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

Abstract

We consider a hitherto unexplored setting of stacked multilayer ($\mathcal{N}$) 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 $\mathcal{N}$-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 $\mathcal{N}$.

12 pages and 11 figures

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Cited by in corpus (2)

• Tight-binding model with sublattice-asymmetric spin-orbit coupling for square-net nodal line Dirac semimetals
• Topological phases of monolayer and bilayer depleted Lieb lattices