Scattering theory of topological invariants in nodal superconductors

Dahlhaus, J. P.; Gibertini, Marco; Beenakker, C. W. J.

doi:10.1103/physrevb.86.174520

Cited by 14 publications

(26 citation statements)

References 29 publications

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“…The analytical results in Eq. (12) suggest that the penetrating ZESs form the resonant transmission channels. Such degenerate ZESs in a spin-triplet junction are called Majorana flat band in recent literature [32][33][34][35][36][37].…”

Section: Atiyah-singer Indexmentioning

confidence: 99%

Quantization of conductance minimum and index theorem

et al. 2016

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We discuss the minimum value of the zero-bias differential conductance G min in a junction consisting of a normal metal and a nodal superconductor preserving time-reversal symmetry. Using the quasiclassical Green function method, we show that G min is quantized at (4e 2 /h)N ZES in the limit of strong impurity scatterings in the normal metal at the zero temperature. The integer N ZES represents the number of perfect transmission channels through the junction. An analysis of the chiral symmetry of the Hamiltonian indicates that N ZES corresponds to the Atiyah-Singer index in mathematics.

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Section: Atiyah-singer Indexmentioning

confidence: 99%

Quantization of conductance minimum and index theorem

et al. 2016

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“…One of the most prominent platforms to realize the topological superconductivity is the class of noncentrosymmetric superconductors (NCSs) [14][15][16][17][18][19][20][21][22][23][24][25][26] .…”

Section: Introductionmentioning

confidence: 99%

Edge currents as a probe of the strongly spin-polarized topological noncentrosymmetric superconductors

et al. 2018

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Recently the influence of antisymmetric spin-orbit coupling has been studied in novel topological superconductors such as half-Heuslers and artificial hetero-structures. We investigate the effect of Rashba and/or Dresselhaus spin-orbit couplings on the band structure and topological properties of a two-dimensional noncentrosymetric superconductor. For this goal, the topological helical edge modes are analyzed for different spin-orbit couplings as well as for several superconducting pairing symmetries. To explore the transport properties, we examine the response of the spin-polarized edge states to an exchange field in a superconductor-ferromagnet heterostructure. The broken chiral symmetry causes the uni-directional currents at opposite edges.

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“…This constitutes a generalization of methods developed for time-independent systems. [29][30][31] For DTQWs with gaps in the quasienergy spectrum at both ε = 0 and ε = π, we obtain the topological invariants as simple functions of the scattering matrix at these quasienergies. For unbalanced quantum walks, where there is an unequal number of left-and rightward shifts in a period, we find an integer number of perfectly transmitting unidirectional modes, that is equal to the quasienergy winding.…”

Section: Introductionmentioning

confidence: 99%

Scattering theory of topological phases in discrete-time quantum walks

2014

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One-dimensional discrete-time quantum walks show a rich spectrum of topological phases that have so far been exclusively analysed based on the Floquet operator in momentum space. In this work we introduce an alternative approach to topology which is based on the scattering matrix of a quantum walk, adapting concepts from time-independent systems. For quantum walks with gaps in the quasienergy spectrum at 0 and π, we find three different types of topological invariants, which apply dependent on the symmetries of the system. These determine the number of protected boundary states at an interface between two quantum walk regions. Unbalanced quantum walks on the other hand are characterised by the number of perfectly transmitting unidirectional modes they support, which is equal to their non-trivial quasienergy winding. Our classification provides a unified framework that includes all known types of topology in one dimensional discrete-time quantum walks and is very well suited for the analysis of finite size and disorder effects. We provide a simple scheme to directly measure the topological invariants in an optical quantum walk experiment.

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Scattering theory of topological invariants in nodal superconductors

Cited by 14 publications

References 29 publications

Quantization of conductance minimum and index theorem

Quantization of conductance minimum and index theorem

Edge currents as a probe of the strongly spin-polarized topological noncentrosymmetric superconductors

Scattering theory of topological phases in discrete-time quantum walks

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