Gravitational Response of Topological Quantum States of Matter
arXiv:2204.06268 · doi:10.1103/PhysRevB.107.195403
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.
References in corpus (30)
- Quantum Spin Hall Effect in Graphene
- Topological Order and the Quantum Spin Hall Effect
- Topological Photonics
- Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
- Topology and Dynamics of Active Nematic Vesicles
- Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
- Viscosity of Quantum Hall Fluids
- Two-Dimensional Matter: Order, Curvature and Defects
- Hall Viscosity and Electromagnetic Response
- Nematic textures in spherical shells
- Fractional disclination charge in two-dimensional symmetric topological crystalline insulators
- Probing the Berry Curvature and Fermi Arcs of a Weyl Circuit
- Quantum Spin Dynamics with Pairwise-Tunable, Long-Range Interactions
- Geometrical engineering of a two-bands Chern insulator in two dimensions with arbitrary topological index
- Viscosity of strongly interacting quantum fluids: spectral functions and sum rules
- Shift insulators: rotation-protected two-dimensional topological crystalline insulators
- Lorentz shear modulus of a two-dimensional electron gas at high magnetic field
- Quantum mechanics and quantum Hall effect on Riemann surfaces
- Lorentz shear modulus of fractional quantum Hall states
- Intrinsic anomalous Hall conductivity in a nonuniform electric field
- Geometric Theory of Columnar Phases on Curved Substrates
- Corner states of topological fullerenes
- Fractional charge and inter-Landau level states at points of singular curvature
- Disclination classes, fractional excitations, and the melting of quantum liquid crystals
- Uhlmann number in translational invariant systems
- Fractional Chern Insulators in Singular Geometries
- Chern Insulators on Singular Geometries
- Defect absorption and emission for -atic liquid crystals on cones
- Generating and detecting topological phases with higher Chern number
- Geometric response of quantum Hall states to electric fields