A general algorithm for computing bound states in infinite tight-binding systems

Abstract

We propose a robust and efficient algorithm for computing bound states of infinite tight-binding systems that are made up of a finite scattering region connected to semi-infinite leads. Our method uses wave matching in close analogy to the approaches used to obtain propagating states and scattering matrices. We show that our algorithm is robust in presence of slowly decaying bound states where a diagonalization of a finite system would fail. It also allows to calculate the bound states that can be present in the middle of a continuous spectrum. We apply our technique to quantum billiards and the following topological materials: Majorana states in 1D superconducting nanowires, edge states in the 2D quantum spin Hall phase, and Fermi arcs in 3D Weyl semimetals.

21 pages, 13 figures, minors changes according to the referees comments, https://scipost.org/submissions/1711.08250v1/

References in corpus (8)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Decoherence-protected quantum gates for a hybrid solid-state spin register
• Quantum Monte-Carlo for correlated out-of-equilibrium nanoelectronics devices
• A generalization of Bloch's theorem for arbitrary boundary conditions: Theory
• Andreev billiards
• Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions
• Weyl-Majorana solenoid

Cited by in corpus (10)

• Linear Scaling Quantum Transport Methodologies
• Tkwant: a software package for time-dependent quantum transport
• Amorphous topological phases protected by continuous rotation symmetry
• Control of Andreev bound states using superconducting phase texture
• Role of the quasi-particles in an electric circuit with Josephson junctions
• Pushing the limit of quantum transport simulations
• 2D topological matter from a boundary Green's functions perspective: Faddeev-LeVerrier algorithm implementation
• Bound states in and out of the continuum in nanoribbons with wider sections: A novel recursive S-matrix method
• Robust Topological Bound States in the Continuum in a Quantum Hall Bar with an Anti-dot
• Interplay between evanescent scattering modes and finite dispersion in superconducting junctions