Anderson localization of a Majorana fermion

Иванов, Д. А.; Ostrovsky, P. M.; Skvortsov, M. A.

doi:10.1209/0295-5075/106/37006

Cited by 3 publications

(6 citation statements)

References 41 publications

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“…Is something left of the spectral peak? The answer is "yes" for tunnel coupling [8][9][10][11][12][13][14][15], as it should be if the level broadening is less than the level spacing in the quantum dot. What we have found is that the answer is "no" for ballistic coupling, with level broadening comparable to level spacing.…”

Section: Discussionmentioning

confidence: 99%

“…It is known [1,6,[8][9][10][11][12][13][14][15] that the tunneling density of states of a superconducting quantum dot with broken time-reversal symmetry, weakly coupled to the outside, has a Fermi-level anomaly consisting of a narrow dip in symmetry class C and a narrow peak in class D. Equation (22) shows the effect of level broadening upon coupling via M channels to the continuum. For M → ∞ the normal-state result 1/δ 0 is recovered, but for small M the Fermi-level anomaly persists.…”

Section: Fermi-level Anomaly In the Density Of States A Analyticmentioning

confidence: 99%

“…that eliminates most of the eigenvector components from the class-C thermopower expression (15). We are left with…”

Section: A Class Cmentioning

confidence: 99%

“…We focus on the strong-coupling limit, typically realized by a ballistic point contact, complementing earlier work on the limit of weak coupling by a tunnel barrier or a localized conductor [8][9][10][11][12][13][14][15]. The simplicity of the strong-coupling limit allows for an analytical calculation using random-matrix theory of the entire probability distribution of the Fermi-level density of statesnot just the ensemble average.…”

Section: Introductionmentioning

confidence: 99%

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Time-delay matrix, midgap spectral peak, and thermopower of an Andreev billiard

2014

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We derive the statistics of the time-delay matrix (energy derivative of the scattering matrix) in an ensemble of superconducting quantum dots with chaotic scattering (Andreev billiards), coupled ballistically to M conducting modes (electron-hole modes in a normal metal or Majorana edge modes in a superconductor). As a first application we calculate the density of states ρ 0 at the Fermi level. The ensemble average ρ 0 = δdeviates from the bulk value 1/δ 0 by an amount depending on the Altland-Zirnbauer symmetry indices α,β. The divergent average for M = 1,2 in symmetry class D (α = −1, β = 1) originates from the midgap spectral peak of a closed quantum dot, but now no longer depends on the presence or absence of a Majorana zero mode. As a second application we calculate the probability distribution of the thermopower, contrasting the difference for paired and unpaired Majorana edge modes.

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Section: Discussionmentioning

confidence: 99%

Section: Fermi-level Anomaly In the Density Of States A Analyticmentioning

confidence: 99%

“…that eliminates most of the eigenvector components from the class-C thermopower expression (15). We are left with…”

Section: A Class Cmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Time-delay matrix, midgap spectral peak, and thermopower of an Andreev billiard

2014

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“…This calculation will be the subject of a separate forthcoming publication. 55 Research (BMBF) (P.O. and M.S.).…”

Section: Discussionmentioning

confidence: 99%

Superconducting proximity effect in quantum wires without time-reversal symmetry

et al. 2013

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We study the superconducting proximity effect in a quantum wire with broken time-reversal (TR) symmetry connected to a conventional superconductor. We consider the situation of a strong TRsymmetry breaking, so that Cooper pairs entering the wire from the superconductor are immediately destroyed. Nevertheless, some traces of the proximity effect survive: for example, the local electronic density of states (LDOS) is influenced by the proximity to the superconductor, provided that localization effects are taken into account. With the help of the supersymmetric sigma model, we calculate the average LDOS in such a system. The LDOS in the wire is strongly modified close to the interface with the superconductor at energies near the Fermi level. The relevant distances from the interface are of the order of the localization length, and the size of the energy window around the Fermi level is of the order of the mean level spacing at the localization length. Remarkably, the sign of the effect is sensitive to the way the TR symmetry is broken: In the spin-symmetric case (orbital magnetic field), the LDOS is depleted near the Fermi energy, whereas for the broken spin symmetry (magnetic impurities), the LDOS at the Fermi energy is enhanced.

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Dynamics of Anderson localization in disordered wires

Khalaf

Ostrovsky

2017

Phys. Rev. B

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We consider the dynamics of an electron in an infinite disordered metallic wire. We derive exact expressions for the probability of diffusive return to the starting point in a given time. The result is valid for wires with or without time-reversal symmetry and allows for the possibility of topologically protected conducting channels. In the absence of protected channels, Anderson localization leads to a nonzero limiting value of the return probability at long times, which is approached as a negative power of time with an exponent depending on the symmetry class. When topologically protected channels are present (in a wire of either unitary or symplectic symmetry), the probability of return decays to zero at long time as a power law whose exponent depends on the number of protected channels. Technically, we describe the electron dynamics by the one-dimensional supersymmetric non-linear sigma model. We derive an exact identity that relates any local dynamical correlation function in a disordered wire of unitary, orthogonal, or symplectic symmetry to a certain expectation value in the random matrix ensemble of class AIII, CI, or DIII, respectively. The established exact mapping from one-to zero-dimensional sigma model is very general and can be used to compute any local observable in a disordered wire. Introduction.-Quantum interference leads to localization of electrons in the presence of disorder. In one-(1D) and two-dimensional (2D) systems, even weak random potential localizes all eigenstates, while in three dimensions (3D) localization occurs when disorder is stronger than a certain threshold level [1][2][3]. In the past few years, the phenomenon of Anderson localization has witnessed a revival of activity due to discoveries made in several fields. On the experiment side, Anderson localization has been observed in a multitude of systems including cold atoms [4-6], light waves [7], ultrasound [8], as well as optically driven atomic systems [9]. On the theory side, dynamical phenomena such as thermalization and relaxation after a quantum quench in disordered systems have been the subject of growing interest [10][11][12][13][14]. This has been inspired, in part, by the discovery of manybody localization [15][16][17][18][19], which is an interacting analog of Anderson localization, and more recently by the proposal to diagnose quantum chaotic behavior by means of out-of-time-order correlations [20][21][22][23][24]. Furthermore, the discovery [25][26][27][28][29][30][31] and complete classification [32][33][34][35][36] of topological insulators has opened the door to a new arena where the interplay between disorder and topology leads to unusual localization-related effects. These include ultra-slow (Sinai) diffusion at the critical phase between two topological insulator phases [37], as well as enhanced localization effects in systems where topologically protected and unprotected channels coexist [38,39].Despite more than half a century since Anderson's original paper [40], there exists very few exact results [41] ...

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Anderson localization of a Majorana fermion

Cited by 3 publications

References 41 publications

Time-delay matrix, midgap spectral peak, and thermopower of an Andreev billiard

Time-delay matrix, midgap spectral peak, and thermopower of an Andreev billiard

Superconducting proximity effect in quantum wires without time-reversal symmetry

Dynamics of Anderson localization in disordered wires

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