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Register a new userTopological minigap in quasi-one-dimensional spin-orbit-coupled semiconductor Majorana wires
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The excitation gap above the Majorana fermion (MF) modes at the ends of 1D topological superconducting (TS) semiconductor wires scales with the bulk quasiparticle gap E_{qp}. This gap, also called minigap, facilitates experimental detection of the pristine TS state and MFs at experimentally accessible temperatures T << E_{qp}. Here we show that the linear scaling of minigap with E_{qp} can fail in quasi-1D wires with multiple confinement bands when the applied Zeeman field is greater than or equal to about half of the confinement-induced bandgap. TS states in such wires have an approximate chiral symmetry supporting multiple near zero energy modes at each end leading to a minigap which can effectively vanish. We show that the problem of small minigap in such wires can be resolved by forcing the system to break the approximate chirality symmetry externally with a second Zeeman field. Although experimental signatures such as zero bias peak from the wire ends is suppressed by the second Zeeman field above a critical value, such a field is required in some important parameter regimes of quasi-1D wires to isolate the topological physics of end state MFs. We also discuss the crucial difference of our minigap calculations from the previously reported minigap results appropriate for idealized spinless p-wave superconductors and explain why the clustering of fermionic subgap states around the zero energy Majorana end state with increasing chemical potential seen in the latter system does not apply to the experimental TS states in spin-orbit coupled nanowires.
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We study the effect of Rashba spin-orbit coupling (SOC) on the charge and spin degrees of freedom of a quasi-one-dimensional (quasi-1D) Wigner crystal. As electrons in a quasi-1D Wigner crystal can move in the transverse direction, SOC cannot be gauged away in contrast to the pure 1D case. We show that for weak SOC, a partial gap in the spectrum opens at certain ratios between density of electrons and the inverse Rashba length. We present how the low-energy branch of charge degrees of freedom deviates due to SOC from its usual linear dependence at small wave vectors. In the case of strong SOC, we show that spin sector of a Wigner crystal cannot be described by an isotropic antiferromagnetic Heisenberg Hamiltonian any more, and that instead the ground state of neighboring electrons is mostly a triplet state. We present a new spin sector Hamiltonian and discuss the spectrum of Wigner crystal in this limit.
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.
A time-reversal invariant topological superconductivity is suggested to be realized in a quasi-one dimensional structure on a plane, which is fabricated by filling the superconducting materials into the periodic channel of dielectric matrices like zeolite and asbestos under high pressure. The topological superconducting phase sets up in the presence of large spin-orbit interactions when intra-wire s-wave and inter-wire d-wave pairings take place. Kramers pairs of Majorana bound states emerge at the edges of each wire. We analyze effects of Zeeman magnetic field on Majorana zero-energy states. In-plane magnetic field was shown to make asymmetric the energy dispersion, nevertheless Majorana fermions survive due to protection of a particle-hole symmetry. Tunneling of Majorana quasi-particle from the end of one wire to the nearest-neighboring one yields edge fractional Josephson current with $4pi$-periodicity.
Majorana fermions are promising candidates for storing and processing information in topological quantum computation. The ability to control such individual information carriers in trapped ultracold atomic Fermi gases is a novel theme in quantum information science. However, fermionic atoms are neutral and thus are difficult to manipulate. Here, we theoretically investigate the control of emergent Majorana fermions in one-dimensional spin-orbit coupled atomic Fermi gases. We discuss (i) how to move Majorana fermions by increasing or decreasing an effective Zeeman field, which acts like a solid state control voltage gate; and (ii) how to create a pair of Majorana fermions by adding a magnetic impurity potential. We discuss the experimental realization of our control scheme in an ultracold Fermi gas of $^{40}$K atoms.
Motivated by the spin-momentum locking of electrons at the boundaries of topological insulators, we study a one-dimensional system of spin-orbit coupled massless Dirac electrons with $s$-wave superconducting pairing. As a result of the spin-orbit coupling, our model has only two kinds of linearly dispersing modes, which we take to be right-moving spin-up and left-moving spin-down. Both lattice and continuum models are studied. In the lattice model, we find that a single Majorana zero energy mode appears at each end of a finite system provided that the $s$-wave pairing has an extended form, with the nearest-neighbor pairing being larger than the on-site pairing. We confirm this both numerically and analytically by calculating the winding number. Next we study a lattice version of a model with both Schrodinger and Dirac-like terms and find that the model hosts a topological transition between topologically trivial and non-trivial phases depending on the relative strength of the Schrodinger and Dirac terms. We then study a continuum system consisting of two $s$-wave superconductors with different phases of the pairing. Remarkably, we find that the system has a {it single} Andreev bound state which is localized at the junction. When the pairing phase difference crosses a multiple of $2 pi$, an Andreev bound state touches the top of the superconducting gap and disappears, and a different state appears from the bottom of the gap. We also study the AC Josephson effect in such a junction with a voltage bias that has both a constant $V_0$ and a term which oscillates with a frequency $omega$. We find that, in contrast to standard Josephson junctions, Shapiro plateaus appear when the Josephson frequency $omega_J= 2eV_0/hbar$ is a rational fraction of $omega$. We discuss experiments which can realize such junctions.
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