Quantum Metric in Step Response

Abstract

Quantum geometry of Bloch wavefunctions has gained considerable interest with the discovery of moiré materials that exhibit bands flattened by quantum interference. The quantum metric, the symmetric part of the quantum geometric tensor, influences several observables, such as the dielectric constant, superfluid stiffness and optical spectral weight. However, a direct measurement of the metric itself has remained elusive so far. In linear response functions such as the conductivity, the matrix elements of the metric typically appear convoluted with energy prefactors, preventing finding an observable that is directly proportional to the total quantum metric. The only observable that may extract it is the integrated optical spectral weight weighted by the inverse frequency, a generalized sum rule known as the Souza-Wilkens-Martin (SWM) sum rule. However, the sum rule comes with experimental challenges, such as requiring a large spectrum of frequency resolution. In this work, we propose relaxation from constrained equilibrium as a method to directly measure the symmetric part of the time-dependent quantum geometric tensor (tQGT), which at $t=0$ is the quantum metric. Additionally, we comment on other geometric properties of insulators that are absent in the frequency expansions of conductivity in insulators but can, in principle, be revealed in step response.

6 pages, 2 figures

References in corpus (8)

• Localization of interacting fermions at high temperature
• Orbital magnetization in periodic insulators
• Essay: Where Can Quantum Geometry Lead Us?
• Universal relation between energy gap and dielectric constant
• Topological bound on structure factor
• Drude weight of an interacting flat-band metal
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Cited by in corpus (8)

• Instantaneous response and quantum geometry of insulators
• Quantum Geometry and the Hidden Scales in Materials
• Scaling of the Integrated Quantum Metric in Disordered Topological Phases
• Quantum geometric bounds for observables: Linear responses, Drude weight, and orbital magnetization
• Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry
• Imaginary Time Formalism for Causal Nonlinear Response Functions
• Probing the Quantum Geometry of Correlated Metals using Optical Conductivity
• Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective