Gravitational Response of Topological Quantum States of Matter

TL;DR

This paper demonstrates that a broad class of topological quantum states of matter exhibit a quantized gravitational response, linking charge response to intrinsic spatial curvature, which advances understanding of their topological properties.

Contribution

It reveals that many lattice topological states have a topologically quantized gravitational coupling, extending quantum Hall insights to a wider class of topological materials.

Findings

Charge response to intrinsic spatial curvature is quantized.

The gravitational coupling constant is topologically quantized.

The charge-curvature relationship is linear up to maximum lattice curvature.

Abstract

Identifying novel topological properties of topological quantum states of matter, such as exemplified by the quantized Hall conductance, is a valuable step towards realizing materials with attractive topological attributes that guarantee their imperviousness to realistic imperfections, disorder and environmental disturbances. Is the gravitational coupling coefficient of topological quantum states of matter a promising candidate? Substantially building on well established results for quantum Hall states, using disclinations as tools for controlled creation of pristine spatial curvature free of undesirable artifacts such as would interfere with the electronic motion of interest, herein we report that a large class of lattice topological states of matter exhibit gravitational response, i.e., charge response to intrinsic spatial curvature. This phenomenon is characterized by a topologically quantized coupling constant. Remarkably, the charge-gravity relationship remains linear in the curvature, up to the maximum curvature achievable on the lattice, demonstrating absence of higher order nonlinear response. Our findings facilitate articulating the physical principles underlying the topological quantization of the gravitational coupling constant, in analogy with the insights offered by the Chern number description of the quantized Hall conductance.