Formalism of general boundary conditions for continuum models and its application to Majorana bound states in generic 1D superconductors
Date/Time: 18:00 28-Jun-2021
Abstract:
Bound/edge/surface states are the key and most interesting physical manifestation of nontrivial bulk topology. Low-energy continuum models of topological systems are particularly appealing for the theoretical analysis due to the minimalistic simplicity of their bulk Hamiltonians. However, description of the boundary within such models can be challenging. I will present the formalism for continuum models that allows one to derive the boundary conditions of the most general possible form. Such general boundary conditions arise from the fundamental principle of the norm conservation of the wave function, which manifests at the boundary as the conservation of the probability current. When present, symmetry constraints can also naturally be incorporated into this formalism. As one application, I will present the analysis of Majorana bound states in 1D superconductors within this formalism. I will demonstrate that, in the case of odd number of Fermi surfaces, for the whole family of normal-reflection boundary conditions, which describes a generic interface of a superconductor with vacuum or an insulator, there always exists a Majorana bound state at the Fermi level, thus explicitly generalizing earlier demonstrations based on specific microscopic models.
Video
Authors
Kharitonov Maxim
(Presenter)
(no additional information)