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Register a new userDisorder-induced topological transitions in multichannel Majorana wires
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In this work, we investigate the effect of disorder on the topological properties of multichannel superconductor nanowires. While the standard expectation is that the spectral gap is closed and opened at transitions that change the topological index of the wire, we show that the closing and opening of a transport gap can also cause topological transitions, even in the presence of nonzero density of states across the transition. Such transport gaps induced by disorder can change the topological index, driving a topologically trivial wire into a nontrivial state or vice versa. We focus on the Rashba spin-orbit coupled semiconductor nanowires in proximity to a conventional superconductor, which is an experimentally relevant system, and obtain analytical formulas for topological transitions in these wires, valid for generic realizations of disorder. Full tight-binding simulations show excellent agreement with our analytical results without any fitting parameters.
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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.
An $N$-channel spinless p-wave superconducting wire is known to go through a series of $N$ topological phase transitions upon increasing the disorder strength. Here, we show that at each of those transitions the density of states shows a Dyson singularity $ u(varepsilon) propto varepsilon^{-1}|lnvarepsilon|^{-3} $, whereas $ u(varepsilon) propto varepsilon^{|alpha|-1}$ has a power-law singularity for small energies $varepsilon$ away from the critical points. Using the concept of superuniversality [Gruzberg, Read, and Vishveshwara, Phys. Rev. B 71, 245124 (2005)], we are able to relate the exponent $alpha$ to the wires transport properties at zero energy and, hence, to the mean free path $l$ and the superconducting coherence length $xi$.
Contrary to the widespread belief that Majorana zero-energy modes, existing as bound edge states in 2D topological insulator (TI)-superconductor (SC) hybrid structures, are unaffected by non-magnetic static disorder by virtue of Andersons theorem, we show that such a protection against disorder does not exist in realistic multi-channel TI/SC/ferromagnetic insulator (FI) sandwich structures of experimental relevance since the time-reversal symmetry is explicitly broken locally at the SC/FI interface where the end Majorana mode (MM) resides. We find that although the MM itself and the emph{bulk} topological superconducting phase inside the TI are indeed universally protected against disorder, disorder-induced subgap states are generically introduced at the TI edge due to the presence of the FI/SC interface as long as multiple edge channels are occupied. We discuss the implications of the finding for the detection and manipulation of the edge MM in realistic TI/SC/FI experimental systems of current interest.
We study a realistic Floquet topological superconductor, a periodically driven nanowire proximitized to an equilibrium s-wave superconductor. Due to both strong energy and density fluctuations caused from the superconducting proximity effect, the Floquet Majorana wire becomes dissipative. We show that the Floquet band structure is still preserved in this dissipative system. In particular, we find that both the Floquet Majorana zero and pi modes can no longer be simply described by the Floquet topological band theory. We also propose an effective model to simplify the calculation of the lifetime of these Floquet Majoranas, and find that the lifetime can be engineered by the external driving field.
We investigate effects of ordinary nonmagnetic disorder in the bulk of a superconductor on magnetic adatom-induced Shiba states and on the proximity-induced superconductivity in a nanowire that is tunnel coupled to the bulk superconductor. Within the formalism of self-consistent Born approximation, we show that, contrary to widespread belief, the proximity-induced topological superconductivity can be adversely affected by the bulk superconducting disorder even in the absence of any disorder in the nanowire (or the superconductor-nanowire interface) when the proximity tunnel coupling is strong. In particular, bulk disorder can effectively randomize the Shiba-state energies. In the case of a proximate semiconductor nanowire, we numerically compute the dependence of the effective disorder and pairing gap induced on the wire as a function of the semiconductor-superconductor tunnel coupling. We find that the scaling exponent of the induced disorder with respect to coupling is always larger than that of the induced gap, implying that at weak coupling, the proximity-induced pairing gap dominates, whereas at strong coupling, the induced disorder dominates. These findings bring out the importance of improving the quality of the bulk superconductor itself (in addition to the quality of the nanowire and the interface) in the experimental search for solid-state Majorana fermions in proximity-coupled hybrid structures and, in particular, points out the pitfall of pursuing strong coupling between the semiconductor and the superconductor in a goal toward having a large proximity gap. In particular, our work establishes that the bulk superconductor in strongly coupled hybrid systems for Majorana studies must be in the ultraclean limit, since otherwise the bulk disorder is likely to completely suppress all induced topological superconductivity effects.
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