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Register a new userUniversal nonequilibrium signatures of Majorana zero modes in quench dynamics
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The quantum evolution after a metallic lead is suddenly connected to an electron system contains information about the excitation spectrum of the combined system. We exploit this type of quantum quench to probe the presence of Majorana fermions at the ends of a topological superconducting wire. We obtain an algebraically decaying overlap (Loschmidt echo) ${cal L}(t)=| < psi(0) | psi(t) > |^2sim t^{-alpha}$ for large times after the quench, with a universal critical exponent $alpha$=1/4 that is found to be remarkably robust against details of the setup, such as interactions in the normal lead, the existence of additional lead channels or the presence of bound levels between the lead and the superconductor. As in recent quantum dot experiments, this exponent could be measured by optical absorption, offering a new signature of Majorana zero modes that is distinct from interferometry and tunneling spectroscopy.
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We propose an alternative route to engineer Majorana zero modes (MZMs), which relies on inducing shift or spin vortex defects in magnetic textures which microscopically coexist or are in proximity to a superconductor. The present idea applies to a variety of superconducting materials and hybrid structures, irrespectively of their spin-singlet, -triplet, or mixed type of pairing, as long as their bulk energy spectrum contains robust point nodes. Our mechanism provides a new framework to understand the recent observations of pairs of MZMs in superconductor - magnetic adatom systems. Moreover, it can inspire the experimental development of new platforms, consisting of nanowires in proximity to conventional superconductors with strong Rashba spin-orbit coupling.
A pair of Majorana zero modes (MZMs) constitutes a nonlocal qubit whose entropy is $log 2$. Upon strongly coupling one of the constituent MZMs to a reservoir with a continuous density of states, a universal entropy change of $frac{1}{2}log 2$ is expected to be observed across an intermediate temperature plateau. We adapt the entropy-measurement scheme that was the basis of a recent experiment [Hartman et. al., Nat. Phys. 14, 1083 (2018)] to the case of a proximitized topological system hosting MZMs, and propose a method to measure this $frac{1}{2}log 2$ entropy change --- an unambiguous signature of the nonlocal nature of the topological state. This approach offers an experimental strategy to distinguish MZMs from non-topological states.
Conductance signatures that signal the presence of Majorana zero modes in a three terminal nanowire-topological superconductor hybrid system are analyzed in detail, in both the clean nanowire limit and in the presence of non-coherent dephasing interactions. In the coherent transport regime for a clean wire, we point out contributions of the local Andreev reflection and the non-local transmissions toward the total conductance lineshapes while clarifying the role of contact broadening on the Majorana conductance lineshapes at the magnetic field parity crossings. Interestingly, at larger $B$-field parity crossings, the contribution of the Andreev reflection process decreases which is compensated by the non-local processes in order to maintain the conductance quantum regardless of contact coupling strength. In the non-coherent transport regime, we include dephasing that is introduced by momentum randomization processes, that allows one to smoothly transition to the diffusive limit. Here, as expected, we note that while the Majorana character of the zero modes is unchanged, there is a reduction in the conductance peak magnitude that scales with the strength of the impurity scattering potentials. Important distinctions between the effect of non-coherent dephasing processes and contact-induced tunnel broadenings in the coherent regime on the conductance lineshapes are elucidated. Most importantly our results reveal that the addition of dephasing in the set up does not lead to any notable length dependence to the conductance of the zero modes, contrary to what one would expect in a gradual transition to the diffusive limit. We believe this work paves a way for a systematic introduction of scattering processes into the realistic modeling of Majorana nanowire hybrid devices and assessing topological signatures in such systems in the presence of non-coherent scattering processes.
We study Majorana zero modes properties in cylindrical cross-section semiconductor quantum wires based on the $k cdot p$ theory and a discretized lattice model. Within this model, the influence of disorder potentials in the wire and amplitude and phase fluctuations of the superconducting order-parameter are discussed. We find that for typical wire geometries, pairing potentials, and spin-orbit coupling strengths, coupling between quasi-one-dimensional sub-bands is weak, low-energy quasiparticles near the Fermi energy are nearly completely spin-polarized, and the number of electrons in the active sub-bands of topological states is small.
Topological phases of the famous Altland-Zirnbauer (AZ) tenfold classes are defined on the equilibrium ground states. Whether such equilibrium topological phases have universal correspondence to far-from-equilibrium quantum dynamics is a fundamental issue of both theoretical and experimental importance. Here we uncover the universal topological quench dynamics linking to the equilibrium topological phases for the complete AZ tenfold classes, with a general framework being established. We show a fundamental result that a $d$-dimensional topological phase of the tenfold class, with an integer invariant or $mathbb{Z}_{2}$ index defined on high symmetry momenta, is generically characterized by topology reduced to the highest-order band-inversion surfaces located at arbitrary discrete momenta of Brillouin zone. Such dimension-reduced topology is further captured by universal topological patterns emerging in far-from-equilibrium quantum dynamics by quenching the system from trivial phase to the topological regime, rendering the dynamical hallmark of the equilibrium topological phase. This work establishes a universal dynamical characterization for the complete AZ symmetry classes of topological phases, which has broad applications in theory and experiment.
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