Majorana零模式的电导与低压振荡散粒噪声

Low-bias oscillations of shot noise as signatures of Majorana zero modes

Majorana零能量模式是自身的反粒子,在拓扑量子计算中有重要应用.本文研究量子点与拓扑超导纳米线混合结构,通过量子点的输运电荷检测Majorana零模式.利用量子主方程方法,发现有无Majorana零模式的电流与散粒噪声存在明显差别.零模式导致稳态电流差呈反对称,在零偏压处显示反常电导峰.电流差随零模式分裂能的增大而减小,随量子点与零模式耦合的增强而增大.另一方面,零模式导致低压散粒噪声相干振荡,零频噪声显著增强.分裂能导致相干振荡愈加明显且零频噪声减小,而量子点与零模式的耦合使零频噪声增强.当量子点与电极非对称耦合时,零模式使电子由反聚束到聚束输运,亚泊松噪声增强为超泊松噪声.稳态电流差结合低压振荡的散粒噪声能够揭示Majorana零模式是否存在.

Majorana zero-energy modes are their own antiparticles, which are potential building blocks of topological quantum computing. Recently, there has been growing the interest in searching for Majorana zero modes in condensed matter physics. Semiconductor-superconductor hybrid systems have received particular attention because of easy realization and high-degree experimental control. The Majorana zero-energy modes are predicted to appear at two ends of a semiconductor nanowire, in the proximity of an s-wave superconductor and under a proper external magnetic field.Experimental signatures of Majorana zero modes in semiconductor-superconductor systems typically consist of zero-bias conductance peaks in tunneling spectra. So far it is universally received that an ideal semiconductor-superconductor hybrid structure should possess Majorana zero-energy modes. However, an unambiguous verification remains elusive because zero-bias conductance peaks can also have non-topological origins, such as Kondo effect, Andreev bound states or disorder effect. Therefore, it is important to investigate additional evidences to conclusively confirm the presence of Majorana zero modes in the hybrid solid state devices. It has been suggested that the Majorana-quantum dot hybrid system might be one of the solutions to the problem. Up to now, various Majorana-dot hybrid devices have been proposed to detect the existence of Majorana zero modes. Most of these studies mainly focused on the limits of transport at zero temperature, large bias voltage or zero frequency shot noise. Then a natural question is how the current correlations between the electrons transport through the topological nanowire, especially still in the zero-bias regime. In this paper,a specific spinless model consisting of a quantum dot tunnel-coupled to topological nanowire is considered. We present a systematic investigation of the electron transport by using a particle-number resolved master equation. We pay particular attention to the effects of Majorana＇s dynamics on the current fluctuations（shot noise） at nonzero temperature and finite bias voltage as well as at finite frequencies, especially in the low-bias regime. It is shown that the difference between the electrode currents combined with the low-bias oscillations of finite-frequency shot noise can identify Majorana zero modes from the usual resonant-tunneling levels. When there exist Majorana zero modes, on the one hand, the current difference depends on the asymmetry of electron tunneling rate. The asymmetric behaviors can expose the essential features of the Majorana zero modes since the symmetric current difference is zero. And the zero-bias conductance peak appears for the asymmetric coupling. Moreover, as the Majorana splitting energy increases, the current difference is suppressed while it is increased with the dot-wire coupling increasing. On the other hand, the dynamics of Majorana coherent oscillations between the dot and the wire is revealed in the finite-frequency shot noise. Due to the existence of Majorana zero modes the finite-frequency shot noise shows oscillations with a pronounced zero-frequency noise enhancement. Especially in the low-bias regime, the noise spectrum still exhibits an oscillation behavior which is absent from the large-bias voltage limit.Furthermore, with the Majorana splitting energy increasing, the oscillations of shot noise become more obvious, but the zero-frequency peak is lowered. When the dot is asymmetrically coupled to the electrode, the shot noise gradually changes into the super-Poissonian statistics from the sub-Poissonian statistics. This indicates the crossover from antibunched to bunched electron transport. As a result, the combination of the current difference and the low-bias oscillations of finite-frequency shot noise allows one to probe the presence of Majorana zero modes. It is therefore expected that the findings of this work can offer additional guides for experiments to identify signatures of Majorana zero modes in solid state systems.