Current Cross-Correlation Spectroscopy of Majorana Bound States

Abstract

The clock speed of topological quantum computers based on Majorana zero mode (MZM)-supporting nanoscale devices is determined by the time taken for electrons to traverse the device. We employ the time-dependent Landauer-B{ü}ttiker transport theory for current cross-lead correlations in a superconducting nanowire junction hosting MZMs. From the time-dependent quantum noise, we are able to extract traversal times for electrons crossing the system. After demonstrating a linear scaling of traversal times with nanowire length, we present a heuristic formula for the traversal times which accurately captures their behaviour. We then connect our framework to a proposed experimental verification of this discriminant between spurious and genuine MZMs utilizing time-resolved transport measurements.

Figures (3)

• Figure 1: (a) The superconducting nanowire in the presence of an external magnetic field and coupled to normal metal leads, $L$ and $R$. The black and red lines denote schematically the exponentially localized probability density of the Majorana zero mode. (b) Schematic procedure of extracting the traversal time from the distance of current cross-correlation peaks.
• Figure 2: Stationary current cross-correlation versus relative time shifts $\tau$ for superconducting nanowires of length $N=50$ sites. The nanowire is in the ordinary superconducting phase with no zero modes in panel (a) and it hosts in-gap states at zero energy for panels (b-d). Only the panel (b) hosts the topological Majorana zero mode while panels (c) and (d) host topologically trivial in-gap states. Coupling to the normal-metal leads is specified by the tunneling rate $\Gamma=0.01$, and the temperature is set by $\beta=200$.
• Figure 3: Extracted traversal times in terms of the nanowire length $L$. Simple linear fits (dashed lines) are performed as $\tau_{\mathrm{tr}}=\tau_{\mathrm{cont}}+L/v$, where $\tau_{\mathrm{cont}}$ and $1/v$ are obtained as the intercept and slope, respectively. For the Majorana zero mode, a fit with Eq. \ref{['eq:heuristic']} is also included (solid black line) with the parameters $\delta=1.402$ and $z=4$. Other model parameters are $\Gamma=0.01$ and $\beta=200$.