Gravitational Response of Topological Quantum States of Matter

There is an active quest to discover new topologically quantized physical properties of topological quantum states of matter, similar to the quantized Hall conductance in quantum Hall states. The motivation is to discover not only new fundamental physics in exotic materials, but also technologically desirable robust physical properties which are unaffected by modest disorder and manufacturing variations. We establish that a novel topological response is found in a wide variety of topological quantum states — we term this the topological gravitational response — and comment on the still-unknown topological physics underlying the quantization of the corresponding response coefficient, the gravitational coupling constant.