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Since the breakthrough of twistronics a plethora of topological phenomena in two dimensions has appeared, specially relating topology and electronic correlations. These systems can be typically analyzed in terms of lattice models of increasing complexity using Greens function techniques. In this work we introduce a general method to obtain the boundary Greens function of such models taking advantage of the numerical Faddeev-LeVerrier algorithm to circumvent some analytical constraints of previous works. As an illustration we apply our formalism to analyze the edge features of Chern insulators, topological superconductors as the Kitaev square lattice and the Checkerboard lattice in the flat band topological regime. The efficiency of the method is demonstrated by comparison to standard recursive Greens function calculations.
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.
The introduction of topological invariants, ranging from insulators to metals, has provided new insights into the traditional classification of electronic states in condensed matter physics. A sudden change in the topological invariant at the boundar
Topological insulators and superconductors are characterized by their gapless boundary modes. In this paper, we develop a recursive approach to the boundary Green function which encodes this nontrivial boundary physics. Our approach describes the var
The Greens function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Greens functions are correlation functions, from which it is possible to extract in
A systematic study of the microscopic and thermodynamical properties of pure neutron matter at finite temperature within the Self-Consistent Greens Function approach is performed. The model dependence of these results is analyzed by both comparing th