Theory of Majorana zero modes in unconventional superconductors

Abstract

Majorana fermions are spin-1/2 neutral particles that are their own antiparticles and were initially predicted by Ettore Majorana in particle physics but their observation still remains elusive. The concept of Majorana fermions has been borrowed into condensed matter physics, where, unlike particle physics, Majorana fermions emerge as zero-energy quasiparticles that can be engineered by combining electrons and holes and have therefore been coined Majorana zero modes. In this review, we provide a pedagogical explanation of the basic properties of Majorana zero modes in unconventional superconductors and their consequences in experimental observables, putting a special emphasis on the initial theoretical discoveries. In particular, we first show that Majorana zero modes are self-conjugated and emerge as a special type of zero energy surface Andreev bound states at the boundary of unconventional superconductors. We then explore Majorana zero modes in one-dimensional spin-polarized $p$-wave superconductors, where we address the formation of topological superconductivity and the physical realization in superconductor-semiconductor hybrids. In this part we highlight that Majorana quasiparticles appear as zero-energy edge states, exhibiting charge neutrality, spin-polarized, and spatial nonlocality as unique properties that can be already seen from their energies and wavefunctions. Next, we discuss analytically obtained Green's functions of $p$-wave superconductors and demonstrate that the emergence of Majorana zero modes is always accompanied by the formation of odd-frequency spin-triplet pairing as a unique result of the self-conjugate nature of Majorana zero modes. We finally address the signatures of Majorana zero modes in tunneling spectroscopy, including the anomalous proximity effect, and the phase-biased Josephson effect.

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Cited by in corpus (64)

• Superconducting phenomena in systems with unconventional magnets
• $\phi$ Josephson junction induced by altermagnetism
• Theory of Tunneling Spectroscopy in Unconventional $p$-wave Magnet-Superconductor Hybrid Structures
• Josephson effect and odd-frequency pairing in superconducting junctions with unconventional magnets
• Classification of pair symmetries in superconductors with unconventional magnetism
• Non-Hermitian phase-biased Josephson junctions
• Orientation-dependent transport in junctions formed by $d$-wave altermagnets and $d$-wave superconductors
• Identifying trivial and Majorana zero-energy modes using the Majorana polarization
• Anomalous supercurrent and diode effect in locally perturbed topological Josephson junctions
• All-electrically controlled spintronics in altermagnetic heterostructures
• Non-Hermitian multiterminal phase-biased Josephson junctions
• Non-Hermitian zero-energy pinning of Andreev and Majorana bound states in superconductor-semiconductor systems
• Odd-Parity Quasiparticle Interference in the Superconductive Surface State of UTe2
• Entanglement measures of Majorana bound states
• Interplay between Majorana and Shiba states in a minimal Kitaev chain coupled to a superconductor
• Josephson diode effect with Andreev and Majorana bound states
• Theory of universal diode effect in three-terminal Josephson junctions
• Non-Hermitian minimal Kitaev chains
• Floquet engineering spin triplet states in unconventional magnets
• Emergent pair symmetries in systems with poor man's Majorana modes
• Surface density of states and tunneling spectroscopy of a spin-3/2 superconductor with Bogoliubov Fermi Surfaces
• Topological indicators for systems with open boundaries: Application to the Kitaev wire
• Odd-frequency superconducting pairing due to multiple Majorana edge modes in driven topological superconductors
• Tunneling conductance in superconducting junctions with $p$-wave unconventional magnets breaking time-reversal symmetry
• Majorana zero-modes in a dissipative Rashba nanowire
• Odd-frequency pairing due to Majorana and trivial Andreev bound states
• Anisotropic paramagnetic response of topological Majorana surface states in the superconductor ${\text{UTe}}_2$
• Light-induced Floquet spin-triplet Cooper pairs in unconventional magnets
• Disorder effects in planar semiconductor-superconductor structures: Majorana wires versus Josephson junctions
• Single and multi-frequency driving protocols in a Rashba nanowire proximitized to an s-wave superconductor
• Anomalous proximity effect under Andreev and Majorana bound states
• Majorana modes in striped two-dimensional inhomogeneous topological superconductors
• Quantized Andreev conductance in semiconductor nanowires
• Predicting topological invariants and unconventional superconducting pairing from density of states and machine learning
• Spirals, vortices, and helicity entanglements in dynamical Sauter-Schwinger pair creation
• Engineering subgap states in superconductors by the symmetry of altermagnetism
• Topological phase transitions in superconductors with chiral symmetry
• Nonlocal Josephson diode effect in minimal Kitaev chains
• Fragmentation, Zero Modes, and Collective Bound States in Constrained Models
• Non-Hermitian Josephson junctions with four Majorana zero modes
• Side-gate modulation of supercurrent in InSb nanoflag-based Josephson junctions
• Dissipationless topological quantum computation for Majorana objects in sparse-dense mixed encoding process
• Characterizing local Majorana properties using Andreev states
• Thermoelectric fluctuations of interfering Majorana bound states
• Majorana polarization in disordered heterostructures
• Vertex correction for the linear and nonlinear optical responses in superconductors: multiband effect and topological superconductivity
• Quantifying the non-Abelian property of Andreev bound states in inhomogeneous Majorana nanowires
• Optical conductivity of the Majorana mode at the s- and d-wave topological superconductor edge
• Topological zero modes and bounded modes at smooth domain walls: Exact solutions and dualities
• Odd-frequency pairing of Bogoliubov quasiparticles in superconductor junction
• The Josephson effect in Fibonacci superconductors
• Diamagnetic Meissner response of odd-frequency superconducting pairing from quantum geometry
• Visualizing the Odd-parity Superconducting Order Parameter and its Quasiparticle Surface Band in UTe2
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• Fractional spin Josephson effect in topological spin superconductors