Dimensionally hybrid Green's functions and density of states for interfaces

TL;DR

This paper derives an explicit energy-dependent Green's function for interface Hamiltonians that smoothly transition between two and three dimensions, providing a continuous density of states interpolation.

Contribution

It introduces a method to explicitly calculate Green's functions for hybrid dimensional interfaces, bridging 2D and 3D behaviors in density of states analysis.

Findings

Density of states interpolates between 2D and 3D regimes

Green's function explicitly derived for hybrid interfaces

Continuous transition in density of states across energy scales

Abstract

The energy dependent Green's function for an interface Hamiltonian which interpolates between two and three dimensions can be calculated explicitly. This yields an expression for the density of states on the interface which interpolates continuously between the two-dimensional behavior for high energies and the three-dimensional behavior for low energies.