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 (41)

• Superconducting phenomena in systems with unconventional magnets
• Josephson effect and odd-frequency pairing in superconducting junctions with unconventional magnets
• Classification of pair symmetries in superconductors with unconventional magnetism
• Orientation-dependent transport in junctions formed by $d$-wave altermagnets and $d$-wave superconductors
• All-electrically controlled spintronics in altermagnetic heterostructures
• Odd-Parity Quasiparticle Interference in the Superconductive Surface State of UTe2
• Josephson diode effect with Andreev and Majorana bound states
• Floquet engineering spin triplet states in unconventional magnets
• Topological indicators for systems with open boundaries: Application to the Kitaev wire
• Odd-frequency pairing due to Majorana and trivial Andreev bound states
• Light-induced Floquet spin-triplet Cooper pairs in unconventional magnets
• Tunneling conductance in superconducting junctions with $p$-wave unconventional magnets breaking time-reversal symmetry
• Anomalous proximity effect under Andreev and Majorana bound states
• Spirals, vortices, and helicity entanglements in dynamical Sauter-Schwinger pair creation
• Non-Hermitian Josephson junctions with four Majorana zero modes
• Nonlocal Josephson diode effect in minimal Kitaev chains
• Topological phase transitions in superconductors with chiral symmetry
• Engineering subgap states in superconductors by the symmetry of altermagnetism
• Fragmentation, Zero Modes, and Collective Bound States in Constrained Models
• 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
• 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
• The Josephson effect in Fibonacci superconductors
• Many-body wave function and edge magnetization of an open $p+is$ superconducting chain
• Majorana modes in graphene strips: polarization, wavefunctions, disorder, and Andreev states
• Fractional spin Josephson effect in topological spin superconductors
• Adiabatic preparation of a number-conserving atomic Majorana phase
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