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Register a new userMajorana Zero Modes in 1D Quantum Wires Without Long-Ranged Superconducting Order
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We show that long-ranged superconducting order is not necessary to guarantee the existence of Majorana fermion zero modes at the ends of a quantum wire. We formulate a concrete model which applies, for instance, to a semiconducting quantum wire with strong spin-orbit coupling and Zeeman splitting coupled to a wire with algebraically-decaying superconducting fluctuations. We solve this model by bosonization and show that it supports Majorana fermion zero modes. We argue that a large class of models will also show the same phenomenon. We discuss the implications for experiments on spin-orbit coupled nanowires coated with superconducting film and for LaAlO3/SrTiO3 interfaces.
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One-dimensional Majorana modes can be obtained as boundary excitations of topologically nontrivial two-dimensional topological superconductors. Here, we propose instead the bottom-up creation of one-dimensional, counterpropagating, and dispersive Majorana modes as bulk excitations of a periodic chain of partially-overlapping, zero-dimensional Majorana modes in proximitized quantum nanowires via periodically-modulated magnetic fields. These dispersive one-dimensional Majorana modes can be either massive or massless. Massless Majorana modes are pseudohelical, having opposite Majorana pseudospin, and realize emergent quantum mechanical supersymmetry. The system exhibits extended supersymmetry with central extensions and with spontaneous partial breaking. We identify the massless Majorana fermions as Goldstinos, i.e., the Nambu-Goldstone fermions associated with the spontaneous breaking of supersymmetry. The experimental fingerprint of massless Majorana modes and supersymmetry is the presence of a finite zero-bias peak, which is generally not expected for Majorana modes with a finite overlap and localized at a finite distance. Moreover, slowly varying magnetic fields can realize an adiabatic Majorana pump which can be used as a dynamically probe of topological superconductivity.
We analyze the prospects for stabilizing Majorana zero modes in semiconductor nanowires that are proximity-coupled to higher-temperature superconductors. We begin with the case of iron pnictides which, though they are s-wave superconductors, are believed to have superconducting gaps that change sign. We then consider the case of cuprate superconudctors. We show that a nanowire on a step-like surface, especially in an orthorhombic material such as YBCO, can support Majorana zero modes at an elevated temperature.
We provide a current perspective on the rapidly developing field of Majorana zero modes in solid state systems. We emphasize the theoretical prediction, experimental realization, and potential use of Majorana zero modes in future information processing devices through braiding-based topological quantum computation. Well-separated Majorana zero modes should manifest non-Abelian braiding statistics suitable for unitary gate operations for topological quantum computation. Recent experimental work, following earlier theoretical predictions, has shown specific signatures consistent with the existence of Majorana modes localized at the ends of semiconductor nanowires in the presence of superconducting proximity effect. We discuss the experimental findings and their theoretical analyses, and provide a perspective on the extent to which the observations indicate the existence of anyonic Majorana zero modes in solid state systems. We also discuss fractional quantum Hall systems (the 5/2 state) in this context. We describe proposed schemes for carrying out braiding with Majorana zero modes as well as the necessary steps for implementing topological quantum computation.
We investigate the topological properties of spin polarized fermionic polar molecules loaded in a multi-layer structure with the electric dipole moment polarized to the normal direction. When polar molecules are paired by attractive inter-layer interaction, unpaired Majorana fermions can be macroscopically generated in the top and bottom layers in dilute density regime. We show that the resulting topological state is effectively composed by a bundle of 1D Kitaev ladders labeled by in-plane momenta k and -k, and hence belongs to BDI class characterized by the winding number Z, protected by the time reversal symmetry. The Majorana surface modes exhibit a flatband at zero energy, fully gapped from Bogoliubov excitations in the bulk, and hence becomes an idea system to investigate the interaction effects on quantum degenerate Majorana fermions. We further show that additional interference fringes can be identified as a signature of such 2D Majorana surface modes in the time-of-flight experiment.
We study a one-dimensional wire with strong Rashba and Dresselhaus spin-orbit coupling (SOC), which supports Majorana fermions when subject to a Zeeman magnetic field and in proximity of a superconductor. Using both analytical and numerical techniques we calculate the electronic spin texture of the Majorana end states. We find that the spin polarization of these states depends on the relative magnitude of the Rashba and Dresselhaus SOC components. Moreover, we define and calculate a local Majorana polarization and Majorana density and argue that they can be used as order parameters to characterize the topological transition between the trivial system and the system exhibiting Majorana bound modes. We find that the local Majorana polarization is correlated to the transverse spin polarization, and we propose to test the presence of Majorana fermions in a 1D system by a spin-polarized density of states measurement.
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