Topologically trivial zero-bias conductance peak in semiconductor Majorana wires from boundary effects

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Topologically trivial zero-bias conductance peak in semiconductor Majorana wires from boundary effects

Dibyendu Roy, Nilanjan Bondyopadhaya, and Sumanta Tewari

Phys. Rev. B 88, 020502(R) – Published 8 July 2013

Abstract

We show that a topologically trivial zero-bias conductance peak is produced in semiconductor-superconductor hybrid structures due to a suppressed superconducting pair potential and/or an excess Zeeman field at the ends of the heterostructure, both of which can occur in experiments. The zero-bias peak (ZBP) (a) appears above a threshold parallel bulk Zeeman field, (b) is stable for a range of bulk field before splitting, (c) disappears with rotation of the bulk Zeeman field, and (d) is robust to weak disorder fluctuations. The topologically trivial ZBPs are also expected to produce splitting oscillations with the applied field similar to those from Majorana fermions. Because of such strong similarity with the phenomenology expected from Majorana fermions, we find that the only unambiguous way to distinguish these trivial ZBPs (of height $4 e^{2} / h$ ) from those arising from Majorana fermions (of height $2 e^{2} / h$ ) is by comparing the (zero-temperature) peak height and/or through an interference experiment.

Received 24 March 2013

DOI:https://doi.org/10.1103/PhysRevB.88.020502

Authors & Affiliations

Dibyendu Roy¹, Nilanjan Bondyopadhaya², and Sumanta Tewari³

¹Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
²Integrated Science Education and Research Centre, Visva-Bharati University, Santiniketan, WB 731235, India
³Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29634, USA

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Issue

Vol. 88, Iss. 2 — 1 July 2013

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Images

Figure 1
Zero-temperature differential conductance $d I / d V$ vs the applied voltage $V$ for different numbers of transverse chains $W$ for $μ = 0$ . Everywhere, $B_{x} = 0.8$ , $B_{y} = B_{z} = 0.0$ , and $| Δ | = 0.6$ , so $B_{x} > B_{x, c} = | Δ |$ . The number of chains $W$ in the panels is as follows: (a) $W = 1$ , (b) $W = 2$ , (c) $W = 3$ , and (d) $W = 4$ . Since $μ = 0$ in Eqs. (1) (with periodic boundary conditions) corresponds to an equal number of subbands below and above $E = μ$ , only $W = 1, 3$ has a ZBP for $B_{x} > B_{x, c} = | Δ |$ . For $W = 2, 4$ , $B_{x} > | Δ |$ produces no ZBP because only an even number of subbands are occupied.Reuse & Permissions
Figure 2
Emergence of ZBP in the topologically trivial superconducting phase (even band occupancy) due to excess Zeeman field and/or reduced pair potential at the wire ends. In all the panels, $W = 2, Δ = 0.6$ , and $μ = 0$ . In panels (a), (b), and (d), $α_{R} = 0.2, B_{x} = 0.8$ . Note that for these values of $B_{x}$ and $Δ$ , there is no ZBP for $W = 2$ (even band occupancy) in the absence of a local perturbation [Fig. 1b]. The local end perturbations producing the topologically trivial ZBPs are as follows: (a) $δ B_{x} {1, m} = 0.45$ , (b) $δ μ_{↑} {1, m} = 1, δ μ_{↓} {1, m} = 0.2$ , and (d) $δ Δ {1, m} = - 0.35$ , where $m = 1, 2$ . In panel (c), we show, for illustrative purposes, the emergence of the trivial ZBP even for a larger value of the spin-orbit coupling, $α_{R} = 0.5$ and $B_{x} = 1$ . For local end perturbations, we have used $δ B_{x} {1, m} = 0.7, δ B_{x} {2, m} = 0.5$ ; that is, the end perturbation is applied on two sites and gradually disappears towards the bulk.Reuse & Permissions
Figure 3
Dependence of the topologically trivial ZBP on the uniform Zeeman field $B_{x}$ for a fixed perturbation at two end sites on all chains ( $δ B_{x} {1, m} = 0.32$ and $δ B_{x} {2, m} = 0.2$ ). All panels have $W = 2$ (two transverse chains) and $Δ = 0.6$ . The ZBP is (a) split ( $B_{x} = 0.7$ ), (b) fully developed ( $B_{x} = 0.8$ ), and (c) stays ( $B_{x} = 1.0$ ), before splitting again with larger $B_{x}$ (not shown). Panel (d) ( $B_{x} = 0.4$ , $B_{y} = 0.4$ ) shows the disappearance of the ZBP with rotation of the uniform field in the plane formed by the wire and the effective spin-orbit coupling [ $(x$ - $y)$ plane].Reuse & Permissions
Figure 4
Robustness of the topologically trivial ZBP to moderate disorder fluctuations and the role of barrier potential (tunnel coupling with the metallic lead). In all panels, $W = 2$ , $B_{x} = 0.8$ , and $μ_{↑} {1, m} = 1, μ_{↓} {1, m} = 0.2$ . (a) Randomness in $μ$ is chosen from a uniform distribution between 0 and 0.1, $γ_{p}^{'} = 0.2$ and (b) clean wire ( $μ = 0$ ), but a stronger coupling with the lead, $γ_{p}^{'} = 0.3$ ( $p = L, R$ ). These figures should be compared with that in Fig. 2b.Reuse & Permissions

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