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Register a new userFrom Andreev bound states to Majorana fermions in topological wires on superconducting substrates : a story of mutation
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We study the proximity effect in a topological nanowire tunnel coupled to an s-wave superconducting substrate. We use a general Greens function approach that allows us to study the evolution of the Andreev bound states in the wire into Majorana fermions. We show that the strength of the tunnel coupling induces a topological transition in which the Majorana fermionic states can be destroyed when the coupling is very strong. Moreover, we provide a phenomenologial study of the effects of disorder in the superconductor on the formation of Majorana fermions. We note a non-trivial effect of a quasiparticle broadening term which can take the wire from a topological into a non-topological phase in certain ranges of parameters. Our results have also direct consequences for a nanowire coupled to an inhomogenous superconductor.
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We study one-dimensional topological SN and SNS long junctions obtained by placing a topological insulating nanowire in the proximity of either one or two SC finite-size leads. Using the Majorana Polarization order parameter (MP) introduced in Phys. Rev. Lett. 108, 096802 (2012)(arxiv:1109.5697) we find that the extended Andreev bound states (ABS) of the normal part of the wire acquire a finite MP: for a finite-size SN junction the ABS spectrum exhibits a zero-energy extended state which carries a full Majorana fermion, while the ABS of long SNS junctions with phase difference $pi$ transform into two zero-energy states carrying two Majorana fermions with the same MP. Given their extended character inside the whole normal link, and not only close to an interface, these Majorana-Andreev states can be directly detected in tunneling spectroscopy experiments.
We show theoretically that in the generic finite chemical potential situation, the clean superconducting spin-orbit-coupled nanowire has two distinct nontopological regimes as a function of Zeeman splitting (below the topological quantum phase transition): one is characterized by finite-energy in-gap Andreev bound states, while the other has only extended bulk states. The Andreev bound state regime is characterized by strong features in the tunneling spectra creating a gap closure signature, but no gap reopening signature should be apparent above the topological quantum phase transition, in agreement with most recent experimental observations. The gap closure feature is actually the coming together of the Andreev bound states at high chemical potential rather than a simple trivial gap of extended bulk states closing at the transition. Our theoretical finding establishes the generic intrinsic Andreev bound states on the trivial side of the topological quantum phase transition as the main contributors to the tunneling conductance spectra, providing a generic interpretation of existing experiments in clean Majorana nanowires. Our work also explains why experimental tunnel conductance spectra generically have gap closing features below the topological quantum phase transition, but no gap opening features above it.
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.
Sub-gap transport properties of a quantum dot (QD) coupled to two superconducting and one metallic leads are studied theoretically, solving the time-dependent equation of motion by the Laplace transform technique. We focus on time-dependent response of the system induced by a sudden switching on the QD-leads couplings, studying the influence of initial conditions on the transient currents and the differential conductance. We derive analytical expressions for measurable quantities and find that they oscillate in time with the frequency governed by the QD-superconducting lead coupling and acquire damping, due to relaxation driven by the normal lead. Period of these oscillations increases with the superconducting phase difference $phi$. In particular, for $phi=pi$ the QD occupancy and the normal current evolve monotonically (without any oscillations) to their stationary values. In such case the induced electron pairing vanishes and the superconducting current is completely blocked. We also analyze time-dependent development of the Andreev bound states. We show, that the measurable conductance peaks do not appear immediately after sudden switching of the QD coupling to external leads but it takes some finite time-interval for the system needs create these Andreev states. Such time-delay is mainly controlled by the QD-normal lead coupling.
Majorana bound states are interesting candidates for applications in topological quantum computation. Low energy models allowing to grasp their properties are hence conceptually important. The usual scenario in these models is that two relevant gapped phases, separated by a gapless point, exist. In one of the phases, topological boundary states are absent, while the other one supports Majorana bound states. We show that a customary model violates this paradigm. The phase that should not host Majorana fermions supports a fractional soliton exponentially localized at only one end. By varying the parameters of the model, we describe analytically the transition between the fractional soliton and two Majorana fermions. Moreover, we provide a possible physical implementation of the model. We further characterize the symmetry of the superconducting pairing, showing that the odd-frequency component is intimately related to the spatial profile of the Majorana wavefunctions.
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