Abstract
We study the thermodynamic properties of topological Josephson junctions using a quantum spin Hall (QSH) insulator-based junction as an example. In particular, we propose that phase-dependent measurements of the heat capacity offer an alternative to Josephson-current measurements to demonstrate key topological features. Even in an equilibrium situation, where the fermion parity is not conserved, the heat capacity exhibits a pronounced double peak in its phase dependence as a signature of the protected zero-energy crossing in the Andreev spectrum. This double-peak feature is robust against changes of the tunneling barrier and thus allows one to distinguish between topological and trivial junctions. At short time scales fermion parity is conserved and the heat capacity is $4\pi$-periodic in the superconducting phase difference. We propose a dispersive setup coupling the Josephson junction to a tank LC circuit to measure the heat capacity of the QSH-based Josephson junction sufficiently fast to detect the $4\pi$-periodicity. Although explicitly calculated for a short QSH-based Josephson junction, our results are also applicable to long as well as nanowire-based topological Josephson junctions.
Highlights
Topological superconductors [1,2,3,4,5,6,7,8,9,10] offer the prospect of encoding and manipulating quantum information in a faulttolerant, topologically protected manner [11,12,13]
It has been shown that topological phases exhibit unexpected universalities in their thermodynamic signatures [57,58]. Motivated by this and by advances in the understanding of the thermodynamics of nontopological superconductors [59,60,61,62,63,64,65,66,67,68,69,70,71], we have recently applied these thermodynamic concepts to topological Josephson junctions to propose a topological Josephson heat engine [72]. We discuss another way of utilizing coherent thermodynamics to demonstrate the peculiar nature of topological Josephson junctions: We show that measurements of the phase-dependent heat capacity can provide distinct signatures originating from the topological Andreev bound states (ABS) and represent an alternative property which can be investigated in topological Josephson junctions
We have analyzed key properties of the thermodynamics in topological Josephson junctions based on quantum spin Hall insulators
Summary
Topological superconductors [1,2,3,4,5,6,7,8,9,10] offer the prospect of encoding and manipulating quantum information in a faulttolerant, topologically protected manner [11,12,13]. As a hallmark of their topological nature such junctions exhibit a ground-state fermion parity that is 4π periodic in the superconducting phase difference φ and Andreev bound states (ABS) with a protected zero-energy crossing [45,46]. Topological Josephson junction based on a quantum spin Hall (QSH) insulator, where the length LN of the normal (N) region is small compared to the Josephson penetration depth In this setup, a QSH insulator is partially covered by s-wave superconductors, which proximity-induce pairing to the QSH edge states via tunneling and define the superconducting (S) regions (see Fig. 1). While these continuum states reduce the effective superconducting gap, the ABS residing in this gap still exhibit a protected crossing [Figs. If |vF pS| > 2 , there are bound states, but these are all coexisting with continuum states as the superconducting gap is closed [Fig. 2(c)]
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