Quantum charge fluctuations of a proximitized nanowire

Abstract

Motivated by recent experiment, we consider charging of a nanowire which is proximitized by a superconductor and connected to a normal-state lead by a single-channel junction. The charge $Q$ of the nanowire is controlled by gate voltage $e{\mathcal{N}}_g/C$. A finite conductance of the contact allows for quantum charge fluctuations, making the function $Q({\mathcal{N}}_g)$ continuous. It depends on the relation between the superconducting gap $\Delta$ and the effective charging energy $E_C^{\ast }$. The latter is determined by the junction conductance, in addition to the geometrical capacitance of the proximitized nanowire. We investigate $Q({\mathcal{N}}_g)$ at zero magnetic field $B$, and at fields exceeding the critical value $B_c$ corresponding to the topological phase transition. Unlike the case of $\Delta =0$, the function $Q({\mathcal{N}}_g)$ is analytic even in the limit of negligible level spacing in the nanowire. At $B=0$ and $\Delta >E_C^{\ast }$, the maxima of $dQ/d{\mathcal{N}}_g$ are smeared by $2e$-fluctuations described by a single-channel "charge Kondo" physics, while the $B=0$, $\Delta <E_C^{\ast }$ case is described by a crossover between the Kondo and mixed-valence regimes of the Anderson impurity model. In the topological phase, $Q({\mathcal{N}}_g)$ is analytic function of the gate voltage with $e$-periodic steps. In the weak tunneling limit, $dQ/d{\mathcal{N}}_g$ has peaks corresponding to Breit-Wigner resonances, whereas in the strong tunneling limit (i.e., small reflection amplitude $r$ ) these resonances are broadened, and $dQ/d{\mathcal{N}}_g-e\propto r\cos (2\pi {\mathcal{N}}_g)$.

11 pages, 5 figures

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• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• Observation of 2e-periodic Supercurrents in Nanowire Single-Cooper-Pair Transistors
• Electron Teleportation in Multi-Terminal Majorana Islands: Statistical Transmutation and Fractional Quantum Conductance
• Suppressing quasiparticle poisoning with a voltage-controlled filter
• Coulomb blockade of a nearly-open Majorana island
• Transport through a Majorana island: strong tunneling regime
• Coulomb Blockade in Fractional Topological Superconductors
• Signatures of topological ground state degeneracy in Majorana islands
• Strongly correlated electrons in superconducting islands with fluctuating Cooper pairs
• Majorana Conductances in Three-Terminal Transports
• Cross-correlation mediated by Majorana island with finite charging energy