Direct observation of vortices in an electron fluid.

Vortices are the hallmarks of hydrodynamic flow. Strongly interacting electrons in ultrapure conductors can display signatures of hydrodynamic behaviour, including negative non-local resistance1-4, higher-than-ballistic conduction5-7, Poiseuille flow in narrow channels8-10 and violation of the Wiedemann-Franz law11. Here we provide a visualization of whirlpools in an electron fluid. By using a nanoscale scanning superconducting quantum interference device on a tip12, we image the current distribution in a circular chamber connected through a small aperture to a current-carrying strip in the high-purity type II Weyl semimetal WTe2. In this geometry, the Gurzhi momentum diffusion length and the size of the aperture determine the vortex stability phase diagram. We find that vortices are present for only small apertures, whereas the flow is laminar (non-vortical) for larger apertures. Near the vortical-to-laminar transition, we observe the single vortex in the chamber splitting into two vortices; this behaviour is expected only in the hydrodynamic regime and is not anticipated for ballistic transport. These findings suggest a new mechanism of hydrodynamic flow in thin pure crystals such that the spatial diffusion of electron momenta is enabled by small-angle scattering at the surfaces instead of the routinely invoked electron-electron scattering, which becomes extremely weak at low temperatures. This surface-induced para-hydrodynamics, which mimics many aspects of conventional hydrodynamics including vortices, opens new possibilities for exploring and using electron fluidics in high-mobility electron systems.

Long-range nontopological edge currents in charge-neutral graphene.

Van der Waals heterostructures display numerous unique electronic properties. Nonlocal measurements, wherein a voltage is measured at contacts placed far away from the expected classical flow of charge carriers, have been widely used in the search for novel transport mechanisms, including dissipationless spin and valley transport1-9, topological charge-neutral currents10-12, hydrodynamic flows13 and helical edge modes14-16. Monolayer1-5,10,15-19, bilayer9,11,14,20 and few-layer21 graphene, transition-metal dichalcogenides6,7 and moiré superlattices8,10,12 have been found to display pronounced nonlocal effects. However, the origin of these effects is hotly debated3,11,17,22-24. Graphene, in particular, exhibits giant nonlocality at charge neutrality1,15-19, a striking behaviour that has attracted competing explanations. Using a superconducting quantum interference device on a tip (SQUID-on-tip) for nanoscale thermal and scanning gate imaging25, here we demonstrate that the commonly occurring charge accumulation at graphene edges23,26-31 leads to giant nonlocality, producing narrow conductive channels that support long-range currents. Unexpectedly, although the edge conductance has little effect on the current flow in zero magnetic field, it leads to field-induced decoupling between edge and bulk transport at moderate fields. The resulting giant nonlocality at charge neutrality and away from it produces exotic flow patterns that are sensitive to edge disorder, in which charges can flow against the global electric field. The observed one-dimensional edge transport is generic and nontopological and is expected to support nonlocal transport in many electronic systems, offering insight into the numerous controversies and linking them to long-range guided electronic states at system edges.

Fizeau drag in graphene plasmonics.

Dragging of light by moving media was predicted by Fresnel1 and verified by Fizeau's celebrated experiments2 with flowing water. This momentous discovery is among the experimental cornerstones of Einstein's special relativity theory and is well understood3,4 in the context of relativistic kinematics. By contrast, experiments on dragging photons by an electron flow in solids are riddled with inconsistencies and have so far eluded agreement with the theory5-7. Here we report on the electron flow dragging surface plasmon polaritons8,9 (SPPs): hybrid quasiparticles of infrared photons and electrons in graphene. The drag is visualized directly through infrared nano-imaging of propagating plasmonic waves in the presence of a high-density current. The polaritons in graphene shorten their wavelength when propagating against the drifting carriers. Unlike the Fizeau effect for light, the SPP drag by electrical currents defies explanation by simple kinematics and is linked to the nonlinear electrodynamics of Dirac electrons in graphene. The observed plasmonic Fizeau drag enables breaking of time-reversal symmetry and reciprocity10 at infrared frequencies without resorting to magnetic fields11,12 or chiral optical pumping13,14. The Fizeau drag also provides a tool with which to study interactions and nonequilibrium effects in electron liquids.

Spin-orbit-driven band inversion in bilayer graphene by the van der Waals proximity effect.

Spin-orbit coupling (SOC) is the key to realizing time-reversal-invariant topological phases of matter1,2. SOC was predicted by Kane and Mele3 to stabilize a quantum spin Hall insulator; however, the weak intrinsic SOC in monolayer graphene4-7 has precluded experimental observation in this material. Here we exploit a layer-selective proximity effect-achieved via a van der Waals contact with a semiconducting transition-metal dichalcogenide8-21-to engineer Kane-Mele SOC in ultra clean bilayer graphene. Using high-resolution capacitance measurements to probe the bulk electronic compressibility, we find that SOC leads to the formation of a distinct, incompressible, gapped phase at charge neutrality. The experimental data agree quantitatively with a simple theoretical model in which the new phase results from SOC-driven band inversion. In contrast to Kane-Mele SOC in monolayer graphene, the inverted phase is not expected to be a time-reversal-invariant topological insulator, despite being separated from conventional band insulators by electric-field-tuned phase transitions where crystal symmetry mandates that the bulk gap must close22. Our electrical transport measurements reveal that the inverted phase has a conductivity of approximately e2/h (where e is the electron charge and h Planck's constant), which is suppressed by exceptionally small in-plane magnetic fields. The high conductivity and anomalous magnetoresistance are consistent with theoretical models that predict helical edge states within the inverted phase that are protected from backscattering by an emergent spin symmetry that remains robust even for large Rashba SOC. Our results pave the way for proximity engineering of strong topological insulators as well as correlated quantum phases in the strong spin-orbit regime in graphene heterostructures.

Nanoscale thermal imaging of dissipation in quantum systems.

Energy dissipation is a fundamental process governing the dynamics of physical, chemical and biological systems. It is also one of the main characteristics that distinguish quantum from classical phenomena. In particular, in condensed matter physics, scattering mechanisms, loss of quantum information or breakdown of topological protection are deeply rooted in the intricate details of how and where the dissipation occurs. Yet the microscopic behaviour of a system is usually not formulated in terms of dissipation because energy dissipation is not a readily measurable quantity on the micrometre scale. Although nanoscale thermometry has gained much recent interest, existing thermal imaging methods are not sensitive enough for the study of quantum systems and are also unsuitable for the low-temperature operation that is required. Here we report a nano-thermometer based on a superconducting quantum interference device with a diameter of less than 50 nanometres that resides at the apex of a sharp pipette: it provides scanning cryogenic thermal sensing that is four orders of magnitude more sensitive than previous devices-below 1 µK Hz-1/2. This non-contact, non-invasive thermometry allows thermal imaging of very low intensity, nanoscale energy dissipation down to the fundamental Landauer limit of 40 femtowatts for continuous readout of a single qubit at one gigahertz at 4.2 kelvin. These advances enable the observation of changes in dissipation due to single-electron charging of individual quantum dots in carbon nanotubes. They also reveal a dissipation mechanism attributable to resonant localized states in graphene encapsulated within hexagonal boron nitride, opening the door to direct thermal imaging of nanoscale dissipation processes in quantum matter.

Photoexcitation Cascade and Quantum-Relativistic Jets in Graphene.

In Dirac materials linear band dispersion blocks momentum-conserving interband transitions, creating a bottleneck for electron-hole pair production and carrier multiplication in the photoexcitation cascade. Here we show that the decays are unblocked and the bottleneck is relieved by subtle many-body effects involving multiple off-shell e-h pairs. The decays result from a collective behavior due to simultaneous emission of many soft pairs. We discuss characteristic signatures of the off-shell pathways, in particular the sharp angular distribution of secondary carriers, resembling relativistic jets in high-energy physics. The jets can be directly probed using solid-state equivalent of particle detectors. Collinear scattering enhances carrier multiplication, allowing for emission of as many as ∼10 secondary carriers per single absorbed photon.

Nonlocal Response and Anamorphosis: The Case of Few-Layer Black Phosphorus.

Few-layer black phosphorus was recently rediscovered as a narrow-bandgap atomically thin semiconductor, attracting unprecedented attention due to its interesting properties. One feature of this material that sets it apart from other atomically thin crystals is its structural in-plane anisotropy which manifests in strongly anisotropic transport characteristics. However, traditional angle-resolved conductance measurements present a challenge for nanoscale systems, calling for new approaches in precision studies of transport anisotropy. Here, we show that the nonlocal response, being exponentially sensitive to the anisotropy value, provides a powerful tool for determining the anisotropy in black phosphorus. This is established by combining measurements of the orientation-dependent nonlocal resistance response with the analysis based on the anamorphosis relations. We demonstrate that the nonlocal response can differ by orders of magnitude for different crystallographic directions even when the anisotropy is at most order-one, allowing us to extract accurate anisotropy values.

Coulomb drag mechanisms in graphene.

Recent measurements revealed an anomalous Coulomb drag in graphene, hinting at new physics at charge neutrality. The anomalous drag is explained by a new mechanism based on energy transport, which involves interlayer energy transfer, coupled to charge flow via lateral heat currents and thermopower. The old and new drag mechanisms are governed by distinct physical effects, resulting in starkly different behavior, in particular for drag magnitude and sign near charge neutrality. The new mechanism explains the giant enhancement of drag near charge neutrality, as well as its sign and anomalous sensitivity to the magnetic field. Under realistic conditions, energy transport dominates in a wide temperature range, giving rise to a universal value of drag which is essentially independent of the electron-electron interaction strength.

Self-sustaining dynamical nuclear polarization oscillations in quantum dots.

Early experiments on spin-blockaded double quantum dots revealed robust, large-amplitude current oscillations in the presence of a static (dc) source-drain bias. Despite experimental evidence implicating dynamical nuclear polarization, the mechanism has remained a mystery. Here we introduce a minimal albeit realistic model of coupled electron and nuclear spin dynamics which supports self-sustained oscillations. Our mechanism relies on a nuclear spin analog of the tunneling magnetoresistance phenomenon (spin-dependent tunneling rates in the presence of an inhomogeneous Overhauser field) and nuclear spin diffusion, which governs dynamics of the spatial profile of nuclear polarization. The proposed framework naturally explains the differences in phenomenology between vertical and lateral quantum dot structures as well as the extremely long oscillation periods.

Out-of-equilibrium criticalities in graphene superlattices.

In thermodynamic equilibrium, current in metallic systems is carried by electronic states near the Fermi energy, whereas the filled bands underneath contribute little to conduction. Here, we describe a very different regime in which carrier distribution in graphene and its superlattices is shifted so far from equilibrium that the filled bands start playing an essential role, leading to a critical-current behavior. The criticalities develop upon the velocity of electron flow reaching the Fermi velocity. Key signatures of the out-of-equilibrium state are current-voltage characteristics that resemble those of superconductors, sharp peaks in differential resistance, sign reversal of the Hall effect, and a marked anomaly caused by the Schwinger-like production of hot electron-hole plasma. The observed behavior is expected to be common to all graphene-based superlattices.

Generating entanglement and squeezed states of nuclear spins in quantum dots.

We present a scheme for achieving coherent spin squeezing of nuclear spin states in semiconductor quantum dots. The nuclear polarization dependence of the electron spin resonance generates a unitary evolution that drives nuclear spins into a collective entangled state. The polarization dependence of the resonance generates an area-preserving, twisting dynamics that squeezes and stretches the nuclear spin Wigner distribution without the need for nuclear spin flips. Our estimates of squeezing times indicate that the entanglement threshold can be reached in current experiments.

Giant spin-Hall effect induced by the Zeeman interaction in graphene.

We propose a new approach to generate and detect spin currents in graphene, based on a large spin-Hall response arising near the neutrality point in the presence of an external magnetic field. Spin currents result from the imbalance of the Hall resistivity for the spin-up and spin-down carriers induced by the Zeeman interaction, and do not involve a spin-orbit interaction. Large values of the spin-Hall response achievable in moderate magnetic fields produced by on-chip sources, and up to room temperature, make the effect viable for spintronics applications.

Peierls-type instability and tunable band gap in functionalized graphene.

Functionalizing graphene was recently shown to have a dramatic effect on the electronic properties of this material. Here we investigate spatial ordering of adatoms driven by the RKKY-type interactions. In the ordered state, which arises via a Peierls-instability-type mechanism, the adatoms reside mainly on one of the two graphene sublattices. Bragg scattering of electron waves induced by sublattice symmetry breaking results in a band gap opening, whereby Dirac fermions acquire a finite mass. The band gap is found to be immune to the adatoms' positional disorder, with only an exponentially small number of localized states residing in the gap. The gapped state is stabilized in a wide range of electron doping. Our findings show that controlled adsorption of adatoms or molecules provides a route to engineering a tunable band gap in graphene.

Dynamical cooling of nuclear spins in double quantum dots.

Electrons trapped in quantum dots can exhibit quantum-coherent spin dynamics over long timescales. These timescales are limited by the coupling of electron spins to the disordered nuclear spin background, which is a major source of noise and dephasing in such systems. We propose a scheme for controlling and suppressing fluctuations of nuclear spin polarization in double quantum dots, which uses nuclear spin pumping in the spin-blockade regime. We show that nuclear spin polarization fluctuations can be suppressed when electronic levels in the two dots are properly positioned near resonance. The proposed mechanism is analogous to that of optical Doppler cooling. The Overhauser shift due to fluctuations of nuclear polarization brings electron levels in and out of resonance, creating internal feedback to suppress fluctuations. Estimates indicate that a better than 10-fold reduction of fluctuations is possible.

Laplacian growth with separately controlled noise and anisotropy.

Conformal mapping models are used to study the competition of noise and anisotropy in Laplacian growth. For this purpose, a family of models is introduced with the noise level and directional anisotropy controlled independently. Fractalization is observed in both anisotropic growth and growth with varying noise. The fractal dimension is determined from the cluster size scaling with cluster area. For isotropic growth d=1.7, at both high and low noise. For anisotropic growth with reduced noise the dimension can be as low as d=1.5 and apparently is not universal. Also, we study the fluctuations of particle areas and observe, in agreement with previous studies, that exceptionally large particles may appear during growth, leading to pathologically irregular clusters. This difficulty is circumvented by using an acceptance window for particle areas.

Detecting topological currents in graphene superlattices.

Topological materials may exhibit Hall-like currents flowing transversely to the applied electric field even in the absence of a magnetic field. In graphene superlattices, which have broken inversion symmetry, topological currents originating from graphene's two valleys are predicted to flow in opposite directions and combine to produce long-range charge neutral flow. We observed this effect as a nonlocal voltage at zero magnetic field in a narrow energy range near Dirac points at distances as large as several micrometers away from the nominal current path. Locally, topological currents are comparable in strength with the applied current, indicating large valley-Hall angles. The long-range character of topological currents and their transistor-like control by means of gate voltage can be exploited for information processing based on valley degrees of freedom.

Giant nonlocality near the Dirac point in graphene.

Transport measurements have been a powerful tool for discovering electronic phenomena in graphene. We report nonlocal measurements performed in the Hall bar geometry with voltage probes far away from the classical path of charge flow. We observed a large nonlocal response near the Dirac point in fields as low as 0.1 tesla, which persisted up to room temperature. The nonlocality is consistent with the long-range flavor currents induced by the lifting of spin/valley degeneracy. The effect is expected to contribute strongly to all magnetotransport phenomena near the neutrality point.

Fractional quantum Hall effect in suspended graphene probed with two-terminal measurements.

Recently, fractional quantization of two-terminal conductance was reported in suspended graphene. The quantization, which was clearly visible in fields as low as 2 T and persistent up to 20 K in 12 T, was attributed to the formation of an incompressible fractional quantum Hall state. Here, we argue that the failure of earlier experiments to detect the integer and fractional quantum Hall effect with a Hall-bar lead geometry is a consequence of the invasive character of voltage probes in mesoscopic samples, which are easily shorted out owing to the formation of hot spots near the edges of the sample. This conclusion is supported by a detailed comparison with a solvable transport model. We also consider, and rule out, an alternative interpretation of the quantization in terms of the formation of a p-n-p junction, which could result from contact doping or density inhomogeneity. Finally, we discuss the estimate of the quasi-particle gap of the quantum Hall state. The gap value, obtained from the transport data using a conformal mapping technique, is considerably larger than in GaAs-based two-dimensional electron systems, reflecting the stronger Coulomb interactions in graphene.

Topological transition in a non-Hermitian quantum walk.

We analyze a quantum walk on a bipartite one-dimensional lattice, in which the particle can decay whenever it visits one of the two sublattices. The corresponding non-Hermitian tight-binding problem with a complex potential for the decaying sites exhibits two different phases, distinguished by a winding number defined in terms of the Bloch eigenstates in the Brillouin zone. We find that the mean displacement of a particle initially localized on one of the nondecaying sites can be expressed in terms of the winding number, and is therefore quantized as an integer, changing from zero to one at the critical point. We show that the topological transition is relevant for a variety of experimental settings. The quantized behavior can be used to distinguish coherent from incoherent dynamics.

Coherent particle transfer in an on-demand single-electron source.

Electron transfer from a localized state in a quantum dot into a ballistic conductor generally results in particle-hole excitations. We study this effect, considering a resonance level with time-dependent energy coupled to particle states in the Fermi sea. We find that, as the resonance level is driven through the Fermi-level, particle-hole excitations can be suppressed for certain driving protocols. In particular, such noiseless transfer occurs if the level moves with constant rapidity, its energy changing linearly with time. A scheme to study the coherence of particle transfer is proposed.