Abstract
The promise of fault-tolerant quantum computing has made topological
superconductors the focus of intense research during the past decade. In this
context, topological Josephson junctions based on nanowires or on topological
insulators provide an alternative route for probing topological
superconductivity. As a hallmark of their topological nature, such junctions
exhibit a ground-state fermion parity that is $4\pi$-periodic in the
superconducting phase difference $\phi$. Finding unambiguous experimental
evidence for this $4\pi$-periodicity still proves a difficult task, however.
Here we propose a topological Josephson heat engine implemented by a
Josephson-Stirling cycle as an alternative thermodynamic approach to test the
ground-state parity. Using a Josephson junction based on a quantum spin Hall
(QSH) insulator, we show how the thermodynamic cycle can be used to test the
$4\pi$-periodicity of the topological ground state and to distinguish between
parity-conserving and non-parity-conserving engines. Interestingly, we find
that parity conservation generally boosts both the efficiency and power of the
topological heat engine with respect to its non-topological counterpart. Our
results, applicable not only to QSH-based junctions but also to any topological
Josephson junction, demonstrate the potential of the intriguing and fruitful
marriage between topology and coherent thermodynamics.
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