Fingerprint of topological Andreev bound states in phase-dependent heat transport

Abstract

We demonstrate that phase-dependent heat currents through superconductor-topological insulator Josephson junctions provide a useful tool to probe the existence of topological Andreev bound states, even for multi-channel surface states. We predict that in the tunneling regime topological Andreev bound states lead to a minimum of the thermal conductance for a phase difference φ = π, in clear contrast to a maximum of the thermal conductance at φ = π that occurs for trivial Andreev bound states in superconductor-normal metal tunnel junctions. This opens up the possibility that phasedependent heat transport can distinguish between topologically trivial and nontrivial 4π modes. Furthermore, we propose a superconducting quantum interference device geometry where phasedependent heat currents can be measured using available experimental technology.Introduction.-At the interface between a normal metal and a superconductor, an electron with an energy inside the superconducting gap gets reflected from the superconductor as a hole in a process called Andreev reflection [1]. In a superconductor-normal metalsuperconductor (S-N-S) junction, this electron-hole conversion leads to the formation of Andreev bound states with discrete energies [2]. In the case of a short, onedimensional junction there is exactly one pair of such bound states with energy ε = ±∆ 1 − D sin 2 φ/2 where D denotes the transmission probability of the junction in the normal state, ∆ is the absolute value of the superconducting pair potential and φ the phase difference across the junction [3].Recently, there has been a growing interest in Josephson junctions based on topological insulators (TIs). The surface states of a three-dimensional TI give rise to the formation of topologically nontrivial helical Andreev bound states with energy ε = ±∆ cos φ/2 [4], i.e., they exhibit a zero-energy crossing at φ = π. In contrast to the S-N-S case where even weak backscattering leads to a splitting of the accidental degeneracy of Andreev bound states at φ = π, the crossing in the S-TI-S case is robust due to topological protection. It gives rise to a 4π-periodic Josephson current [5]. The latter is difficult to observe in experiment [6,7] as it is a single-channel effect and subject to quasiparticle poisoning. Although recent experiments provide some evidence for the existence of helical Andreev bound states in the non-sinusoidal current phase relation [8], in the diffraction pattern [9] and missing Shapiro steps in the ac Josephson effect [10], it is still an outstanding challenge to distinguish between topologically trivial and nontrivial 4π modes.Interestingly, not only the Josephson current but also the heat current between two superconductors kept at different temperatures depends on the phase difference across the junction. The effect arises due to the interference between quasiparticles carrying heat and Cooper pairs carrying phase information. It was theoretically Since heat currents are carried by quasiparticles with energies above or below the superconducting g...

High-efficiency thermal switch based on topological Josephson junctions

“…We omit here Andreev bound state transmission functions, since only quasiparticles above the superconducting gap give rise to the thermal transport. The general form of the transmission function is similar to that obtained for a Josephson junction based on surface states of a three-dimensional topological insulator [34]. We remark that the energy-dependent term inside the cosine arises from the energy dependence of the electron and hole wave vectors and reflects an additional phase picked up by an electron-hole pair making a roundtrip through the junction.…”

Josephson junction dynamics in the presence of 2π - and 4π -periodic supercurrents

“…Proposals based on dynamical transitions allow to overcome these difficulties [27][28][29][30][31][32][33][34][35][36]. Further proposals overcome some of these problems by studying the skewness of the 4π -periodic supercurrent profile [37,38] or the phase-dependent thermal conductance with minimum at ϕ = π independent of the barrier strength in the heat transport setup [39].…”

Phase-coherent caloritronics with ordinary and topological Josephson junctions

“…While the above discussion has been carried out for the case of a one-dimensional junction, it has been shown in Ref. [63] that qualitatively similar results also hold for a two-dimensional junction based on surface states of a three-dimensional topological insulator. This is again in contrast to S-N-S junction.…”

“…(b) Phase-dependent thermal conductance κ(φ) in units of thermal conductance quantum GQ at kBT = ∆/2 with different barrier transparencies Z for a short one-dimensional S-N-S and S-TI-S junctions. Adapted from Ref [63]…”