Tangent fermions: massless fermions on a lattice

Donís Vela, A. (2024)

Doctoral Thesis

In some condensed matter systems, such as the surface of a 3D topological insulator, the electrons are effectively massless and we must necessarily use the massless Dirac equation to describe them.
A very convenient way to numerically solve this equation is to discretise them. However, the Nielsen-Ninomiya theorem proves that if we try to do it naively, extra unphysical massless fermion species appear, giving rise to a number of undesired artefacts. This is known as fermion doubling, and the main focus of this thesis is to tackle this problem via the discretisation method of tangent fermions.
Chapters 2,3 and 4 are devoted to developing various aspects of this method. Chapters 5 and 6 are not directly related to the method of tangent fermions but still describe processes that arise in materials with a Dirac-like dispersion relation. In chapter 5, we study the effect a non-zero net supercurrent parallel to the edges of a topological superconductor. We find that the supercurrent can induce a "chirality inversion'' of the Majorana edge modes.
In the last chapter, we simulate the injection of "edge-vortices'' into a topological superconductor. These are a type of quasiparticles that can theoretically be used to realise a quantum computer.

• Topological states of matter
• Quantum transport
• Dirac fermions
• Non-abelian braiding
• Majorana

• All authors: Donís Vela, A.
• Supervisor: Beenakker, C.W.J.; Tworzydło, J.
• Committee: Tong, D.; Wimmer, M.; Achúcarro, A.; Cheianov, V.; Molen, S.J. van der
• Qualification: Doctor (dr.)
• Awarding Institution: Leiden Institute of Physics (LION), Faculty of Science, Leiden University
• Date: 2024-07-03