Higher Chern numbers in multilayer ($\mathcal{N} \ge 2$) Lieb lattices: Topological transitions and quadratic band crossing lines

Saikat Banerjee; Avadh Saxena

doi:10.1103/PhysRevB.103.235125

paper

Higher Chern numbers in multilayer ( $N \geq 2$ ) Lieb lattices: Topological transitions and quadratic band crossing lines

arXiv:2008.03814 · doi:10.1103/PhysRevB.103.235125

Abstract

We consider a hitherto unexplored setting of stacked multilayer ( $N$ ) Lieb lattice which undergoes an unusual topological transition in the presence of intra-layer spin-orbit coupling (SOC). The specific stacking configuration induces an effective non-symmorphic 2D lattice structure, even though the constituent monolayer Lieb lattice is characterized by a symmorphic space group. This emergent non-symmorphicity leads to multiple doubly-degenerate bands extending over the edge of the Brillouin zone (i.e. Quadratic Band Crossing Lines). In the presence of intra-layer SOC, these doubly-degenerate bands typically form three $N$ -band subspaces, mutually separated by two band gaps. We analyze the topological properties of these multi-band subspaces, using specially devised Wilson loop operators to compute non-abelian Berry phases, in order to show that they carry a higher Chern number $N$ .

arXiv comment12 pages and 11 figures

Higher Chern numbers in multilayer ( $N \geq 2$ ) Lieb lattices: Topological transitions and quadratic band crossing lines

Abstract

References in corpus (46)

Cited by in corpus (2)

Higher Chern numbers in multilayer (N≥2) Lieb lattices: Topological transitions and quadratic band crossing lines

Abstract

References in corpus (46)

Cited by in corpus (2)

Higher Chern numbers in multilayer ( $N \geq 2$ ) Lieb lattices: Topological transitions and quadratic band crossing lines