Emergence and Control of Dirac and Weyl Fermions in Twistronic Platforms

In this talk I will explore new modalities for manipulating and creating Dirac and Weyl quasiparticles using twist engineering of 2D materials, focusing on unconventional superconductors and Γ-valley semiconductors. Beyond purely 2D platforms, examples of finite-thickness systems realizing tunable nodal fermions will be presented.

First, I will focus on superconducting systems, where Dirac points arise in the quasiparticle dispersions of nodal superconductors. In bilayers of nodal superconductors, twisting allows to control these Dirac points. In particular, the breaking of symmetries by the twist [1] and moire umklapp scattering [2] lead to the realization of tunable gapped phases with diverse topological properties. In finite-thickness flakes of nodal superconductors with N layers, current can be used to generate new Dirac points and drive topological transitions with the number of edge modes scaling as N^2 [3].

In the second part, I will discuss the potential to realize emergent nodal fermion physics in twisted semiconductor multilayers. Focusing on systems with band extrema at the Γ point of the Brillouin zone, I will show that the transformations of single-particle orbitals under twist allow for new terms in the electronic Hamiltonians [4]. In multilayer systems with continuously increasing twist (such as recently realized ``supertwisted spirals"), they suggest the possibility to realize Weyl fermions in the bulk limit. I will discuss the evolution of the electronic structure with increasing layer number and experimental approaches that can be used to probe it.