For example, let's consider a quadratic fermionic Hamiltonian on a 2D lattice with translation symmetry, and assume that the Fourier transformed Hamiltonian is described by a $2\times2$ Hermitian ...
The first Chern number $\cal C$ is known to be related to various physical objects. Gauge fields are known as connections of some principle bundles. In particular, principle $U(1)$ bundle is said to ...
I am reading the famous and concise Thouless-Kohmoto-Nightingale-den Nijs (TKNN) paper Quantized Hall Conductance in a Two-Dimensional Periodic Potential, Phys. Rev. Lett. 49, 405–408 (1982), where I ...
In mathematics, the Chern number is defined in terms of the Chern class of a manifold. What is the exact definition of Chern number in condensed matter physics, i.e. quantum hall system?