Hydrodynamics is a general description for the flow of a fluid, and is expected to hold even for fundamental particles such as electrons when inter-particle interactions dominate. While various aspects of electron hydrodynamics were revealed in recent experiments, the fundamental spatial structure of hydrodynamic electrons, the Poiseuille flow profile, has remained elusive. In this work we provide the first real-space imaging of Poiseuille flow of an electronic fluid, as well as visualization of its evolution from ballistic flow. Utilizing a scanning nanotube single electron transistor, 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 temperature 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 long-sought, direct confirmation of Poiseuille flow in the solid state, and enable a new approach for exploring the rich physics of interacting electrons in real space.

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 CrI 3 , 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.

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To assess the strength of nematic fluctuations with a finite wave vector in a two-dimensional metal, we compute the static d-wave polarization function for tight-binding electrons on a square lattice. At Van Hove filling and zero temperature the function diverges logarithmically at q = 0. Away from Van Hove filling the ground state polarization function exhibits finite peaks at finite wave vectors. A nematic instability driven by a sufficiently strong attraction in the d-wave charge channel thus leads naturally to a spatially modulated nematic state, with a modulation vector that increases in length with the distance from Van Hove filling. Above Van Hove filling, for a Fermi surface crossing the magnetic Brillouin zone boundary, the modulation vector connects antiferromagnetic hot spots with collinear Fermi velocities.

Nonlinear optical response is well studied in the context of semiconductors and has gained a renaissance in studies of topological materials in the recent decade. So far it mainly deals with nonmagnetic materials and it is believed to root in the Berry curvature of the material band structure. In this work we revisit the general formalism for the second-order optical response and focus on the consequences of the time-reversal-symmetry (T) breaking, by a diagrammatic approach. We have identified three physical mechanisms to generate a DC photocurrent, i.e., the Berry curvature, a term closely related to the quantum metric, and the diabatic motion. All three effects can be understood intuitively from the anomalous acceleration. The first two terms are respectively the antisymmetric and symmetric parts of the quantum geometric tensor. The last term is due to the dynamical antilocalization that appears from the phase accumulation between time-reversed fermion loops. Additionally, we derive the semiclassical conductivity that includes both intra-and interband effects. We find that T breaking can lead to a greatly enhanced nonlinear anomalous Hall effect that is beyond the contribution by the Berry curvature dipole.