Théorique, numérique
In many topological semimetallic materials, the electrons behave as 3D Weyl/Dirac ultrarelativistic pseudo-spin-S quantum particles such that the electron's wavefunction carries a Berry curvature monopole that is at the origin of many anomalous low and high magnetic field magnetotransport properties. In a recent work we have predicted [1] that new kinds of massless quantum particle can exist, in which now the Berry curvature is a singular multipole (dipole, quadrupole, octupole). For such systems we have predicted distinct magnetotransport as compared to those of pseudospin-S Dirac/Weyl semimetals. We have also shown that “multifold dipole" semimetals naturally appear at the transition between two distinct topological Hopf- insulating phases [2]. The aim of this PhD project is to continue the exploration of this novel family of multifold semimetals associated to singular multipoles of Berry curvature, using analytical band-topological and numerical methods on tight-binding and continuum models. It consists to systematically construct models and explore their key features such as symmetries and topological properties and reveal their consequences on various physical properties. The project also envisions a challenging study of the stability of such semimetals to the breaking of symmetries and the electron-electron interactions. [1] A.Graf and F.Piéchon, Phys.Rev.B 108,115105 (2023). [2]A.Nelson,T.Neupert,A.Alexandradinata,and T.Bzdušek, Phys.Rev.B 106,075124(2022).