# Pedagogical introduction to vertex, domain wall, and kink

Recently, Majorana fermion becomes hot in condensed matter physics. The concepts: vertex, domain wall, and kink often appear in these articles about Majorana fermion. I have no idea about the different characteristic of these concepts.

Please pedagogical introduction these definition and list the common and different characteristic of the vertex, domain wall, and kink in detail.

## 1 Answer

I think a good introduction are these two talks:

Roman Jackiw: "Fractional charge, Majorana fermions: the Physics of isolated zero modes" - 1

and

Fabian Hassler Lecture 1: Topological quantum computing

A short summary is that for 1D systems Majorana bound states can exist at domain walls. Let say you have a long wire and you can divide it in two subsystems, where the left one is in the trivial phase and the right one in the non-trivial phase. A domain wall is in principle the transition region between the trivial and non-trivial phase and there can a Majorana bound state emerge (a good explanation is in the talk by Fabian Hassler). I think that a kink is the quantum field theory name of a domain wall, but I can be wrong. A Vortex is the same but in two dimension (here you can read the excellent paper by cond-mat/9906453).