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.

Unification of Nonlinear Anomalous Hall Effect and Nonreciprocal Magnetoresistance in Metals by the Quantum Geometry.

The quantum geometry has significant consequences in determining transport and optical properties in quantum materials. Here, we use a semiclassical formalism coupled with perturbative corrections unifying the nonlinear anomalous Hall effect and nonreciprocal magnetoresistance (longitudinal resistance) from the quantum geometry. In the dc limit, both transverse and longitudinal nonlinear conductivities include a term due to the normalized quantum metric dipole. The quantum metric contribution is intrinsic and does not scale with the quasiparticle lifetime. We demonstrate the coexistence of a nonlinear anomalous Hall effect and nonreciprocal magnetoresistance in films of the doped antiferromagnetic topological insulator MnBi_{2}Te_{4}. Our work indicates that both longitudinal and transverse nonlinear transport provide a sensitive probe of the quantum geometry in solids.

Direct observation of the collective modes of the charge density wave in the kagome metal CsV3Sb5.

A recently discovered group of kagome metals AV[Formula: see text]Sb[Formula: see text] (A = K, Rb, Cs) exhibit a variety of intertwined unconventional electronic phases, which emerge from a puzzling charge density wave phase. Understanding of this charge-ordered parent phase is crucial for deciphering the entire phase diagram. However, the mechanism of the charge density wave is still controversial, and its primary source of fluctuations-the collective modes-has not been experimentally observed. Here, we use ultrashort laser pulses to melt the charge order in CsV[Formula: see text]Sb[Formula: see text] and record the resulting dynamics using femtosecond angle-resolved photoemission. We resolve the melting time of the charge order and directly observe its amplitude mode, imposing a fundamental limit for the fastest possible lattice rearrangement time. These observations together with ab initio calculations provide clear evidence for a structural rather than electronic mechanism of the charge density wave. Our findings pave the way for a better understanding of the unconventional phases hosted on the kagome lattice.

Quantum-metric-induced nonlinear transport in a topological antiferromagnet.

The Berry curvature and quantum metric are the imaginary part and real part, respectively, of the quantum geometric tensor, which characterizes the topology of quantum states1. The Berry curvature is known to generate a number of important transport phenomena, such as the quantum Hall effect and the anomalous Hall effect2,3; however, the consequences of the quantum metric have rarely been probed by transport measurements. Here we report the observation of quantum-metric-induced nonlinear transport, including both a nonlinear anomalous Hall effect and a diode-like non-reciprocal longitudinal response, in thin films of a topological antiferromagnet, MnBi2Te4. Our observations reveal that the transverse and longitudinal nonlinear conductivities reverse signs when reversing the antiferromagnetic order, diminish above the Néel temperature and are insensitive to disorder scattering, thus verifying their origin in the band-structure topology. They also flip signs between electron- and hole-doped regions, in agreement with theoretical calculations. Our work provides a means to probe the quantum metric through nonlinear transport and to design magnetic nonlinear devices.

General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect.

Can a generic magnetic insulator exhibit a Hall current? The quantum anomalous Hall effect (QAHE) is one example of an insulating bulk carrying a quantized Hall conductivity while insulators with zero Chern number present zero Hall conductance in the linear response regime. Here, we find that a general magnetic insulator possesses a nonlinear Hall conductivity quadratic to the electric field if the system breaks inversion symmetry, which can be identified as a new type of multiferroic coupling. This conductivity originates from an induced orbital magnetization due to virtual interband transitions. We identify three contributions to the wavepacket motion, a velocity shift, a positional shift, and a Berry curvature renormalization. In contrast to the crystalline solid, we find that this nonlinear Hall conductivity vanishes for Landau levels of a 2D electron gas, indicating a fundamental difference between the QAHE and the integer quantum Hall effect.

Para-hydrodynamics from weak surface scattering in ultraclean thin flakes.

Electron hydrodynamics typically emerges in electron fluids with a high electron-electron collision rate. However, new experiments with thin flakes of WTe2 have revealed that other momentum-conserving scattering processes can replace the role of the electron-electron interaction, thereby leading to a novel, so-called para-hydrodynamic regime. Here, we develop the kinetic theory for para-hydrodynamic transport. To this end, we consider a ballistic electron gas in a thin three-dimensional sheet where the momentum-relaxing (lmr) and momentum-conserving (lmc) mean free paths are decreased due to boundary scattering from a rough surface. The resulting effective mean free path of the in-plane components of the electronic flow is then expressed in terms of microscopic parameters of the sheet boundaries, predicting that a para-hydrodynamic regime with lmr ≫ lmc emerges generically in ultraclean three-dimensional materials. Using our approach, we recover the transport properties of WTe2 in the para-hydrodynamic regime in good agreement with existing experiments.

Unconventional Superconductivity in Systems with Annular Fermi Surfaces: Application to Rhombohedral Trilayer Graphene.

We show that in a two-dimensional electron gas with an annular Fermi surface, long-range Coulomb interactions can lead to unconventional superconductivity by the Kohn-Luttinger mechanism. Superconductivity is strongly enhanced when the inner and outer Fermi surfaces are close to each other. The most prevalent state has chiral p-wave symmetry, but d-wave and extended s-wave pairing are also possible. We discuss these results in the context of rhombohedral trilayer graphene, where superconductivity was recently discovered in regimes where the normal state has an annular Fermi surface. Using realistic parameters, our mechanism can account for the order of magnitude of T_{c}, as well as its trends as a function of electron density and perpendicular displacement field. Moreover, it naturally explains some of the outstanding puzzles in this material, that include the weak temperature dependence of the resistivity above T_{c}, and the proximity of spin singlet superconductivity to the ferromagnetic phase.

Half- and quarter-metals in rhombohedral trilayer graphene.

Ferromagnetism is most common in transition metal compounds where electrons occupy highly localized d orbitals. However, ferromagnetic order may also arise in low-density two-dimensional electron systems1-5. Here we show that gate-tuned van Hove singularities in rhombohedral trilayer graphene6 drive spontaneous ferromagnetic polarization of the electron system into one or more spin and valley flavours. Using capacitance and transport measurements, we observe a cascade of transitions tuned to the density and electronic displacement field between phases in which quantum oscillations have fourfold, twofold or onefold degeneracy, associated with a spin- and valley-degenerate normal metal, spin-polarized 'half-metal', and spin- and valley-polarized 'quarter-metal', respectively. For electron doping, the salient features of the data are well captured by a phenomenological Stoner model7 that includes valley-anisotropic interactions. For hole filling, we observe a richer phase diagram featuring a delicate interplay of broken symmetries and transitions in the Fermi surface topology. Finally, we introduce a moiré superlattice using a rotationally aligned hexagonal boron nitride substrate5,8. Remarkably, we find that the isospin order is only weakly perturbed, with the moiré potential catalysing the formation of topologically nontrivial gapped states whenever itinerant half- or quarter-metal states occur at half- or quarter-superlattice band filling. Our results show that rhombohedral graphene is an ideal platform for well-controlled tests of many-body theory, and reveal magnetism in moiré materials4,5,9,10 to be fundamentally itinerant in nature.

Specific Heat of a Quantum Critical Metal.

We investigate the specific heat c, near an Ising nematic quantum critical point (QCP), using sign problem-free quantum Monte Carlo simulations. Cooling towards the QCP, we find a broad regime of temperature where c/T is close to the value expected from the noninteracting band structure, even for a moderately large coupling strength. At lower temperature, we observe a rapid rise of c/T, followed by a drop to zero as the system becomes superconducting. The spin susceptibility begins to drop at roughly the same temperature where the enhancement of c/T onsets, most likely due to the opening of a gap associated with superconducting fluctuations. These findings suggest that superconductivity and non-Fermi liquid behavior (manifested in an enhancement of the effective mass) onset at comparable energy scales. We support these conclusions with an analytical perturbative calculation.

Chirality-Induced Giant Unidirectional Magnetoresistance in Twisted Bilayer Graphene.

Twisted bilayer graphene (TBG) exhibits fascinating correlation-driven phenomena like the superconductivity and Mott insulating state, with flat bands and a chiral lattice structure. We find by quantum-transport calculations that the chirality leads to a giant unidirectional magnetoresistance (UMR) in TBG, where the unidirectionality refers to the resistance change under the reversal of the direction of current or magnetic field. We point out that flat bands significantly enhance this effect. The UMR increases quickly upon reducing the twist angle, and reaches about 20% for an angle of 1.5° in a 10 T in-plane magnetic field. We propose the band structure topology (asymmetry), which leads to a direction-sensitive mean free path, as a useful way to anticipate the UMR effect. The UMR provides a probe for chirality and band flatness in the twisted bilayers.

Nonvanishing Subgap Photocurrent as a Probe of Lifetime Effects.

For semiconductors and insulators, it is commonly believed that in-gap transitions into nonlocalized states are smoothly suppressed in the clean limit; i.e., at zero temperature, their contribution vanishes due to the unavailability of states. We present a novel type of subgap response which shows that this intuition does not generalize beyond linear response. Namely, we find that the dc current due to the bulk photovoltaic effect can be finite and mostly temperature independent in an allowed window of subgap transitions. We expect that a moderate range of excitation energies lies between the bulk energy gap and the mobility edge where this effect is observable. Using a simplified relaxation time model for the band broadening, we find the subgap dc current to be temperature independent for noninteracting systems but temperature dependent for strongly interacting systems. Thus, the subgap response may be used to distinguish whether a state is single-particle localized or many-body localized.

Visualizing Poiseuille flow of hydrodynamic electrons.

Hydrodynamics, which generally describes the flow of a fluid, is expected to hold even for fundamental particles such as electrons when inter-particle interactions dominate1. Although various aspects of electron hydrodynamics have been revealed in recent experiments2-11, the fundamental spatial structure of hydrodynamic electrons-the Poiseuille flow profile-has remained elusive. Here we provide direct imaging of the Poiseuille flow of an electronic fluid, as well as a visualization of its evolution from ballistic flow. Using a scanning carbon nanotube single-electron transistor12, we image the Hall voltage of electronic flow through channels of high-mobility graphene. We find that the profile of the Hall field across the channel is a key physical quantity for distinguishing ballistic from hydrodynamic flow. We image the transition from flat, ballistic field profiles at low temperatures into parabolic field profiles at elevated temperatures, which is the hallmark of Poiseuille flow. The curvature of the imaged profiles is qualitatively reproduced by Boltzmann calculations, which allow us to create a 'phase diagram' that characterizes the electron flow regimes. Our results provide direct confirmation of Poiseuille flow in the solid state, and enable exploration of the rich physics of interacting electrons in real space.

Unified Description of the Classical Hall Viscosity.

In the absence of time-reversal symmetry, viscous electron flow hosts a number of interesting phenomena, of which we focus here on the Hall viscosity. Taking a step beyond the hydrodynamic definition of the Hall viscosity, we derive a generalized relation between the Hall viscosity and the transverse electric field using a kinetic equation approach. We explore two different geometries where the Hall viscosity is accessible to measurement. For hydrodynamic flow of electrons in a narrow channel, we find that the viscosity may be measured by a local probe of the transverse electric field near the center of the channel. Ballistic flow, on the other hand, is dominated by boundary effects. In a Corbino geometry, viscous effects arise not from boundary friction but from the circular flow pattern of the Hall current. In this geometry, we introduce a viscous Hall angle that remains well defined throughout the crossover from ballistic to hydrodynamic flow and captures the bulk viscous response of the fluid.

Switchable magnetic bulk photovoltaic effect in the two-dimensional magnet CrI3.

The bulk photovoltaic effect (BPVE) rectifies light into the dc current in a single-phase material and attracts the interest to design high-efficiency solar cells beyond the pn junction paradigm. Because it is a hot electron effect, the BPVE surpasses the thermodynamic Shockley-Queisser limit to generate above-band-gap photovoltage. While the guiding principle for BPVE materials is to break the crystal centrosymmetry, here we propose a magnetic photogalvanic effect (MPGE) that introduces the magnetism as a key ingredient and induces a giant BPVE. The MPGE emerges from the magnetism-induced asymmetry of the carrier velocity in the band structure. We demonstrate the MPGE in a layered magnetic insulator CrI3, with much larger photoconductivity than any previously reported results. The photocurrent can be reversed and switched by controllable magnetic transitions. Our work paves a pathway to search for magnetic photovoltaic materials and to design switchable devices combining magnetic, electronic, and optical functionalities.