Majorana bound states in semiconducting nanostructures

Abstract

In this Tutorial, we give a pedagogical introduction to Majorana bound states (MBSs) arising in semiconducting nanostructures. We start by briefly reviewing the well-known Kitaev chain toy model in order to introduce some of the basic properties of MBSs before proceeding to describe more experimentally relevant platforms. Here, our focus lies on simple `minimal' models where the Majorana wave functions can be obtained explicitly by standard methods. In a first part, we review the paradigmatic model of a Rashba nanowire with strong spin-orbit interaction (SOI) placed in a magnetic field and proximitized by a conventional $s$-wave superconductor. We identify the topological phase transition separating the trivial phase from the topological phase and demonstrate how the explicit Majorana wave functions can be obtained in the limit of strong SOI. In a second part, we discuss MBSs engineered from proximitized edge states of two-dimensional (2D) topological insulators. We introduce the Jackiw-Rebbi mechanism leading to the emergence of bound states at mass domain walls and show how this mechanism can be exploited to construct MBSs. Due to their recent interest, we also include a discussion of Majorana corner states in 2D second-order topological superconductors. This Tutorial is mainly aimed at graduate students -- both theorists and experimentalists -- seeking to familiarize themselves with some of the basic concepts in the field.

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• Decaying spectral oscillations in a Majorana wire with finite coherence length
• Topological Massive Dirac Edge Modes and Long-Range Superconducting Hamiltonians
• Majorana bound states and non-local spin correlations in a quantum wire on an unconventional superconductor
• Second-order Topological Superconductors with Mixed Pairing
• Approximating the Sachdev-Ye-Kitaev model with Majorana wires
• Majorana fermion exchange in quasi-one-dimensional networks
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• In-plane Zeeman field induced Majorana corner and hinge modes in an $s$-wave superconductor heterostructure
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• Kitaev spin models from topological nanowire networks
• Identification of topological superconductivity in magnetic impurity systems using bulk spin-polarization
• Conductance feature smearing and anisotropic suppression of induced superconductivity in a Majorana nanowire
• Universal Finite-Size Scaling around Topological Quantum Phase Transitions
• Skyrmion-induced subgap states in p-wave superconductors
• Entangled end states with fractionalized spin projection in a time-reversal-invariant topological superconducting wire
• Staircase to Higher-Order Topological Phase Transitions
• Investigation of Supercurrent in the Quantum Hall Regime in Graphene Josephson Junctions
• Volkov-Pankratov states in topological superconductors
• Majorana Zero-Modes in a Two-Dimensional $p$-Wave Superconductor
• Rashba Sandwiches with Topological Superconducting Phases
• Durability of the superconducting gap in Majorana nanowires under orbital effects of a magnetic field
• Emergence of Majorana modes in cylindrical nanowires
• Majorana zero modes and their bosonization
• Influence of long-range interaction on Majorana zero modes
• Bosonization for fermions and parafermions
• Cusps near Topological Phase Transitions: Signatures of Majorana fermions and interactions with fluctuations
• All-electrical spectroscopy of topological phases in semiconductor-superconductor heterostructures

Cited by in corpus (47)

• Majorana nanowires for topological quantum computation
• Superconducting diode effect due to magnetochiral anisotropy in topological insulator and Rashba nanowires
• Theory of Majorana zero modes in unconventional superconductors
• Parity protected superconducting diode effect in topological Josephson junctions
• Trivial Andreev band mimicking topological bulk gap reopening in the non-local conductance of long Rashba nanowires
• Helical Liquids in Semiconductors
• Hole spin qubits in thin curved quantum wells
• Crossed Andreev reflection in spin-polarized chiral edge states due to the Meissner effect
• Planar Josephson junctions in germanium: Effect of cubic spin-orbit interaction
• High-fidelity two-qubit gates of hybrid superconducting-semiconducting singlet-triplet qubits
• Prevalence of trivial zero-energy sub-gap states in non-uniform helical spin chains on the surface of superconductors
• Enhanced orbital magnetic field effects in Ge hole nanowires
• Tunable planar Josephson junctions driven by time-dependent spin-orbit coupling
• Mitigating disorder-induced zero-energy states in weakly-coupled semiconductor-superconductor hybrid systems
• From perfect to imperfect poor man's Majoranas in minimal Kitaev chains
• Majorana bound states in germanium Josephson junctions via phase control
• Metallization and proximity superconductivity in topological insulator nanowires
• Accessing the degree of Majorana nonlocality in a quantum dot-optical microcavity system
• Fate of poor man's Majoranas in the long Kitaev chain limit
• Determination of spin-orbit interaction in semiconductor nanostructures via non-linear transport
• Microscopic analysis of proximity-induced superconductivity and metallization effects in superconductor-germanium hole nanowires
• Reshaping the Jaynes-Cummings ladder with Majorana bound states
• Majorana correlations in quantum impurities coupled to a topological wire
• Microwave Signatures of Topological Superconductivity in Planar Josephson Junctions
• Beyond the standard model of topological Josephson junctions: From crystalline anisotropy to finite-size and diode effects
• Single and multi-frequency driving protocols in a Rashba nanowire proximitized to an s-wave superconductor
• Signatures of enhanced spin-triplet superconductivity induced by interfacial properties
• Majorana modes in striped two-dimensional inhomogeneous topological superconductors
• RKKY interaction at helical edges of topological superconductors
• Relations between normal state nonreciprocal transport and the superconducting diode effect in the trivial and topological phases
• Spin-resolved nonlocal transport in proximitized Rashba nanowires
• Rashba spin-orbit coupling enhanced magnetoresistance in junctions with one ferromagnet
• Fractionalization of Majorana-Ising-type quasiparticles
• Spin-Exchange Induced Spillover on Poor Man's Majoranas in Minimal Kitaev Chains
• Surface step states and Majorana end states in profiled topological insulator thin films
• Perfectly localized Majorana corner modes in fermionic lattices
• Topological zero modes and bounded modes at smooth domain walls: Exact solutions and dualities
• Revisiting the Poor Man's Majoranas: The Spin-Exchange Induced Spillover Effect
• Properties and prevalence of false poor man's Majoranas in two- and three-site artificial Kitaev chains
• Zero energy modes with Gaussian, exponential, or polynomial decay: Exact solutions in hermitian and nonhermitian regimes
• Majorana bound states with chiral magnetic textures
• Rashba spin-orbit coupling and artificially engineered topological superconductors
• Electrostatic gating and the interference of chiral Majoranas in thin slabs of magnetic topological insulators
• Distinguishing Majorana bound states from accidental zero-energy modes with a microwave cavity
• Ballistic transport in 1D Rashba systems in the context of Majorana nanowires
• Giant and robust Josephson diode effect in multiband topological nanowires
• Current cross-correlation spectroscopy of Majorana bound states