We propose various tight-binding models with arbitrary Chern number $n$, constructed from one-dimensional (1D) tight-binding models with winding number $m$, where $n$ is divisible by $m$. Our approach relies on the Thouless adiabatic charge pumping mechanism applied to 1D insulators, where the cyclic time parameter is reinterpreted as an additional momentum dimension. Equivalently, this yields protocols for adiabatically pumping $n$ charges per cycle in a 1D lattice with winding number $m$. As a concrete example, we use an extended Su-Schrieffer-Heeger (SSH) model with long-range hoppings, which allows for arbitrary winding numbers. By promoting the cyclic parameter to a momentum coordinate, we generalize this 1D model to two dimensions (2D), producing a square-lattice model with an arbitrary Chern number. Furthermore, we derive the full real-space Hamiltonians for other lattice geometries, including hexagonal and triangular lattices, by deforming the square lattice. We analyze the role of lattice geometry and identify the simplest Chern insulator models with rotational symmetry—both with and without spin degrees of freedom. This provides alternatives to the Haldane model for realizing Chern insulators and generalizes the construction to arbitrary Chern numbers.

Close

PrevNext

View figure in article

• Edge states
• Electronic structure
• Symmetry protected topological states
• Topological insulators
• Topological phase transition
• Topological phases of matter