Topological bands in metals

Abstract

In crystalline systems with a superstructure, the electron dispersion can form a nontrivial covering of the Brillouin zone. It is proved that the number of sheets in this covering and its monodromy are topological invariants under ambient isotopy. As a concrete manifestation of this nontrivial topology, we analyze three-sublattice models for 120$^\circ$-ordered helimagnets in one, two, and three dimensions. The two-dimensional system exhibits unconventional $f$-wave magnetism and a specific topological metal state characterized by a spin-textured, one-sheeted Fermi surface. The observable transport signatures of the topological metal and its potential experimental realization are briefly discussed.

Figures (5)

• Figure 1: 1D band structures and their topological classification. The right panels provide a schematic topological representation, depicting the Brillouin zone as a circle ($S^1$).
• Figure 2: Schematic views of 2D and 3D coverings: (a) plane representation of torus (base), (b) plane representation of a 3-sheeted covering over $T^2$, and (c) solid representation of a 3-sheeted covering over $T^3$. The sheets of covering spaces are distinguished by color and texture.
• Figure 3: Helical structures with the 120$^\circ$-order on (a) 1D, (b) 2D, and (c) 3D lattices. The magnetic field at the sites is indicated by color and arrows.
• Figure 4: The band structure in the tight-binding model for (a) 1D chain ($h_0=0.25$) and (b) 2D hexagonal ($h_0=1$) lattices. The average spin projection on the axis perpendicular to the magnetic plane is indicated by color and arrows: red and blue if $|\langle \hat{\mathbf{\sigma}}_z\rangle|>1/2$, green otherwise.
• Figure 5: Fermi surface in the 2D tight-binding model for Fermi levels corresponding to (a) $E_1$ and (b) $E_2$ in Fig. \ref{['f4']}b. The average spin projection is indicated in the same manner as in Fig. \ref{['f4']}.