The Euler number of Bloch states manifold and the quantum phases in gapped fermionic systems
The Euler number of Bloch states manifold and the quantum phases in gapped fermionic systems
We propose a topological Euler number to characterize nontrivial topological phases of gapped fermionic systems, which originates from the Gauss-Bonnet theorem on the Riemannian structure of Bloch states established by the real part of the quantum geometric tensor in momentum space. Meanwhile, the imaginary part of the geometric tensor corresponds …