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Register a new userDensity of states at disorder-induced phase transitions in a multichannel Majorana wire
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Added by
Maria-Theresa Rieder
Publication date
2014
fields
Physics
and research's language is
English
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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 $xi$.
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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 show that the resistivity rho(T) of disordered ferromagnets near, and above, the Curie temperature T_c generically exhibits a stronger anomaly than the scaling-based Fisher-Langer prediction. Treating transport beyond the Boltzmann description, we find that within mean-field theory, drho/dT exhibits a |T-T_c|^{-1/2} singularity near T_c. Our results, being solely due to impurities, are relevant to ferromagnets with low T_c, such as SrRuO3 or diluted magnetic semiconductors, whose mobility near T_c is limited by disorder.
Weyl semimetals are a newly discovered class of materials that host relativistic massless Weyl fermions as their low-energy bulk excitations. Among this new class of materials, there exist two general types of semimetals that are of particular interest: type-I Weyl semimetals, that have broken inversion or time-reversal symmetry symmetry, and type-II Weyl semimetals, that additionally breaks Lorentz invariance. In this work, we use Born approximation to analytically demonstrate that the type-I Weyl semimetals may undergo a quantum phase transition to type-II Weyl semimetals in the presence of the finite charge and magnetic disorder when non-zero tilt exist. The phase transition occurs when the disorder renormalizes the topological mass, thereby reducing the Fermi velocity near the Weyl cone below the tilt of the cone. We also confirm the presence of the disorder induced phase transition in Weyl semimetals using exact diagonalization of a three-dimensional tight-binding model to calculate the resultant phase diagram of the type-I Weyl semimetal.
We propose a new setup for creating Majorana bound states in a two-dimensional electron gas Josephson junction. Our proposal relies exclusively on a supercurrent parallel to the junction as a mechanism of breaking time-reversal symmetry. We show that combined with spin-orbit coupling, supercurrents induce a Zeeman-like spin splitting. Further, we identify a new conserved quantity---charge-momentum parity---that prevents the opening of the topological gap by the supercurrent in a straight Josephson junction. We propose breaking this conservation law by adding a third superconductor, introducing a periodic potential, or making the junction zigzag-shaped. By comparing the topological phase diagrams and practical limitations of these systems we identify the zigzag-shaped junction as the most promising option.
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