Analytical results for the Green's functions of lattice fermions

Abstract

We present a further development of methods for analytical calculations of Green's functions of lattice fermions based on recurrence relations. Applying it to tight-binding systems and topological superconductors in different dimensions we obtain a number of new results. In particular we derive an explicit expression for arbitrary Green's function of an open Kitaev chain and discover non-local fermionic corner states in a 2D p-wave superconductor. PACS numbers: 73.20.-r, 71.15.-m, 71.20.-b, 02.10.Yn arXiv:1706.06463v1 [cond-mat.mes-hall]

Green’s Functions and DOS for Some 2D Lattices

“…Fermionic lattice models are widely used not only as a purely theoretical tool but also as a basis for investigation and modelling of physical properties of real materials [1]. Despite their relative formal simplicity-the Hamiltonians of many of them can be written down as bilinears of fermionic operators-analytical calculation of the lattice Green's functions can present substantial difficulties.…”

Universal properties of boundary and interface charges in multichannel one-dimensional models without symmetry constraints

“…To calculate the invariants we use the method of boundary Green's functions (BGF) [41][42][43][44][45][46][47][48]. Complementary to the method of [10] this technique allows for the direct construction of the open boundary lattice Green's function, avoiding the computation of eigenstates [45].…”

“…To calculate the invariants we use the method of boundary Green's functions (BGF) [41][42][43][44][45][46][47][48]. Complementary to the method of [10] this technique allows for the direct construction of the open boundary lattice Green's function, avoiding the computation of eigenstates [45]. The BGF method proved to be useful in analyzing electronic transport in superconducting systems [44,46], thermal transport in spin heterostructures [41], as well as transport in topological superconductors hosting Majorana bound states [42,48].…”

Boundary Green's function approach for spinful single-channel and multichannel Majorana nanowires

“…[52][53][54][55][56][57][58]. The present study will employ the complementary boundary Green's function (bGF) method [59][60][61][62][63], which is particularly useful for analyzing nonequilibrium transport properties in different types of hybrid nanojunctions. The bGF approach also allows one to examine other electronic properties such as the tunneling density of states or the bulk-boundary correspondence expected for topological phases [64][65][66].…”

“…In the present work, we extend and generalize the bGF approach for 1D or quasi-1D proximitized nanowires, which has been introduced in Refs. [59][60][61][62][63], along several directions. First, we demonstrate that a bGF construction in terms of the roots of a secular equation extended to complex momenta (as discussed in Ref.…”