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

  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},
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… 

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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)