Random-matrix theory of Majorana fermions and topological superconductors


I. Introduction (What is new in RMT, Superconducting quasiparticles, Experimental platforms) II. Topological superconductivity (Kitaev chain, Majorana operators, Majorana zero-modes, Phase transition beyond mean-field) III. Fundamental symmetries (Particle-hole symmetry, Majorana representation, Time-reversal and chiral symmetry) IV. Hamiltonian ensembles (The ten-fold way, Midgap spectral peak, Energy level repulsion) V. Scattering matrix ensembles (Fundamental symmetries, Chaotic scattering, Circular ensembles, Topological quantum numbers) VI. Electrical conduction (Majorana nanowire, Counting Majorana zero-modes, Conductance distribution, Weak antilocalization, Andreev resonances, Shot noise of Majorana edge modes) VII. Thermal conduction (Topological phase transitions, Super-universality, Heat transport by Majorana edge modes, Thermopower and time-delay matrix, Andreev billiard with chiral symmetry) VIII. Josephson junctions (Fermion parity switches, 4{\pi}-periodic Josephson effect, Discrete vortices) IX. ConclusionComment: V1: 18 pages, 16 figures; pre-submission version, for feedback; V2: 33 pages, 31 figures; greatly expanded in response to feedback, thank you!; V3: minor corrections, version to be published in Reviews of Modern Physic

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