Compressibility as a probe of quantum phase transitions in topological superconductors

Abstract

The non-Abelian statistics of Majorana fermions, their role in topological quantum computation, and the possibility of realizing them in condensed matter systems, has attracted considerable attention. While there have been recent reports of zero energy modes in single particle tunneling density of states, their identity as Majorana modes has so far not been unequivocally established. We make predictions for the local compressibility ${\kappa }_{\mathrm{loc}}$, tuned by changing the chemical potential $\mu$ in a semiconducting nanowire with strong spin-orbit coupling and in a Zeeman field in proximity to a superconductor, that has been proposed as a candidate system for observing Majorana modes. We show that in the center of the wire, the topological phase transition is signaled by a divergence of ${\kappa }_{\mathrm{loc}}$ as a function of $\mu$ which is an important diagnostic of the topological phase transition. We also find that a single strong impurity potential can lead to a local {\it negative} compressibility at the topological phase transition. The origin of such anomalous behavior can be traced to the formation of Andreev bound states close to topological phase transitions. Measurable by a scanning electron transistor, the compressibility includes contributions from both single particle states and collective modes and is therefore a complimentary probe from scanning tunneling spectroscopy.

5 pages, 6 eps figures

References in corpus (8)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Zero bias conductance peak in Majorana wires made of semiconductor-superconductor hybrid structures
• Fractional ac Josephson effect in unconventional superconductors
• Detecting Majoranas in 1D wires by charge sensing

Cited by in corpus (11)

• Approaching a topological phase transition in Majorana nanowires
• Multiple signatures of topological transitions for interacting fermions in chain lattices
• Interacting Hofstadter Interface
• Quantum Phase Transition and Entanglement in Topological Quantum Wires
• From Topological Superconductivity to Quantum Hall States in Coupled Wires
• Bipartite charge fluctuations in one-dimensional ${\mathbb{Z}}_2$ superconductors and insulators
• Nonequilibrium electrical, thermal and spin transport in open quantum systems of topological superconductors, semiconductors and metals
• Dual Majorana universality in thermally induced nonequilibrium
• Radio-frequency C-V measurements with sub-attofarad sensitivity
• Real space renormalization of Majorana fermions in quantum nano-wire superconductors
• Macroscopic states in Bose-Einstein condensate dark matter model with axionlike interaction