Colloquium: Majorana Fermions in nuclear, particle and solid-state physics

Abstract

Ettore Majorana (1906-1938) disappeared while traveling by ship from Palermo to Naples in 1938. His fate has never been fully resolved and several articles have been written that explore the mystery itself. His demise intrigues us still today because of his seminal work, published the previous year, that established symmetric solutions to the Dirac equation that describe a fermionic particle that is its own anti-particle. This work has long had a significant impact in neutrino physics, where this fundamental question regarding the particle remains unanswered. But the formalism he developed has found many uses as there are now a number of candidate spin-1/2 neutral particles that may be truly neutral with no quantum number to distinguish them from their anti-particles. If such particles exist, they will influence many areas of nuclear and particle physics. Most notably the process of neutrinoless double beta decay can only exist if neutrinos are massive Majorana particles. Hence, many efforts to search for this process are underway. Majorana's influence doesn't stop with particle physics, however, even though that was his original consideration. The equations he derived also arise in solid state physics where they describe electronic states in materials with superconducting order. Of special interest here is the class of solutions of the Majorana equation in one and two spatial dimensions at exactly zero energy. These Majorana zero modes are endowed with some remarkable physical properties that may lead to advances in quantum computing and, in fact, there is evidence that they have been experimentally observed. This review first summarizes the basics of Majorana's theory and its implications. It then provides an overview of the rich experimental programs trying to find a fermion that is its own anti-particle in nuclear, particle, and solid state physics.

Invited review for Reviews of Modern Physics; v2: shortened and reorganized version to appear in RMP, 28 pages 12 figures. This version emphasizes the distinction between the generic Majorana fermions in particle physics and Majorana zero modes discussed in condensed matter physics

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• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Leptogenesis
• Double Beta Decay, Majorana Neutrinos, and Neutrino Mass
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• Limit on Neutrinoless ββ Decay of Xe-136 from the First Phase of KamLAND-Zen and Comparison with the Positive Claim in Ge-76
• The Large Underground Xenon (LUX) Experiment
• Chiral P-Wave Order in Sr_2RuO_4
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• Precise half-life values for two neutrino double beta decay
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• An introduction to leptogenesis and neutrino properties
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• Experimental study of double beta decay modes using a CdZnTe detector array
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Cited by in corpus (78)

• Topological Photonics
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• High-temperature topological superconductivity in twisted double layer copper oxides
• On the Remarkable Superconductivity of FeSe and its Close Cousins
• Probing topological quantum matter with scanning tunnelling microscopy
• Majorana corner modes and tunable patterns in an altermagnet heterostructure
• Majorana-like zero modes in Kekulé distorted sonic lattices
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• Strongly interacting Majorana fermions
• Electron temperature and tunnel coupling dependence of zero-bias and almost-zero-bias conductance peaks in Majorana nanowires
• Assembling Fibonacci Anyons From a ${\mathbb{Z}}_3$ Parafermion Lattice Model
• Finite-size effects in non-Hermitian topological systems
• Majorana Fermions in Magnetic Chains
• Tunable magnetic textures in spin valves: From spintronics to Majorana bound states
• Topologically protected localised states in spin chains
• Topological superconductivity in planar Josephson junctions: Narrowing down to the nanowire limit
• Parity-to-charge conversion in Majorana qubit readout
• Detecting topological superconductivity using low-frequency doubled Shapiro steps
• Characterization of topological phases of modified dimerized Kitaev chain via edge correlation functions
• Exact solution to an interacting dimerized Kitaev model at symmetric point
• Exact solutions and topological phase diagram in interacting dimerized Kitaev topological superconductors
• Topological superconductivity and Majorana states in low-dimensional systems
• Robustness of Majorana bound states in the short junction limit
• Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires
• Full proximity treatment of topological superconductors in Josephson-junction architectures
• Topological features of ground states and topological solitons in generalized Su-Schrieffer-Heeger models using generalized time-reversal, particle-hole, and chiral symmetries
• Aspects of topological superconductivity in 2D systems: noncollinear magnetism, skyrmions, and higher-order topology
• Spin-resolved interference due to Majorana state on interface between normal and superconducting leads
• Rearrangement of valence neutrons in the neutrinoless double-$\beta$ decay of ${}^{136}$Xe
• Phenomenology of soft gap, zero bias peak, and zero mode splitting in ideal Majorana nanowires
• Conductance spectroscopy of nontopological-topological superconductor junctions
• Majorana quasiparticles of inhomogeneous Rashba chain
• Weyl-Majorana solenoid
• Numerical calculation of the complex berry phase in non-Hermitian systems
• Emergent vortex Majorana zero mode in iron-based superconductors
• Fingerprints of Majorana fermions in current-correlations measurements from a superconducting tunnel microscope
• Electrically tunable chiral Majorana edge modes in quantum anomalous Hall insulator-topological superconductor systems
• Topological phases and Anderson localization in off-diagonal mosaic lattices
• Dynamics of hybrid junctions of Majorana wires
• Absence of supercurrent sign reversal in a topological junction with a quantum dot
• Multiple topological transitions driven by the interplay of normal scattering and Andreev scattering
• Effect of chiral symmetry on chaotic scattering from Majorana zero modes
• Tuning ferromagnetic BaFe${}_2$(PO${}_4$)${}_2$ through a high Chern number topological phase
• Quantum spin Hall effect in rutile-based oxide multilayers
• High-temperature Majorana corner modes in a $d+i{d}^{\prime }$ superconductor heterostructure: Application to twisted bilayer cuprate superconductors
• Piezo-driven sample rotation system with ultra-low electron temperature
• Chiral $p$-wave superconductivity in a twisted array of proximitized quantum wires
• Majorana bound states in vortex lattices on iron-based superconductors
• Incarnation of Majorana Fermions in Kitaev Quantum Spin Lattice
• Evidence of decoupling of surface and bulk states in Dirac semimetal $C{d}_{3}A{s}_2$
• Probing Majorana bound states through an inhomogeneous Andreev double dot interferometer
• Majorana phi0 Junction in a Disordered Spin-orbit Coupling Nanowire with Tilted Magnetic Field
• Observation of the Critical State to Multiple-Type Dirac Semimetal Phases in KMgBi
• Generic theory of characterizing topological phases under quantum slow dynamics
• Rigidity of topological invariants to symmetry breakings
• Topological metals constructed by sliding quantum wire arrays
• Majorana zero mode-soliton duality and in-gap and BIC bound states in modified Toda model coupled to fermion
• Impurity-induced subgap states in superconductors with inhomogeneous pairing
• Effect of charge renormalization on electric and thermo-electric transport along the vortex lattice of a Weyl superconductor
• Critical Current Anomaly at the Topological Quantum Phase Transition in a Majorana Josephson Junction
• Interacting Majorana modes at surfaces of noncentrosymmetric superconductors
• Dynamics of a Majorana trijunction in a microwave cavity
• 4$\pi$ and 8$\pi$ dual Josephson effects induced by symmetry defects
• Spin-flavor oscillations of Dirac neutrinos in matter under the influence of a plane electromagnetic wave
• Magnetic impurities on superconducting Pb surfaces
• Interaction effects in superconductor/quantum spin Hall devices: universal transport signatures and fractional Coulomb blockade
• Many-body Majorana-like zero modes without gauge symmetry breaking
• Polynomial description of inhomogeneous topological superconducting wires
• Robust topological state against magnetic impurities observed in superconductor PbTaSe2
• Hall Effect for Dirac Electrons in Graphene Exposed to an Abrikosov Flux Lattice
• Effects of Majorana bound states on dissipation and charging in a quantum resistor-capacitor circuit
• Revealing inverted chirality of hidden domain wall states in multiband systems without topological transition
• Two-dimensional hourglass Weyl nodal loop in monolayer Pb(ClO${}_2$)${}_2$ and Sr(ClO${}_2$)${}_2$
• Vector currents of integer-spin Majorana particles
• Universal Broadening of Zero Modes: A General Framework and Identification
• Majorana flat bands at structured surfaces of nodal noncentrosymmetric superconductors
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal
• Possible topological phases in quantum anomalous Hall insulator/unconventional superconductor hybrid systems