AI 中文总结
该研究针对仅靠量子电容无法识别拓扑超导电性的问题，计算了不同纳米线干涉仪的宇称分辨量子电容和逆量子电感，发现类马约拉纳特征非拓扑专属，而双近零能安德烈夫态的$h/(2e)$周期分量为非马约拉纳的明确特征。
AI 中文摘要
量子电容测量可将通量穿线纳米线回路中量子点能量的曲率转换为快速的宇称敏感信号，因此已成为马约拉纳器件的一种有前景的读出工具。然而，类马约拉纳的量子电容响应也可源于拓扑平庸的安德烈夫束缚态，仅靠电容不足以识别拓扑相。为分析该问题，我们考虑一个量子点耦合到四种纳米线结构的两端：包含马约拉纳束缚态的拓扑纳米线、包含1个或2个安德烈夫束缚态的非拓扑超导纳米线，以及完全正常的纳米线。受将量子电感用作额外相位敏感探针的提议启发，我们通过精确对角化计算了宇称分辨量子电容$C_\text{Q}$和逆量子电感$L_\text{Q}^{-1}$随磁通量的变化。我们表明，与零能马约拉纳束缚态相关的特征，如$h/e$周期性以及$C_\text{Q}$和$L_\text{Q}^{-1}$中偶宇称与奇宇称扇区之间的$h/(2e)$通量偏移，不足以作为拓扑超导电性的指标。在某些现实参数范围内，类似马约拉纳的行为可源于平庸安德烈夫束缚态，甚至纯正常纳米线。相比之下，两个近零能安德烈夫束缚态可产生与电荷$2e$转移相关的显著$h/(2e)$周期分量，提供了清晰的非马约拉纳特征。低能投影显示，马约拉纳、单安德烈夫态和正常情况可映射到同一最小低能模型，解释了它们尽管物理起源不同却具有相似通量相关响应的原因。
英文摘要
Quantum-capacitance measurements convert the curvature of a quantum-dot energy in a flux-threaded nanowire loop into fast parity-sensitive signals and, therefore, have become a promising readout tool for Majorana devices. However, Majorana-like quantum-capacitance responses can also arise from topologically trivial Andreev bound states, making capacitance alone insufficient to identify a topological phase. To analyze this problem, we consider a quantum dot coupled to both ends of four nanowire realizations: a topological nanowire hosting Majorana bound states, non-topological superconducting nanowires hosting one or two Andreev bound states, and a fully normal nanowire. Motivated by proposals to use quantum inductance as an additional phase-sensitive probe, we compute both the parity-resolved quantum capacitance $C_\mathrm{Q}$ and inverse quantum inductance $L_\mathrm{Q}^{-1}$ as functions of the magnetic flux by exact diagonalization. We show that signatures associated with zero-energy Majorana bound states, such as $h/e$ periodicity and an $h/(2e)$ flux shift between even and odd parity sectors in $C_\mathrm{Q}$ and $L_\mathrm{Q}^{-1}$, are not sufficient indicators of topological superconductivity. In certain realistic parameter regimes, similar Majorana-like behavior can arise from a trivial Andreev bound state and even from a purely normal nanowire. By contrast, two nearly zero-energy Andreev bound states can generate a pronounced $h/(2 e)$-periodic component associated with charge-$2e$ transfer, providing a clear non-Majorana signature. A low-energy projection shows that the Majorana, single-Andreev-state, and normal cases can be mapped onto the same minimal low-energy model explaining their similar flux-dependent responses despite their different physical origins.
