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

Abstract

Majorana modes emerge in non-trivial topological phases at the edges of specific materials such as proximitized semiconducting nanowires under an external magnetic field. Ideally, they are non-local states that are charge-neutral superpositions of electrons and holes. However, in nanowires of realistic length their wave functions overlap and acquire a finite charge that makes them susceptible to interactions, specifically with the image charges that arise in the electrostatic environment. Considering a realistic three-dimensional model of the dielectric surroundings, here we show that, under certain circumstances, these interactions lead to a suppression of the Majorana oscillations predicted by simpler theoretical models, and to the formation of low-energy quantum-dot states that interact with the Majorana modes. Both features are observed in recent experiments on the detection of Majoranas and could thus help to properly characterize them.

Effects of the electrostatic environment on superlattice Majorana nanowires

“…This is not the case for the superlattices since their wave functions decay more slowly. To quantify this, we finally compute the absolute value of the Majorana charge Q M that measures the wave function overlap between the right and the left Majoranas 30,45,46…”

“…However, in the last couple of years it has been shown that the electrostatic environment and the three-dimensionality of these wires play an important role in all aspects concern-ing the trivial/topological phases and the appearance of MBSs. For instance, the electrostatic profile is not homogeneous along (and across) the wire, which creates a position-dependent chemical potential 23,24,26,[41][42][43] that has consequences for the topological phase transition and the shape and the overlap of MBSs [44][45][46][47] . It also creates a position-dependent Rashba spin-orbit coupling [48][49][50] .…”

Quantifying wave-function overlaps in inhomogeneous Majorana nanowires

“…This may trap discrete states around x = 0 in an effective quantum dot-superconductor configuration. Additionally, screening effects in the nanowire may produce, in a mean-field approximation, a quantum dot-superconductor profile spontaneously [38,70] that can also trap states. To gain insight into these cases we simulate nanowires with short, normal dot regions abruptly connected to the nanowire (ζ = 0) without an additional intervening barrier, so the confinement is merely the result of the potential and pairing mismatch at L N .…”

Unified numerical approach to topological semiconductor-superconductor heterostructures

“…The simultaneous treatment of these ingredients was not achieved in previous numerical works to date [23][24][25][28][29][30][31][32][33], which relied on effective phenomenological models neglecting the treatment of electrostatics and/or assuming the weak tunneling limit at the semiconductor-superconductor interface. Several recent works developed Schrödinger-Poisson calculations for proximitized nanowires [26,27,[34][35][36][37], crucial for understanding electrostatics and gating effects, but they similarly neglected some of the other key ingredients listed above (most notably, the orbital effect of the magnetic field). The present approach builds on the recently improved treatment of electrostatic effects in the strong tunneling limit [26,27], incorporating the orbital effect of the magnetic field [31,38] as well as the dependence of the spin-orbit coupling on the external electric field.…”