Nonreciprocal Directional Dichroism Induced by the Quantum Metric Dipole

Geometric Stiffness in Interlayer Exciton Condensates

Recent experiments have confirmed the presence of interlayer excitons in the ground state of transition metal dichalcogenide bilayers. The interlayer excitons are expected to show remarkable transport properties when they undergo Bose condensation. In this Letter, we demonstrate that quantum geometry of Bloch wave functions plays an important role in the phase stiffness of the interlayer exciton condensate. Notably, we identify a geometric contribution that amplifies the stiffness, leading to the formation of a robust condensate with an increased Berezinskii-Kosterlitz-Thouless temperature. Our results have direct implications for the ongoing experimental efforts on interlayer excitons in materials that have nontrivial quantum geometry. We provide estimates for the geometric contribution in transition metal dichalcogenide bilayers through a realistic continuum model with gated Coulomb interaction, and find that the substantially increased stiffness may allow an interlayer exciton condensate to be realized at amenable experimental conditions.

The quantum geometric origin of capacitance in insulators

In band insulators, without a Fermi surface, adiabatic transport can exist due to the geometry of the ground state wavefunction. Here we show that for systems driven at a small but finite frequency ω, transport likewise depends sensitively on quantum geometry. We make this statement precise by expressing the Kubo formula for conductivity as the variation of the time-dependent polarization with respect to the applied field. We find that at linear order in frequency, the longitudinal conductivity results from an intrinsic capacitance determined by the ratio of the quantum metric and the spectral gap, establishing a fundamental link between the dielectric response and the quantum metric of insulators. We demonstrate that quantum geometry is responsible for the electronic contribution to the dielectric constant in a wide range of insulators, including the free electron gas in a quantizing magnetic field, for which we show the capacitance is quantized. We also study gapped bands of hBN-aligned twisted bilayer graphene and obstructed atomic insulators such as diamond. In the latter, we find its abnormally large refractive index to have a topological origin.

Nonlinear optical diode effect in a magnetic Weyl semimetal

Diode effects are of great interest for both fundamental physics and modern technologies. Electrical diode effects (nonreciprocal transport) have been observed in Weyl systems. Optical diode effects arising from the Weyl fermions have been theoretically considered but not probed experimentally. Here, we report the observation of a nonlinear optical diode effect (NODE) in the magnetic Weyl semimetal CeAlSi, where the magnetization introduces a pronounced directionality in the nonlinear optical second-harmonic generation (SHG). We demonstrate a six-fold change of the measured SHG intensity between opposite propagation directions over a bandwidth exceeding 250 meV. Supported by density-functional theory, we establish the linearly dispersive bands emerging from Weyl nodes as the origin of this broadband effect. We further demonstrate current-induced magnetization switching and thus electrical control of the NODE. Our results advance ongoing research to identify novel nonlinear optical/transport phenomena in magnetic topological materials and further opens new pathways for the unidirectional manipulation of light.

Spin-Triplet Superconductivity from Quantum-Geometry-Induced Ferromagnetic Fluctuation

We show that quantum geometry induces ferromagnetic fluctuation resulting in spin-triplet superconductivity. The criterion for ferromagnetic fluctuation is clarified by analyzing contributions from the effective mass and quantum geometry. When the non-Kramers band degeneracy is present near the Fermi surface, the Fubini-Study quantum metric strongly favors ferromagnetic fluctuation. Solving the linearized gap equation with the effective interaction obtained by the random phase approximation, we show that the spin-triplet superconductivity is mediated by quantum-geometry-induced ferromagnetic fluctuation.

Berry-Curvature Engineering for Nonreciprocal Directional Dichroism in Two-Dimensional Antiferromagnets

In two-dimensional antiferromagnets, we find that the mixed Berry curvature can be attributed as the geometrical origin of the nonreciprocal directional dichroism (NDD), which refers to the difference in light absorption between opposite propagation directions. This Berry curvature is closely related to the uniaxial strain in accordance with the symmetry constraint, leading to a highly tunable NDD, whose sign and strength can be tuned via strain direction. We choose the lattice model of MnBi_{2}Te_{4} as a concrete example. The coupling between mixed Berry curvature and strain also suggests the magnetic quadrupole of the Bloch wave packet as the macroscopic order parameter probed by the NDD in two dimensions, which is distinct from the multiferroic order P×M or the spin toroidal and quadrupole order within a unit cell in previous studies. Our work paves the way for the Berry-curvature engineering for optical nonreciprocity in two-dimensional antiferromagnets.

Mapping the intrinsic photocurrent streamlines through micromagnetic heterostructure devices

Photocurrent in quantum materials is often collected at global contacts far away from the initial photoexcitation. This collection process is highly nonlocal. It involves an intricate spatial pattern of photocurrent flow (streamlines) away from its primary photoexcitation that depends sensitively on the configuration of current collecting contacts as well as the spatial nonuniformity and tensor structure of conductivity. Direct imaging to track photocurrent streamlines is challenging. Here, we demonstrate a microscopy method to image photocurrent streamlines through ultrathin heterostructure devices comprising platinum on yttrium iron garnet (YIG). We accomplish this by combining scanning photovoltage microscopy with a uniform rotating magnetic field. Here, local photocurrent is generated through a photo-Nernst type effect with its direction controlled by the external magnetic field. This enables the mapping of photocurrent streamlines in a variety of geometries that include conventional Hall bar-type devices, but also unconventional wing-shaped devices called electrofoils. In these, we find that photocurrent streamlines display contortion, compression, and expansion behavior depending on the shape and angle of attack of the electrofoil devices, much in the same way as tracers in a wind tunnel map the flow of air around an aerodynamic airfoil. This affords a powerful tool to visualize and characterize charge flow in optoelectronic devices.

Topological Circular Dichroism in Chiral Multifold Semimetals

Uncovering the physical contents of the nontrivial topology of quantum states is a critical problem in condensed matter physics. Here, we study the topological circular dichroism in chiral semimetals using linear response theory and first-principles calculations. We show that, when the low-energy spectrum respects emergent SO(3) rotational symmetry, topological circular dichroism is forbidden for Weyl fermions, and thus is unique to chiral multifold fermions. This is a result of the selection rule that is imposed by the emergent symmetry under the combination of particle-hole conjugation and spatial inversion. Using first-principles calculations, we predict that topological circular dichroism occurs in CoSi for photon energy below about 0.2 eV. Our Letter demonstrates the existence of a response property of unconventional fermions that is fundamentally different from the response of Dirac and Weyl fermions, motivating further study to uncover other unique responses.

Quantum Plasmonic Nonreciprocity in Parity-Violating Magnets

The optical responses of metals are often dominated by plasmonic resonances, that is, the collective oscillations of interacting electron liquids. Here we unveil a new class of plasmons─quantum metric plasmons (QMPs)─that arise in a wide range of parity-violating magnetic metals. In these materials, a dipolar distribution of the quantum metric (a fundamental characteristic of Bloch wave functions) produces intrinsic nonreciprocal bulk plasmons. Strikingly, QMP nonreciprocity manifests even when the single-particle dispersion is symmetric: QMPs are sensitive to time-reversal and parity violations hidden in the Bloch wave function. In materials with asymmetric single-particle dispersions, quantum metric dipole induced nonreciprocity can continue to dominate at large frequencies. We anticipate that QMPs can be realized in a wide range of parity-violating magnets, including twisted bilayer graphene heterostructures, where quantum geometric quantities can achieve large values.

Theory of optical axion electrodynamics and application to the Kerr effect in topological antiferromagnets

Emergent axion electrodynamics in magneto-electric media is expected to provide novel ways to detect and control material properties with electromagnetic fields. However, despite being studied intensively for over a decade, its theoretical understanding remains mostly confined to the static limit. Here, we introduce a theory of axion electrodynamics at general frequencies. We define a proper optical axion magneto-electric coupling through its relation to optical surface Hall conductivity and provide ways to calculate it in lattice systems. By employing our formulas, we show that axion electrodynamics can lead to a significant Kerr effect in thin-film antiferromagnets at wavelengths that are seemingly too long to resolve the spatial modulation of magnetism. We identify the wavelength scale above which the Kerr effect is suppressed. Our theory is particularly relevant to materials like MnBi₂Te₄, a topological antiferromagnet whose magneto-electric response is shown here to be dominated by the axion contribution even at optical frequencies.

Resonant Second-Harmonic Generation as a Probe of Quantum Geometry

Nonlinear responses are actively studied as probes of topology and band geometric properties of solids. Here, we show that second harmonic generation serves as a probe of the Berry curvature, quantum metric, and quantum geometric connection. We generalize the theory of second harmonic generation to include Fermi surface effects in metallic systems, and finite scattering timescale. In doped materials the Fermi surface and Fermi sea cause all second harmonic terms to exhibit resonances, and we identify two novel contributions to the second harmonic signal: a double resonance due to the Fermi surface and a higher-order pole due to the Fermi sea. We discuss experimental observation in the monolayer of time reversal symmetric Weyl semimetal WTe_{2} and the parity-time reversal symmetric topological antiferromagnet CuMnAs.

Intrinsic Anomalous Hall Conductivity in a Nonuniform Electric Field

We study how the intrinsic anomalous Hall conductivity is modified in two-dimensional crystals with broken time-reversal symmetry due to weak inhomogeneity of the applied electric field. Focusing on a clean noninteracting two-band system without band crossings, we derive the general expression for the Hall conductivity at small finite wave vector q to order q^{2}, which governs the Hall response to the second gradient of the electric field. Using the Kubo formula, we show that the answer can be expressed through the Berry curvature, Fubini-Study quantum metric, and the rank-3 symmetric tensor which is related to the quantum geometric connection and physically corresponds to the gauge-invariant part of the third cumulant of the position operator. We further compare our results with the predictions made within the semiclassical approach. By deriving the semiclassical equations of motion, we reproduce the result obtained from the Kubo formula in some limits. We also find, however, that the conventional semiclassical description in terms of the definite position and momentum of the electron is not fully consistent because of singular terms originating from the Heisenberg uncertainty principle. We thus present a clear example of a case when the semiclassical approach inherently suffers from the uncertainty principle, implying that it should be applied to systems in nonuniform fields with extra care.