Effective theory approach to the Schrödinger-Poisson problem in semiconductor Majorana devices

  title={Effective theory approach to the Schr{\"o}dinger-Poisson problem in semiconductor Majorana devices},
  author={Benjamin D. Woods and Tudor D Stanescu and Sankar Das Sarma},
  journal={Physical Review B},
We propose a method for solving to the Schrodinger-Poisson problem that can be efficiently implemented in realistic 3D tight-binding models of semiconductor-based Majorana devices. The method is based on two key ideas: i) For a given geometry, the Poisson problem is only solved once (for each local orbital) and the results are stored as an interaction tensor; using this Green's function scheme, the Poisson component of the iteration procedure is reduced to a few simple summations. ii) The 3D… 
Charge-Impurity Effects in Hybrid Majorana Nanowires
We address an outstanding problem that represents a critical roadblock in the development of the Majoranabased topological qubit using semiconductor-superconductor hybrid structures: the quantitative
The self-consistent quantum-electrostatic problem in strongly non-linear regime
The self-consistent quantum-electrostatic (also known as Poisson-Schrödinger) problem is notoriously difficult in situations where the density of states varies rapidly with energy. At low
Effects of the electrostatic environment on superlattice Majorana nanowires
Finding ways of creating, measuring and manipulating Majorana bound states (MBSs) in superconducting-semiconducting nanowires is a highly pursued goal in condensed matter physics. It was recently
Hybridization at Superconductor-Semiconductor Interfaces
Hybrid superconductor-semiconductor devices are currently one of the most promising platforms for realizing Majorana zero modes. Their topological properties are controlled by the band alignment of
Unified numerical approach to topological semiconductor-superconductor heterostructures
We develop a unified numerical approach for modeling semiconductor-superconductor heterostructures. All the key physical ingredients of these systems - orbital effect of magnetic field,
Majorana versus Andreev bound state energy oscillations in a 1D semiconductor-superconductor heterostructure
The recent experimental observations of decaying energy oscillations in semiconductor-superconductor Majorana nanowires is in contrast with the typical expectations based on the presence of Majorana
Conductance-matrix symmetries of multiterminal semiconductor-superconductor devices
Nonlocal tunneling spectroscopy of multiterminal semiconductor-superconductor hybrid devices is a powerful tool to investigate the Andreev bound states below the parent superconducting gap. We
Electronic structure of full-shell InAs/Al hybrid semiconductor-superconductor nanowires: Spin-orbit coupling and topological phase space
We study the electronic structure of full-shell superconductor-semiconductor nanowires, which have recently been proposed for creating Majorana zero modes, using an eight-band $\vec{k} \cdot \vec{p}$
Renormalization of the quantum dot g -factor in superconducting Rashba nanowires
We study analytically and numerically the renormalization of the g-factor in semiconducting Rashba nanowires (NWs), consisting of a normal and superconducting section. If the potential barrier
Subband occupation in semiconductor-superconductor nanowires
Subband occupancy (i.e. the number of occupied subbands or energy levels in the semiconductor) is a key physical parameter characterizing the topological properties of superconductor-semiconductor


Coulomb interaction effects on the Majorana states in quantum wires
The stability of the Majorana modes in the presence of a repulsive interaction is studied in the standard semiconductor wire-metallic superconductor configuration and the minimum Zeeman energy needed to realize Majorana fermions decreases with the increasing strength of the Coulomb repulsion.
Towards a realistic transport modeling in a superconducting nanowire with Majorana fermions
Motivated by recent experiments searching for Majorana fermions (MFs) in hybrid semiconducting-superconducting nanostructures, we consider a realistic tight-binding model and analyze its transport
Effects of the electrostatic environment on the Majorana nanowire devices
One of the promising platforms for creating Majorana bound states is a hybrid nanostructure consisting of a semiconducting nanowire covered by a superconductor. We analyze the previously disregarded
Observation of the fractional ac Josephson effect: the signature of Majorana particles
Topological superconductors which support Majorana fermions are thought to be realized in one-dimensional semiconducting wires coupled to a superconductor [1–3]. Such excitations are expected to
Fermionic and Majorana bound states in hybrid nanowires with non-uniform spin-orbit interaction
We study intragap bound states in the topological phase of a Rashba nanowire in the presence of a magnetic field and with non-uniform spin orbit interaction (SOI) and proximity-induced
Zero-energy pinning from interactions in Majorana nanowires
Majorana zero modes at the boundaries of topological superconductors are charge-neutral, an equal superposition of electrons and holes. This ideal situation is, however, hard to achieve in physical
Majorana fermions in semiconductor nanowires: fundamentals, modeling, and experiment
  • T. Stanescu, S. Tewari
  • Physics
    Journal of physics. Condensed matter : an Institute of Physics journal
  • 2013
This review provides an update on the current status of the search for Majorana fermions in semiconductor nanowires by focusing on the recent developments, in particular the period following the first reports of experimental signatures consistent with the realization of Majorana bound states in semiconducting nanowire-superconductor hybrid structures.
Quantized Majorana conductance
The observation of a quantized conductance plateau at 2e2/h in the zero-bias conductance measured in indium antimonide semiconductor nanowires covered with an aluminium superconducting shell strongly supports the existence of Majorana zero-modes in the system.
Proximity effect at the superconductor–topological insulator interface
We study the excitation spectrum of a topological insulator in contact with an s-wave superconductor, starting from a microscopic model, and develop an effective low-energy model for the proximity
Two-Dimensional Platform for Networks of Majorana Bound States.
It is demonstrated that topological superconducting channels are formed when stripes of the superconductor layer are removed and, as a consequence, Majorana bound states (MBSs) are created at the ends of the stripes.