Effect of incommensurate potential on the resonant tunneling through Majorana bound states on the topological superconductor chains (original) (raw)
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2021
Majorana bound states (MBSs) offer a promising route to fault-tolerant quantum computation, because of their non-Abelian anyonic exchange statistics. They emerge as protected boundary modes of one dimensional topological superconductors (TSCs). Due to the finite size of these TSCs the wave functions of the two MBSs can spread across the whole TSC which leads to the possibility to access both MBSs at the same end of the TSC. First, we consider a spinless metallic lead-TSC-quantum dot setup in which the Majorana system is described with a Kitaev chain. Here, we show that a pair of Fano resonances arises as a function of dot level energy in the differential conductance. In an analytical low-energy description, we show that in the case of isolated MBS, i.e. only one MBS is contacted by the lead and the second MBS is only contacted by the quantum dot, these Fano resonances are invariant under a sign change of the dot level energy. This symmetry, however, is broken as soon as we allow the...
2013
Rashba spin-orbit coupled semiconductor-superconductor hybrid structures in the presence of Zeeman splitting have emerged as the first experimentally realizable topological superconductor supporting zero-energy Majorana bound states. However, recent experimental studies in these hybrid structures are not in complete agreement with the theoretical predictions, for example, the observed height of the zero-bias conductance peak (ZBCP) associated with the Majorana bound states is less than 10% of the predicted quantized value 2e 2 /h. We try to understand the sources of various discrepancies between the recent experiments and the earlier theories by starting from a microscopic theory and studying non-equilibrium transport in these systems at arbitrary temperatures and applied bias voltages. Our approach involves quantum Langevin equations and non-equilibrium Green's functions. Here we are able to model the tunnel coupling between the one-dimensional semiconductor-superconductor hybrid structure and the metallic leads realistically; study the role of tunnel coupling on the height of the ZBCP and the subgap conductance; predict the nature of the splitting of the ZBCP with an increasing magnetic field beyond the critical field; show the behavior of the ZBCP with an increasing gate-controlled onsite potential; and study the evolution of the full differential conductance across the topological quantum phase transition. When the applied magnetic field is quite large compared to the Rashba splitting and the bulk energy gap is much reduced, we find the ZBCP even for an onsite potential much larger than the applied magnetic field. The height of the corresponding ZBCP depends on the tunnel coupling even at zero temperature and can be much smaller than 2e 2 /h.
Physical Review Letters, 2012
We investigate theoretically the low-energy physics of semiconductor Majorana wires in the vicinity of a magnetic field-driven topological quantum phase transition (TQPT). The local density of states at the end of the wire, which is directly related to the differential conductance in the limit of point-contact tunneling, is calculated numerically.We find that the dependence of the end-of-wire local density of states on the magnetic field is nonuniversal and that the signatures associated with the closing of the superconducting gap at the Majorana TQPT are essentially invisible within a significant range of experimentally relevant parameters. Our results provide a possible explanation for the recent observation of the apparent nonclosure of the gap at the Majorana TQPT in semiconductor nanowires.
Majorana flat bands in s-wave gapless topological superconductors
We demonstrate how the non-trivial interplay between spin-orbit coupling and nodeless s-wave superconductivity can drive a fully gapped two-band topological insulator into a time-reversal invariant gapless topological superconductor supporting symmetry-protected Majorana flat bands. We characterize topological phase diagrams by a Z2 × Z2 partial Berry-phase invariant, and show that, despite the trivial crystal geometry, no unique bulk-boundary correspondence exists. We trace this behavior to the anisotropic quasiparticle bulk gap closing, linear vs. quadratic, and argue that this provides a unifying principle for gapless topological superconductivity. Experimental implications for tunneling conductance measurements are addressed, relevant for lead chalcogenide materials.
Physical Review B, 2018
Recent observations of robust zero bias quantized conductance plateaus of height 2e 2 /h in quantum dot-semiconductor-superconductor nanowire heterostructures have been interpreted as clear evidence for the presence of non-Abelian topologically protected Majorana zero modes (MZMs), since other sources of low energy conductance are believed to be unable to produce such quantized plateaus. Based on extensive numerical calculations, we show that, in fact, quantized conductance plateaus of height 2e 2 /h can also arise as a result of partially separated Andreev bound states (ps-ABSs), in which the component Majorana bound states are somewhat shifted in space without being topological MZMs. As ps-ABSs can form rather generically in the topologically trivial phase, even in the absence of disorder, our results conclusively establish that the observation of quantized conductance plateaus of height 2e 2 /h does not represent sufficient evidence for the existence of topologically protected MZMs localized at the opposite ends of a wire.
Transport signatures of Majorana bound states in superconducting hybrid structures
The European Physical Journal Special Topics, 2020
In this minireview, we outline the recent experimental and theoretical progress in the creation, characterization and manipulation of Majorana bound states (MBSs) in semiconductor-superconductor (SC) hybrid structures. After an introductory overview of the broader field we specifically focus on four of our recent projects in this direction. We show that the emergence of Fano resonances in the differential conductance in a normal lead-Majorana nanowire-quantum dot setup can be exploited to determine if a single MBS is contacted by the normal lead and the quantum dot providing an experimental test of the non-locality of MBSs. In the second project, the tunnel-coupling to two MBSs in ans-wave SC-Majorana nanowire Josephson junction (JJ) leads to a finite contribution of the MBSs to the equilibrium Josephson current probing directly the local spin-singlet contribution of the Majorana pair. We then shift our focus from MBSs forming in nanowire systems to MBSs forming in topological JJs. ...
Physical Review B, 2013
The possibility to observe and manipulate Majorana fermions as end states of one-dimensional topological superconductors has been actively discussed recently. In a quantum wire with strong spin-orbit coupling placed in proximity to a bulk superconductor, a topological superconductor has been expected to be realized when the band energy is split by the application of a magnetic field. When a periodic lattice modulation is applied, multiple topological superconductor phases appear in the phase diagram. Some of them occur for higher filling factors compared to the case without the modulation. We study the effects of phase jumps and argue that the topologically nontrivial state of the whole system is retained even if they are present. We also study the effect of the spatial modulation in the hopping parameter.
Bulletin of the American Physical Society, 2020
The study of topological classes and their associated edge states has been of ongoing interest. In one dimension, the standard platform of these studies has been the conventional Kitaev wire and its realizations. In this work, we study the edge states in coupled p-wave platforms in 1D, in the presence of experimentally relevant perturbations, like a Zeeman field and s-wave SC. Firstly, we show that the unperturbed coupled p-wave setup by itself can have two types of Majorana edge states, depending on the value of the effective onsite potential. We show that additional components like Zeeman field and s-wave term can cause transitions to different symmetry classes, both topologically trivial or non-trivial, and change the nature of these edge states. In the presence of the perturbations, we show that there are 3 symmetry classes when the effective p-wave pairing is equal between the spin species, and 6 for the second kind, when the pairing differs by a phase π between the two. Some of these classes are topologically non-trivial. Further, we explore the nature of subgap states when we have a junction between two such topological setups and their corresponding behaviour with the phase of the p-wave order parameter. Our work provides a theoretical framework of the different ways to get non-trivial topological classes in coupled p-wave nanowire setup, using experimentally feasible perturbations, and the nature of subgap states across junctions of these platforms.
Topological states in normal and superconducting p-wave chains
Physics Letters A, 2014
We study a two-band model of fermions in a 1d chain with an antisymmetric hybridization that breaks inversion symmetry. We find that for certain values of its parameters, the sp-chain maps formally into a p-wave superconducting chain, the archetypical 1d system exhibiting Majorana fermions. The eigenspectra, including the existence of zero energy modes in the topological phase, agree for both models. The end states too share several similarities in both models, such as the behavior of the localization length, the non-trivial topological index and robustness to disorder. However, we show by mapping the s-and p-fermions to two copies of Majoranas, that the excitations in the ends of a finite sp chain are indeed conventional fermions though endowed with protected topological properties. Our results are obtained by a scattering approach in a semi-infinite chain with an edge defect treated within the T -matrix approximation. We augment the analytical results with exact numerical diagonalization that allow us to extend our results to arbitrary parameters and also to disordered systems.
We report on several low temperature experiments supporting the presence of Majorana fermions in superconducting lead nanowires fabricated with a scanning tunneling microscope, STM. These nanowires are the connecting bridges between the STM tip and the sample resulting from indentation-retraction processes. We show here that by a controlled tuning of the nanowire region, in which superconductivity is confined by applied magnetic fields, the conductance curves obtained in these situations are indicative of topological superconductivity and Majorana fermions. The most prominent feature of this behaviour is the emergence of a zero bias peak in the conductance curves, superimposed on a background characteristic of the conductance between a normal metal and a superconductor in the Andreev regime. The zero bias peak emerges in some nanowires when a magnetic field larger that the lead bulk critical field is applied. This field drives one of the electrodes into the normal state while the other, the tip, remains superconducting on its apex. Meanwhile a topological superconducting state appears in the connecting nanowire of nanometric size.