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Revealing Quantum Geometry in Nonlinear Quantum Materials
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Berry curvature-related topological phenomena have been a central topic in condensed matter physics. Yet, until recently other quantum geometric quantities such as the metric and connection received only little attention due to the relatively few effects which have been documented for them. This review gives a modern perspective how quantum geometric quantities naturally enter the nonlinear responses of quantum materials and demonstrate their deep connection with excitation energy, lifetimes, symmetry, and corresponding physical processes. The multitude of nonlinear responses can be subdivided into nonlinear optical effects, subgap responses, and nonlinear transport phenomena. Such a distinction by energy scales facilitates an intuitive understanding of the underlying electronic transitions, giving rise to a unified picture of the electron motion beyond linear order. The well-known injection and shift currents constitute the main resonances in the optical regime. Exploiting their respective lifetime and symmetry dependencies, this review elucidates how these resonances can be distinguished by a corresponding quantum geometric quantity that shares the same symmetry. This is followed by a brief exposition of the role of quasiparticle lifetimes for nonlinear subgap responses, which presents a window into the microscopic short-term dynamics as well as the ground state correlation and localization. We conclude with an account of the anomalous motion due to the Berry curvature dipole and quantum metric dipole in nonlinear transport, clarifying the correspondence between physical observables and the underlying mechanisms. This review highlights the close relationship between quantum geometry and nonlinear response, showing the way towards promising probes of quantum geometry and enabling novel avenues to characterize complex materials.
Forward citations
Cited by 7 Pith papers
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Quantum Geometric Injection and Shift Optical Forces Drive Coherent Phonons
The paper derives quantum-geometric injection and shift Raman forces, shows the shift force emerges impulsively when time-reversal symmetry is broken, and demonstrates strong tunability in the bilayer Haldane model.
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Modulation of quantum geometry and its coupling to pseudo-electric field by dynamic strain
Oscillatory strain modulates the Berry curvature dipole and produces a pseudo-electric field in bilayer graphene stacks, detected as Hall voltages at mixed strain and current frequencies.
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Sliding-tuned Quantum Geometry in Moir\'e Systems: Nonlinear Hall Effect and Quantum Metric Control
Interlayer sliding in multi-twist moiré systems acts as a tuning knob for Berry curvature and quantum metric, enabling a sliding-driven nonlinear Hall effect and quantum-metric control for testing fractional Chern ins...
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Superdielectrics: Disorder-induced perfect screening in insulators
Bond-disordered chiral insulators, including SSH chains and vacancy-doped Kekulé graphene, can have a divergent static susceptibility with a finite quantum metric and zero dc conductivity, a regime the authors call su...
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Probing quantum geometry with two-dimensional nonlinear optical spectroscopy
Two-dimensional coherent spectroscopy can isolate and measure the imaginary part of the multi-band quantum connection through the diagonal second-order conductivity under time-reversal symmetry.
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Geometric Bloch oscillations and transverse displacement in flat band systems
In flat bands, inhomogeneous electric fields produce wavepacket oscillations and transverse drift driven purely by quantum geometry, not by dispersion.
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Quantum Geometry Phenomena in Condensed Matter Systems
Quantum geometry, especially the quantum metric, is surveyed as a unifying framework for a wide range of transport and optical phenomena, with experimental confirmation in several materials.
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