Wigner-Poisson Statistics of Topological Transitions in a Josephson Junction

Beenakker, C. W. J.; Edge, Jonathan M.; Dahlhaus, J. P.; Pikulin, Dmitry I.; Mi, Shuo; Wimmer, Michael

doi:10.1103/physrevlett.111.037001

Cited by 39 publications

(52 citation statements)

References 44 publications

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“…The usual periodic boundary condition (PBC) and the anti-periodic boundary condition (APBC) are included in the TBC as limiting cases. In practice, such a boundary condition can be realized by magnetic fluxes and Josephson junctions 6,45,[49][50][51][52][53][54][55][56][57][58][59][60][61] . Our work is motivated by the observation that the fermionic parities in the ground states of the Kitaev chain with the PBC and the APBC have opposite signs in the topological phase, hence indicating a level crossing when one continuously changes the parameters so as to connect the PBC with the APBC.…”

Section: Introductionmentioning

confidence: 99%

Exact zero modes in twisted Kitaev chains

Kawabata

Kobayashi

et al. 2017

Phys. Rev. B

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We study the Kitaev chain under generalized twisted boundary conditions, for which both the amplitudes and the phases of the boundary couplings can be tuned at will. We explicitly show the presence of exact zero modes for large chains belonging to the topological phase in the most general case, in spite of the absence of "edges" in the system. For specific values of the phase parameters, we rigorously obtain the condition for the presence of the exact zero modes in finite chains, and show that the zero modes obtained are indeed localized. The full spectrum of the twisted chains with zero chemical potential is analytically presented. Finally, we demonstrate the persistence of zero modes (level crossing) even in the presence of disorder or interactions.

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Section: Introductionmentioning

confidence: 99%

Exact zero modes in twisted Kitaev chains

Kawabata

Kobayashi

et al. 2017

Phys. Rev. B

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“…The Majorana zero-mode produces a resonant peak at V = 0, which survives the average over disorder realizations. Figure adapted from Beenakker et al (2013).…”

Section: Fig 2 Model Calculation Of the Excitation Spectrum Of Amentioning

confidence: 99%

Random-matrix theory of Majorana fermions and topological superconductors

2015

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The theory of random matrices originated half a century ago as a universal description of the spectral statistics of atoms and nuclei, dependent only on the presence or absence of fundamental symmetries. Applications to quantum dots (artificial atoms) followed, stimulated by developments in the field of quantum chaos, as well as applications to Andreev billiards -quantum dots with induced superconductivity. Superconductors with topologically protected subgap states, Majorana zero-modes and Majorana edge modes, provide a new arena for applications of random-matrix theory. We review these recent developments, with an emphasis on electrical and thermal transport properties that can probe the Majorana fermions.

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“…We show that q(H ) is real in classes A, AI, AII, BDI, and D, it is complex in classes AIII, CI, and DIII, and it cannot be defined in classes C and CII. When q is real, sgn q(H ) equals the parity of the topological invariant in d = 0 dimensions [3,9,21,26,27]. In the presence of an additional symmetry [H,U ] = 0,{C,U } = 0, where C is the chiral symmetry operator, q becomes real also in classes AIII, CI, and DIII [28].…”

Section: Introductionmentioning

confidence: 99%

Existence of zero-energy impurity states in different classes of topological insulators and superconductors and their relation to topological phase transitions

Kimme

Hyart

2016

Phys. Rev. B

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Existence of zero-energy impurity states in different classes of topological insulators and superconductors and their relation to topological phase transitions Kimme, Lukas; Hyart, Timo Kimme, L., & Hyart, T. (2016 We consider the effects of impurities on topological insulators and superconductors. We start by identifying the general conditions under which the eigenenergies of an arbitrary Hamiltonian H belonging to one of the Altland-Zirnbauer symmetry classes undergo a robust zero energy crossing as a function of an external parameter which can be, for example, the impurity strength. We define a generalized root of det H and use it to predict or rule out robust zero-energy crossings in all symmetry classes. We complement this result with an analysis based on almost degenerate perturbation theory, which allows a derivation of the asymptotic low-energy behavior of the ensemble averaged density of states ρ ∼ E α for all symmetry classes and makes it transparent that the exponent α does not depend on the choice of the random matrix ensemble. Finally, we show that a lattice of impurities can drive a topologically trivial system into a nontrivial phase, and in particular we demonstrate that impurity bands carrying extremely large Chern numbers can appear in different symmetry classes of two-dimensional topological insulators and superconductors. We use the generalized root of det H (k) to reveal a spiderweblike momentum space structure of the energy gap closings that separate the topologically distinct phases in p x + ip y superconductors in the presence of an impurity lattice.

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Wigner-Poisson Statistics of Topological Transitions in a Josephson Junction

Cited by 39 publications

References 44 publications

Exact zero modes in twisted Kitaev chains

Exact zero modes in twisted Kitaev chains

Random-matrix theory of Majorana fermions and topological superconductors

Existence of zero-energy impurity states in different classes of topological insulators and superconductors and their relation to topological phase transitions

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