Suppression of the overlap between Majorana fermions by orbital magnetic effects in semiconducting-superconducting nanowires

Abstract

We study both analytically and numerically the role of orbital effects caused by a magnetic field applied along the axis of a semiconducting Rashba nanowire in the topological regime hosting Majorana fermions. We demonstrate that the orbital effects can be effectively taken into account in a one-dimensional model by shifting the chemical potential, and, thus modifying the topological criterion. We focus on the energy splitting between two Majorana fermions in a finite nanowire and find a striking interplay between orbital and Zeeman effects on this splitting. In the limit of strong spin-orbit interaction, we find regimes where the amplitude of the oscillating splitting stays constant or even decays with increasing magnetic field, in stark contrast to the commonly studied case where orbital effects of the magnetic field are neglected. The period of these oscillations is found to be almost constant in many parameter regimes. arXiv:1710.01671v1 [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]. …”

Decays of Majorana or Andreev Oscillations Induced by Steplike Spin-Orbit Coupling

“…However, these behaviors are sharply opposite to the theories for the Majorana bound states [29], which predict an enhanced oscillation amplitude and period. Several theoretical studies [37][38][39] have tried to address this discrepancy, but are partially successful, e.g., assumed multiple subbands and temperatures higher than those in the experiments [37] or found that the oscillation period decreases with increasing magnetic field [38,39]. This discrepancy has raised the concerns on the conclusive identification of Majorana bound states, and has even endangered the scheme of Majorana qubits based on the nanowires [40,41].…”

“…µ(x) and α(x) denote the positiondependent chemical potential and spin-orbit coupling, respectively. Quite different from the previous theories which assume a constant spin-orbit coupling [37][38][39], we model that spin-orbit coupling has a profile [see also the green curve in Fig. 1(a)]…”

Evidence for Majorana phases in the magnetoconductance of topological junctions based on two-dimensional electron gases

“…30-36. In this planar geometry, a perpendicular magnetic field has a paramount influence on the motion of quasiparticles in the plane; the scenario of the well studied quantum Hall effect. In our context of hybrid semiconductor-superconductor systems, the relevance of the magneto-orbital effect for the characterization of topological phases has been studied in different geometries; cylinders, [37,38] faceted wires [27,28] and 2D strips or ribbons [39][40][41]. In 2D strips it is generally assumed that a perpendicular field is detrimental for the Majorana modes and a parallel field is more often consid-ered where the magnetic effect is restricted to a Zeeman coupling with the quasiparticle spin.…”