“…Although, Berry curvature and the quantum metric have the same physical dimension and are often combined into a complexvalued quantity called the quantum geometric tensor with Berry curvature (quantum metric) as its imaginary (real) part, the role of the latter in determining the elec- * ajit.srivastava@emory.edu tronic properties of crystals is far less studied. Recently, its importance has been identified in a wide variety of phenomena including localization of Wannier functions [18][19][20], superconductivity and other phenomena in flat bands systems [21][22][23][24][25][26], nonlinear response [23,[27][28][29][30][31][32][33][34][35], fractional Chern insulators [36,37], current noise [38], magnetic susceptibility [39], quantum phase transitions [40][41][42][43], excitonic fine structure [13,14], and has been experimentally measured in photonic and atomic systems [44,45].…”