Scattering formula for the topological quantum number of a disordered multimode wire

@article{Fulga2011ScatteringFF,
  title={Scattering formula for the topological quantum number of a disordered multimode wire},
  author={Ion Cosma Fulga and Fabian Hassler and A. Akhmerov and C. W. J. Beenakker},
  journal={Physical Review B},
  year={2011},
  volume={83},
  pages={155429}
}
The topological quantum number Q of a superconducting or chiral insulating wire counts the number of stable bound states at the end points. We determine Q from the matrix r of reflection amplitudes from one of the ends, generalizing the known result in the absence of time-reversal and chiral symmetry to all five topologically nontrivial symmetry classes. The formula takes the form of the determinant, Pfaffian, or matrix signature of r, depending on whether r is a real matrix, a real… 

Figures and Tables from this paper

Quasiclassical theory of disordered multi-channel Majorana quantum wires
Multi-channel spin–orbit quantum wires, when subjected to a magnetic field and proximity coupled to an s-wave superconductor, may support Majorana states. We study what happens to these systems in
Scattering theory of topological invariants in nodal superconductors
Time-reversal invariant superconductors having nodes of vanishing excitation gap support zero-energy boundary states with topological protection. Existing expressions for the topological invariant
Scattering theory of topological phase transitions
This thesis deals with characterizing topological phases as well as the transitions between them, focusing on transport properties and the effects of disorder. In Chapters 2 and 3 we derived
The Noncommutative Index Theorem and the Periodic Table for Disordered Topological Insulators and Superconductors
We study a wide class of topological free-fermion systems on a hypercubic lattice in spatial dimensions $d\ge 1$. When the Fermi level lies in a spectral gap or a mobility gap, the topological
Magnetic Quantum Walks of Neutral Atoms in Optical Lattices
This thesis focuses on the simulation of the physics of a charged particle under an external magnetic field by using discrete-time quantum walks of a spin-1/2 particle in a two-dimensional lattice.
Transport signatures of a junction between a quantum spin Hall system and a chiral topological superconductor
We investigate transport through a normal-superconductor (NS) junction made from a quantum spin Hall (QSH) system with helical edge states and a two-dimensional (2D) chiral topological superconductor
Topology and Edge Modes in Quantum Critical Chains.
TLDR
It is shown that topology can protect exponentially localized, zero energy edge modes at critical points between one-dimensional symmetry-protected topological phases and can be stable in the presence of interactions and disorder.
Bimodal conductance distribution of Kitaev edge modes in topological superconductors
A two-dimensional superconductor with spin-triplet p-wave pairing supports chiral or helical Majorana edge modes with a quantized (length L-independent) thermal conductance. Sufficiently strong
...
...

References

SHOWING 1-3 OF 3 REFERENCES
If the wire is terminated by reflection matrices r 0 = −1 1 N , r 0 = 1 1 N , the number of end states at the two ends differs by p
    If the wire is terminated by reflection matrices r 0 = −1 N , r 0 = 1 N , the number of end states at the two ends differs by p
      which means that there is no imbalance between the number of degrees of freedom of opposite chirality (equal number of sites on each sublattice in the case of a bipartite lattice)