Thermal conductance as a probe of the non-local order parameter for a topological superconductor with gauge fluctuations

Abstract

We investigate the effect of quantum phase slips on a helical quantum wire coupled to a superconductor by proximity. The effective low-energy description of the wire is that of a Majorana chain minimally coupled to a dynamical ${\mathbb{Z}}_2$ gauge field. Hence the wire emulates a matter-coupled gauge theory, with fermion parity playing the role of the gauged global symmetry. Quantum phase slips lift the ground state degeneracy associated with unpaired Majorana edge modes at the ends of the chain, a change that can be understood as a transition between the confined and the Higgs-mechanism regimes of the gauge theory. We identify the quantization of thermal conductance at the transition as a robust experimental feature separating the two regimes. We explain this result by establishing a relation between thermal conductance and the Fredenhagen-Marcu string order-parameter for confinement in gauge theories. Our work indicates that thermal transport could serve as a measure of non-local order parameters for emergent or simulated topological quantum order.

5 pages, 2 figures; v2: different introduction, added references, updated figure 2; published version to appear in PRB

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• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Diagnosing Deconfinement and Topological Order
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• Exact solution to an interacting dimerized Kitaev model at symmetric point
• Characterization of topological phases of modified dimerized Kitaev chain via edge correlation functions
• Commensurate and Incommensurate States of Topological Quantum Matter
• Changing anyonic ground degeneracy with engineered gauge fields
• Majorana correlations in quantum impurities coupled to a topological wire
• Simulation of supersymmetric quantum mechanics in a Cooper-pair box shunted by a Josephson rhombus
• Scanning qubit probe of edge states in a topological insulator
• Topological ordering in the Majorana Toric Code
• Confinement-Induced Enhancement of Superconductivity in a Spin-$\frac{1}{2}$ Fermion Chain Coupled to a ${\mathbb{Z}}_2$ Lattice Gauge Field