The gate electrodes may be subject to cross-talk, which the described simple processing does not account for. Bearing in mind the remaining residual cross-talk, we construct a slowly varying background hILðRÞðVsg;L; Vsg;RÞi in the following manner (for clarity, let us consider the case left dot): for any fixed

Methods

Results

Conclusion