Two-terminal charge tunneling: Disentangling Majorana zero modes from partially separated Andreev bound states in semiconductor-superconductor heterostructures

Abstract

We show that a pair of overlapping Majorana bound states (MBSs) forming a partially-separated Andreev bound state (ps-ABS) represents a generic low-energy feature in spin-orbit coupled semiconductor-superconductor (SM-SC) hybrid nanowire in the presence of a Zeeman field. In a finite nanowire the ps-ABS interpolates continuously between the "garden variety" ABS, which consists of two MBSs sitting on top of each other, and the topologically protected Majorana zero modes (MZMs), which are separated by a distance given by the length of the wire. The really problematic ps-ABSs consist of component MBSs separated by a distance of the order of the characteristic Majorana decay length ξ, and have nearly zero energy in a significant range of control parameters, such as the Zeeman field and chemical potential, within the topologically trivial phase. Despite being topologically trivial, such ps-ABSs can generate signatures identical to MZMs in local charge tunneling experiments. In particular, the height of the zero bias conductance peak (ZBCP) generated by ps-ABSs has the quantized value, 2e 2 /h, and it can remain unchanged in an extended range of experimental parameters, such as Zeeman field and the tunnel barrier height. We illustrate the formation of such low-energy robust ps-ABSs in two experimentally relevant situations: a hybrid SM-SC system consisting of a proximitized nanowire coupled to a quantum dot and the SM-SC system in the presence of a spatially varying inhomogeneous potential. We then show that, unlike local measurements, a two-terminal experiment involving charge tunneling at both ends of the wire is capable of distinguishing between the generic ps-ABSs and the non-Abelian MZMs. While the MZMs localized at the opposite ends of the wire generate correlated differential conduction spectra, including correlations in energy splittings and critical Zeeman fields associated with the emergence of the ZBCPs, such correlations are absent if the ZBCPs are due to ps-ABSs emerging in the topologically trivial phase. Measuring such correlations is the clearest and most straightforward test of topological MZMs in SM-SC heterostructures that can be done in a currently accessible experimental set-up.arXiv:1711.06256v2 [cond-mat.mes-hall]

Interaction-induced zero-energy pinning and quantum dot formation in Majorana nanowires

“…The Majorana overlap, which is a measurement of the degree of non-locality of the two Majorana wave functions, mostly depends on the length of the nanowire (and to a lesser extent on other parameters, such as the induced superconductor gap and the Rashba coupling), but it is not necessarily correlated to the Majorana energy splitting. Different mechanisms can reduce this splitting, such as interactions with the environment as studied here, smooth potential or gap profiles [21,26–28 30], or orbital magnetic effects [31], and still leave the Majorana overlap unaffected. The behavior of the Majorana wave functions in this case is illustrated in Fig.…”

“…Conspicuously, in most of the available experimental data the emergence of a robust zero-bias conductance peak is observed above some critical Zeeman field without the expected oscillatory pattern [12,19,24–25]. Several mechanisms have been proposed to account for the reduction or lack of oscillations, such as smooth confinement [21,26–28], strong spin–orbit coupling [29], position-dependent pairing [30], orbital magnetic effects [31], Coulomb repulsion among the carriers in the nanowire [22], or the presence of the normal drain lead connected to the hybrid wire [32]. …”

Subband occupation in semiconductor-superconductor nanowires

“…Such low-energy ABSs can be produced by several sources, including soft confinement 24,25 , inhomogeneous superconducting pairing 26 , disorder [27][28][29][30] , accidental quantum dots 31,32 , and inter-subband coupling 33 . This is especially concerning in the case of trivial low-energy states that mimic very faithfully the local phenomenology of Majorana zero modes, the so-called quasi-Majorana 34 , or partially-separated ABS states 35 .…”

Dynamic Majorana resonances and universal symmetry of nonequilibrium thermoelectric quantum noise

“…The overlap of MZMs is achieved via increasing ξ. Note that our model with large values of ξ may also be interpreted as the one where the QD is coupled to a partially separated Andreev bound state [35] localized near the corresponding end of the TS (see also Ref. [36]).…”