Quantum capacitance and parity switching of a quantum-dot-based Kitaev chain

TL;DR

The paper addresses how quantum capacitance can diagnose Majorana-related physics in a quantum-dot–based Kitaev chain. By analyzing a two-site Kitaev chain weakly coupled to a normal lead and a single QD coupled to Andreev bound states, the authors show that $\langle C_q \rangle$ reveals the Majorana sweet spot where normal and superconducting couplings balance, and they derive analytic forms for $C_q$ in both open and nearly closed regimes. They identify parity-switching mechanisms from lead coupling and quasiparticle poisoning and provide ways to extract Hamiltonian parameters such as $t_{sc}$, $t_{sf}$, and ABS coherence factors from capacitance measurements. The results offer practical guidance for interpreting quantum-capacitance experiments and for designing Majorana qubit readout schemes in dot–ABS Kitaev-chain devices.

Abstract

An array of quantum dots coupled via superconductivity provides a new platform for creating Kitaev chains with Majorana zero modes, offering a promising avenue toward topological quantum computing. In this work, we theoretically study the quantum capacitance of a minimal Kitaev chain weakly coupled to an external normal lead. We find that in the open regime, charge stability diagrams of quantum capcaitance can help to identify the sweet spot of a Kitaev chain, consistent with tunnel spectroscopy. Moreover, the quantum capacitance of a single quantum dot coupled to Andreev bound states reveals the interplay between two distinct parity switching mechanisms: coupling to an external normal lead and intrinsic quasiparticle poisoning. Our work provides useful physical insights into the quantum capacitance and parity dynamics in a quantum-dot-based Kitaev chain device.

Figures (4)

• Figure 1: Schematic of a two-site Kitaev chain device. Quantum dots are defined in the semiconductor using electrostatic gates (gray lines). They are connected via Andreev bound states in the hybrid superconducting region. A normal-metal lead is weakly coupled to the device from the left, with the coupling strength controlled by a tunnel gate.
• Figure 2: Conductance and quantum capacitance of a two-site Kitaev chain device. (a)-(c): Conductance in the open regime, assuming $\gamma_{\rm lead} =0.003, k_BT_{\rm lead}=0.005$, and $\gamma_{\rm qpp}=\gamma_{\rm relax}=0$. The three panels correspond to the cases of normal coupling being stronger than, equal to, or weaker than superconducting coupling. (d)-(f): Quantum capacitance in the open regime. (g)-(i): Quantum capacitance in the closed regime, assuming $\gamma_{\rm lead}=0$ and $\gamma_{\rm relax}=1 \gg \gamma_{\rm qpp} =0.001$, and $k_BT_{\rm qpp}=2$. Other parameters: $t_{\rm sc}=0.3, t_{\rm sf}=0.1$.
• Figure 3: (a) Averaged quantum capacitance of a single quantum dot coupled to Andreev bound states in the $(\mu_1, \mu_A)$ plane. (b) Energy difference in the $(\mu_1, \mu_A)$ plane. (c) Solid blue curve: numerically calculated $\expval{C_q}$ as a function of $\mu_1$ for $\mu_A=0.5$. Dashed lines: analytically derived $C_{q,eg}$ and $C_{q,og}$ in Eqs. \ref{['eq:Cq_DA_even']} and \ref{['eq:Cq_DA_odd']}. Note that curves of $C_{q,eg}$ and $C_{q,og}$ are multiplied by a constant which is given by $P_{eg}(\mu_1=-E_A) = P_{og}(\mu_1=E_A) \approx 0.282$. (d) State population of $\ket{eg}$ and $\ket{og}$ as a function of $\mu_1$ for $\mu_A=0.5$. Parameters: $t_{\rm sc}=0.1, t_{\rm sf}=0.03, \gamma_{\rm lead} =0.003, k_BT_{\rm lead}=0.005, \gamma_{\rm qpp}=0.003, k_BT_{\rm qpp}=2, \gamma_{\rm relax}=1$.
• Figure 4: (a) $\langle C_q \rangle$ of a single quantum dot coupled to Andreev bound states in the $(\mu_1, eV)$ plane for $\mu_A=0.5$. (b) Cutlines of $\langle C_q \rangle$ for $\mu_1 = \pm E_A \approx \pm 1.12$. (c) State population as a function of voltage bias. (d) Switching rate of $\ket{eg}$ and $\ket{og}$ as a function of voltage bias. Solid dots in panels (b), (c), and (d) are based on the analytical results obtained in Eqs. \ref{['eq:Gamma_og']}-\ref{['eq:Cq_analytic_Vneg']} Parameters: $t_{\rm sc}=0.1, t_{\rm sf}=0.03, \gamma_{\rm lead} =0.003, k_BT_{\rm lead}=0.005, \gamma_{\rm qpp}=0.003, k_BT_{\rm qpp}=2, \gamma_{\rm relax}=1$.