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We present a further development of methods for analytical calculations of Greens 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 Greens function of an open Kitaev chain and discover non-local fermionic corner states in a 2D p-wave superconductor.
In this note we present the Greens functions and density of states for the most frequently encountered 2D lattices: square, triangular, honeycomb, kagome, and Lieb lattice. Though the results are well know, we hope that their derivation performed in a uniform way is of some pedagogical value.
It is shown that the Greens function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of translation operator. Explicit examples are given for one- and two-dimensional lattices.
An analytical general analysis of the electromagnetic Dyadic Greens Function for two-dimensional sheet (or a very thin film) is presented, with an emphasis on on the case of graphene. A modified steepest descent treatment of the fields from a point d
We develop a theory of the quasi-static electrodynamic Greens function of deep subwavelength optical cavities containing an hyperbolic medium. We apply our theory to one-dimensional cavities realized using an hexagonal boron nitride and a patterned metallic substrate.
We present an alternative approach to studying topology in open quantum systems, relying directly on Greens functions and avoiding the need to construct an effective non-Hermitian Hamiltonian. We define an energy-dependent Chern number based on the e