Quantum Metric Tensor & Berry Curvature

The quantum geometric tensor Q_μν = g_μν + i/2·Ω_μν encodes the geometry of Bloch states over the Brillouin zone. The real part g_μν is the quantum metric (relates to wavepacket spread), the imaginary part Ω is the Berry curvature (Hall conductivity). Here for a 2-band model H(k) = d(k)·σ.

Berry Curvature Ω(k)

Quantum Metric g_xx(k)

Band Structure E±(k)

Mass m 0.5 t_x 1.0 t_y 1.0

Chern number C = 0 | Total Berry curvature: 0 | Max |Ω|: —

Iris Lab · Quantum geometry · Berry curvature · Bloch bands