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Quantum Geometry in Quantum Materials
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Quantum geometry, characterized by the quantum geometric tensor, is pivotal in diverse physical phenomena in quantum materials. In condensed matter systems, quantum geometry refers to the geoemtric properties of Bloch states in the Brillouin zone. This pedagogical review provides an accessible introduction to the concept of quantum geometry, emphasizing its extensive implications across multiple domains. Specifically, we discuss the role of quantum geometry in optical responses, Landau levels, and fractional Chern insulators, as well as its influence on superfluid weight, spin stiffness, exciton condensates, electron-phonon coupling, etc. By integrating these topics, we underscore the pervasive significance of quantum geometry in understanding emergent behaviors in quantum materials. Finally, we present an outlook on open questions and potential future directions, highlighting the need for continued exploration in this rapidly developing field.
Forward citations
Cited by 13 Pith papers
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Perfect elliptic dichroism: Probing the metric of anisotropic quantum Hall droplets
Perfect elliptic dichroism is proposed as a direct diagnostic for the metric of anisotropic quantum Hall droplets, extending to ideal Chern bands via holomorphicity and to lattice models via renormalized emergent metrics.
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Ferromagnetism vs. Antiferromagnetism in Narrow-Band Systems: Competition Between Quantum Geometry and Band Dispersion
In narrow-band Hubbard models, quantum geometry drives ferromagnetism and band dispersion drives antiferromagnetism, with the transition set by a competition between the quantum metric and a dispersion scale.
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Nonlinear Magnetoelectric Edelstein Effect
A new magnetoelectric Edelstein effect generates spin magnetization bilinear in electric and magnetic fields, with an intrinsic part allowed in time-reversal-invariant insulators and an extrinsic part sensitive to Née...
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Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective
The Bures distance between an initial and a time-evolved density matrix defines a time-dependent quantum metric and connection, extending many-body quantum geometry beyond the quantum metric to higher-order correlatio...
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Chiral superconductivity near a fractional Chern insulator
In a minimal model of repulsive spinless electrons in a Landau level, melting a fractional Chern insulator by widening the band produces a chiral f-wave superconducting dome and a nearly degenerate re-entrant integer ...
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Long and short time linear response of metals: a geometric approach
For metals, the time-dependent quantum geometric tensor decomposes into a Drude-weight linear term and a divergent time-independent Fermi-surface term, and the ratio D/S1 distinguishes itinerant from bound charge at t...
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Identifying geometric third-order nonlinear transport in disordered materials
A catalog of 20 third-order nonlinear-transport mechanisms plus a scaling-law fingerprint table for identifying geometric vs. disorder-dominated responses in experiments.
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Effects of Electron Form Factor on Quasiparticle Interference in Twisted Bilayer Graphene
Quasiparticle interference patterns in twisted bilayer graphene directly encode the electron form factor, with chiral interlayer signals explained by the single-layer overlap matrix.
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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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Color and Transparency from Quantum Geometry
The perceived color and transparency of model materials can be changed purely by tuning the quantum geometry of Bloch wavefunctions, with the energy dispersion held fixed.
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Topological control of quantum speed limits
In a flat topological band, momentum-resolved quantum Fisher information is bounded below by the Chern number, so high-Chern materials may enhance metrological sensitivity.
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Imaginary Time Formalism for Causal Nonlinear Response Functions
Causal n-th order response functions are obtained, at every order, by analytic continuation of the corresponding imaginary-time Matsubara functions.
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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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