title: Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions.
abstract: We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s-wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4π-periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary.
authors: Department of Physics and Astronomy, Dartmouth College, 6127 Wilder Laboratory, Hanover, New Hampshire 03755, USA.
authors: Abhijeet
authors: A
authors: Alase
authors: Department of Physics and Astronomy, Dartmouth College, 6127 Wilder Laboratory, Hanover, New Hampshire 03755, USA.
authors: Emilio
authors: E
authors: Cobanera
authors: Department of Physics, Indiana University, Bloomington, Indiana 47405, USA.
authors: Gerardo
authors: G
authors: Ortiz
authors: Department of Physics and Astronomy, Dartmouth College, 6127 Wilder Laboratory, Hanover, New Hampshire 03755, USA.
authors: Lorenza
authors: L
authors: Viola