2D topological matter from a boundary Green's functions perspective: Faddeev-LeVerrier algorithm implementation

Abstract

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 Green's function techniques. In this work we introduce a general method to obtain the boundary Green's 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 Green's function calculations.

10 pages, 6 figures

References in corpus (8)

• Nearly-flat bands with nontrivial topology
• Twistronics: Manipulating the Electronic Properties of Two-dimensional Layered Structures through their Twist Angle
• Simplified topological invariants for interacting insulators
• Transport in superlattices on single layer graphene
• Microscopic theory of the proximity effect in superconductor-graphene nanostructures
• Josephson effect in multiterminal topological junctions
• Elementary band representations for the single-particle Green's function of interacting topological insulators
• Transport and spectral properties of magic angle twisted bilayer graphene junctions based on local orbital models

Cited by in corpus (4)

• Interplay between Majorana and Shiba states in a minimal Kitaev chain coupled to a superconductor
• Intrinsic non-magnetic ${\varphi }_0$ Josephson junctions in twisted bilayer graphene
• Characterizing local Majorana properties using Andreev states
• Optimal Majoranas in Mesoscopic Kitaev Chains