双量子点结构中Majorana费米子的噪声特性

Shot noise characteristics of Majorana fermions in transport through double quantum dots

Majorana费米子是其自身的反粒子,在拓扑量子计算中有着重要的应用.利用粒子数表象下的量子主方程方法,研究双量子点与Majorana费米子混合结构的电子输运特性,特别是散粒噪声.有无Majorana费米子耦合的电流与散粒噪声存在明显差别:有Majorana费米子耦合时稳态电流差呈反对称,噪声谱呈现相干振荡并且低频噪声显著增强.量子点与Majorana费米子对称弱耦合时,零频噪声由"峰"变为"谷",并且"边谷"展宽逐渐减小;当对称强耦合时,零频噪声的谷深增加,"边谷"向高频端移动.改变系统与电极的耦合强度时,零频噪声由谷变成峰.因此,稳态电流结合散粒噪声可以探测双量子点结构中Majorana费米子是否存在.

Majorana fermions are their own antiparticles, which play an important role in fault-tolerant topological quantum computation. Recently, the search for Majorana fermions in condensed matter physics, is attracting a great deal of attention as quasipartieles emerge. In this paper we consider a specific model consisting of double quantum dots and a tunnel-coupled semiconductor nanowire on an s-wave superconductor, since the nanowire may support Majorana fermions under appropriate conditions. We study the electron transport through the double quantum dots by using the particle-number resolved master equation. We pay particular attention to the effects of Majorana＇s dynamics on the current fluctuation （shot noise）. It is shown that the current and the shot noise measurement can be used to distinguish Majorana fermions from the usual resonant-tunneling levels. When there exist Majorana fermions coupling to the double quantum dots, a difference between the steady-state source and drain currents depends on the asymmetry of electron tunneling rates. The asymmetric behaviors of the currents can reveal the essential features of the Majorana fermion. Moreover, the dynamics of Majorana coherent oscillations between the semiconductor nanowire and the double quantum dots is revealed in the shot noise, via spectral dips together with a pronounced zero-frequency noise enhancement effect. We find, on the one hand, that the peak of the zero-frequency noise becomes a dip in the case of weak coupling between double quantum dots and the nanowire; on the other hand, for the strong coupling the dip of the zero-frequency noise becomes even further deep with ＂side dips＂ towards high frequency regimes. Furthermore, the dip of the zero-frequency noise disappears and a zero-frequency noise ＂peak＂ gradually develops when the dot-electrode coupling is tuned by gate voltage. As a result, the combination of the current and the shot noise through double quantum dots allows one to probe the presence of Majorana fermions.