Topological superconductivity and Majorana states in low-dimensional systems

Abstract

We discuss the properties of topologically nontrivial superconducting phases and the conditions for their realization in condensed matter, and the principles for identifying Majorana bound states (MBSs). Along with the well-known Kitaev chain and superconducting nanowire (SW) models with spin-orbit coupling in an external magnetic field, we discuss models of quasi-2D materials in which MBSs are realized in the presence of noncollinear spin ordering. For finite-length SWs, we demonstrate a cascade of quantum transitions occurring with a change in the magnetic field, accompanied by a change in the fermion parity of the ground state. The corresponding anomalous behavior of the magnetocaloric effect can be used as a tool for identifying MBSs. We devote considerable attention to the analysis of the transport characteristics of devices that contain topologically nontrivial materials. The results of studying the conductance of an Aharonov-Bohm ring whose arms are connected by an SW are discussed in detail. An important feature of this device is the appearance of Fano resonances in the dependence of conductance on the magnetic field when the SW is in a topologically nontrivial phase. We establish a relation between the characteristics of such resonances and the spatial structure of the lowest-energy SW state. The conditions for the occurrence of an MBS in the phase of the coexistence of chiral $d+id$ superconductivity and 120-degree spin ordering are determined in the framework of the $t-J-V$ model on a triangular lattice. We take electron-electron interactions into account in discussing the topological invariants of low-dimensional superconducting materials with noncollinear spin ordering. The formation of Majorana modes in regions with an odd value of a topological $\mathbb{Z}$ invariant is demonstrated. The spatial structure of these excitations in the Hubbard fermion ensemble is determined.

114 pages, 31 figures

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Cited by in corpus (7)

• Aspects of topological superconductivity in 2D systems: noncollinear magnetism, skyrmions, and higher-order topology
• Majorana differential shot noise and its universal thermoelectric crossover
• Manifestation of Majorana modes overlap in the Aharonov-Bohm effect
• Probing Majorana bound states through an inhomogeneous Andreev double dot interferometer
• Disentanglement, disorder lines, and Majorana edge states in a solvable quantum chain
• Electron transport in quantum channels with spin-orbit interaction: Effects of the sign of the Rashba coupling and applications to nanowires
• Revealing universal Majorana fractionalization using differential shot noise and conductance in nonequilibrium states controlled by tunneling phases