Symmetry-enforced double Weyl points, multiband quantum geometry, and singular flat bands of doping-induced states at the Fermi level

TL;DR

This paper demonstrates how doping-induced states at the Fermi level can enforce topological features like double Weyl points and flat bands by symmetry reduction, supported by theoretical models and DFT calculations on various materials.

Contribution

It introduces models showing topological phenomena arising from doping-induced symmetry reduction, linking these to real material calculations.

Findings

Presence of double Weyl points and Chern bands in models

Identification of singular flat bands and Van Hove singularities

Correlation of topological features with specific doped materials

Abstract

Two common difficulties in the design of topological quantum materials are that the desired features lie too far from the Fermi level and are spread over a too-large energy range. Doping-induced states at the Fermi level provide a solution, where nontrivial topological properties are enforced by the doping-reduced symmetry. To show this, we consider a regular placement of dopants in a lattice of space group (SG) 176 ($P6\text{}_3/m$), which reduces the symmetry to SG 143 ($P3$). Our two- and four-band models feature double Weyl points, Chern bands, Van Hove singularities, nontrivial multiband quantum geometry due to mixed orbital character, and singular flat bands. We relate these features to density-functional theory (DFT) calculations for dopant and vacancy bands of lead apatite Pb$_{10}($PO$_4)_6$O and Pb$_{10}($PO$_4)_6($OH$)_2$, the van der Waals ferromagnet Cr$_2$Ge$_2$Te$_6$, the semiconductor SiC, and the 2D dichalcogenide MoS$_2$.