Protocol to identify a topological superconducting phase in a three-terminal device

Abstract

We develop a protocol to determine the presence and extent of a topological phase with Majorana zero modes in a hybrid superconductor-semiconductor device. The protocol is based on conductance measurements in a three-terminal device with two normal leads and one superconducting lead. A radio-frequency technique acts as a proxy for the measurement of local conductance, allowing a rapid, systematic scan of the large experimental phase space of the device. Majorana zero modes cause zero bias conductance peaks at each end of the wire, so we identify promising regions of the phase space by filtering for this condition. To validate the presence of a topological phase, a subsequent measurement of the non-local conductance in these regions is used to detect a topological transition via the closing and reopening of the bulk energy gap. We define data analysis routines that allow for an automated and unbiased execution of the protocol. Our protocol is designed to screen out false positives, especially trivial Andreev bound states that mimic Majorana zero modes in local conductance. We apply the protocol to several examples of simulated data illustrating the detection of topological phases and the screening of false positives.

Theory of Berry Singularity Markers: Diagnosing Topological Phase Transitions via Lock-In Tomography

“…Recently, however, a number of theoretical proposals have appeared advocating for alternative experimental ways to infer the bulk topological properties of the system * kotetes@itp.ac.cn of interest. For instance, in connection to MZMs, it has been proposed to probe the nonlocal conductance [30][31][32][33][34][35], the shot noise [36][37][38][39][40][41], or the equilibrium spinsusceptibility [42]. The spin-orbital magnetic susceptibility has been also proposed as a bulk-topology detection means for topological insulators [43].…”

Diagnosing Topological Phase Transitions in 1D Superconductors using Berry Singularity Markers

“…Motivated by the above, a number of theoretical works have appeared recently [27][28][29][30][31][32][33][34], which investigate the role of disorder in such systems, and discuss potential approaches that may quantify the topological quality and visibility that characterizes a hybrid device. Even more, several groups have proposed protocols for evaluating the visibility of the system and the topological character of the bulk energy gap closing by investigating nonlocal responses [35][36][37][38][39]. Nonetheless, up to my knowledge, none of the above approaches has suggested to infer the topological properties of the device by identifying the topological charges of the Berry singularities which are responsible for the various topological phase transitions.…”

Cross-correlation mediated by Majorana island with finite charging energy

“…We notice that either the zero-bias-peak or the quantized conductance is based on the setup of single-lead local measurement, whereas the local measurement is insufficient to fully confirm the existence of the MZMs. Despite that the most convincing signals should be the non-Abelian statistics, the earlier further step can be the measurements based on nonlocal transport of two-lead devices, such as the measurement of nonlocal conductance matrix [26][27][28], and in particular the measurement of nonlocal cross correlation of currents [19,20,[29][30][31][32][33][34][35][36][37][38][39].…”