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Bernal bilayer graphene has recently been discovered to exhibit a wide range of unique ordered phases resulting from interaction-driven effects and encompassing spin and valley magnetism, correlated insulators, correlated metals, and superconductivity. This Letter reports on a novel family of correlated phases characterized by spin and valley ordering, distinct from those reported previously. These phases emerge in electron-doped bilayer graphene where the energy bands are exceptionally flat, manifested through an intriguing nonlinear current-bias behavior that occurs at the onset of the phases and is accompanied by an insulating temperature dependence. These characteristics align with the presence of charge- or spin-density-wave states that open a gap on a portion of the Fermi surface or fully gapped Wigner crystals, resulting in an exceptionally intricate phase diagram.
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Numerous correlated many-body phases, both conventional and exotic, have been reported in magic-angle twisted bilayer graphene (MATBG)1-24. However, the dynamics associated with these correlated states, crucial for understanding the underlying physics, remain unexplored. Here we combine exciton sensing and optical pump-probe spectroscopy to investigate the dynamics of isospin orders in MATBG with WSe2 substrate across the entire flat band, achieving sub-picosecond resolution. We observe remarkably slow isospin dynamics in a broad filling range around ν = 2 and between ν = -3 and -2, with lifetimes of up to 300 ps that decouple from the much faster cooling of electronic temperature (about 10 ps). This non-thermal behaviour demonstrates the presence of abnormally long-lived modes in the isospin degrees of freedom. This observation, not anticipated by theory, implies the existence of long-range propagating collective modes, strong isospin fluctuations and memory effects and is probably associated with an intervalley coherent or incommensurate Kekulé spiral ground state. We further demonstrate non-equilibrium control of the isospin orders previously found around integer fillings. Specifically, through ultrafast manipulation, it can be transiently shifted away from integer fillings. Our study demonstrates a unique probe of collective excitations in MATBG and paves the way for actively controlling non-equilibrium phenomena in moiré systems.
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Bernal bilayer graphene (BLG) offers a highly flexible platform for tuning the band structure, featuring two distinct regimes. One is a tunable band gap induced by large displacement fields. Another is a gapless metallic band occurring at low fields, featuring rich fine structure consisting of four linearly dispersing Dirac cones and van Hove singularities. Even though BLG has been extensively studied experimentally, the evidence of this band structure is still elusive, likely due to insufficient energy resolution. Here, we use Landau levels as markers of the energy dispersion and analyze the Landau level spectrum in a regime where the cyclotron orbits of electrons or holes in momentum space are small enough to resolve the distinct mini Dirac cones. We identify the presence of four Dirac cones and map out topological transitions induced by displacement field. By clarifying the low-energy properties of BLG bands, these findings provide a valuable addition to the toolkit for graphene electronics.
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Understanding electron-phonon interactions is fundamentally important and has crucial implications for device applications. However, in twisted bilayer graphene near the magic angle, this understanding is currently lacking. Here, we study electron-phonon coupling using time- and frequency-resolved photovoltage measurements as direct and complementary probes of phonon-mediated hot-electron cooling. We find a remarkable speedup in cooling of twisted bilayer graphene near the magic angle: The cooling time is a few picoseconds from room temperature down to 5 kelvin, whereas in pristine bilayer graphene, cooling to phonons becomes much slower for lower temperatures. Our experimental and theoretical analysis indicates that this ultrafast cooling is a combined effect of superlattice formation with low-energy moiré phonons, spatially compressed electronic Wannier orbitals, and a reduced superlattice Brillouin zone. This enables efficient electron-phonon Umklapp scattering that overcomes electron-phonon momentum mismatch. These results establish twist angle as an effective way to control energy relaxation and electronic heat flow.
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Quantum oscillations originating from the quantization of electron cyclotron orbits provide sensitive diagnostics of electron bands and interactions. We report on nanoscale imaging of the thermodynamic magnetization oscillations caused by the de Haas-van Alphen effect in moiré graphene. Scanning by means of superconducting quantum interference device (SQUID)-on-tip in Bernal bilayer graphene crystal axis-aligned to hexagonal boron nitride reveals large magnetization oscillations with amplitudes reaching 500 Bohr magneton per electron in weak magnetic fields, unexpectedly low frequencies, and high sensitivity to superlattice filling fraction. The oscillations allow us to reconstruct the complex band structure, revealing narrow moiré bands with multiple overlapping Fermi surfaces separated by unusually small momentum gaps. We identified sets of oscillations that violate the textbook Onsager Fermi surface sum rule, signaling formation of broad-band particle-hole superposition states induced by coherent magnetic breakdown.
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Different superconducting pairing mechanisms are markedly distinct in the underlying Cooper pair kinematics. Quantum-critical soft modes drive pairing interactions in which the pair scattering processes are highly collinear and can be classified into two categories: forward scattering and backscattering. Conversely, in conventional phonon mechanisms, Cooper pair scattering is of a generic noncollinear character. In this study, we present a method to discern the kinematic type by observing the evolution of superconductivity while adjusting the Fermi surface geometry. To demonstrate our approach, we utilize the recently reported phase diagrams of untwisted graphene multilayers. Our analysis connects the emergence of superconductivity at "ghost crossings" of Fermi surfaces in distinct valleys to the pair kinematics of a backscattering type. Together with the observed nonmonotonic behavior of superconductivity near its onset (sharp rise followed by a drop), it lends strong support to a particular quantum-critical superconductivity scenario in which pairing is driven by intervalley coherence fluctuations. These findings offer direct insights into the genesis of pairing in these systems, providing compelling evidence for the electron-electron interactions driving superconductivity. More broadly, our work highlights the potential of tuning bands via ghost crossings as a promising means of boosting superconductivity.
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Viscous electron fluids have emerged recently as a new paradigm of strongly-correlated electron transport in solids. Here we report on a direct observation of the transition to this long-sought-for state of matter in a high-mobility electron system in graphene. Unexpectedly, the electron flow is found to be interaction-dominated but non-hydrodynamic (quasiballistic) in a wide temperature range, showing signatures of viscous flows only at relatively high temperatures. The transition between the two regimes is characterized by a sharp maximum of negative resistance, probed in proximity to the current injector. The resistance decreases as the system goes deeper into the hydrodynamic regime. In a perfect darkness-before-daybreak manner, the interaction-dominated negative response is strongest at the transition to the quasiballistic regime. Our work provides the first demonstration of how the viscous fluid behavior emerges in an interacting electron system.
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Quantum-relativistic matter is ubiquitous in nature; however, it is notoriously difficult to probe. The ease with which external electric and magnetic fields can be introduced in graphene opens a door to creating a tabletop prototype of strongly confined relativistic matter. Here, through a detailed spectroscopic mapping, we directly visualize the interplay between spatial and magnetic confinement in a circular graphene resonator as atomic-like shell states condense into Landau levels. We directly observe the development of a "wedding cake"-like structure of concentric regions of compressible-incompressible quantum Hall states, a signature of electron interactions in the system. Solid-state experiments can, therefore, yield insights into the behavior of quantum-relativistic matter under extreme conditions.
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The speed of solid-state electronic devices, determined by the temporal dynamics of charge carriers, could potentially reach unprecedented petahertz frequencies through direct manipulation by optical fields, consisting in a million-fold increase from state-of-the-art technology. In graphene, charge carrier manipulation is facilitated by exceptionally strong coupling to optical fields, from which stems an important back-action of photoexcited carriers. Here we investigate the instantaneous response of graphene to ultrafast optical fields, elucidating the role of hot carriers on sub-100 fs timescales. The measured nonlinear response and its dependence on interaction time and field polarization reveal the back-action of hot carriers over timescales commensurate with the optical field. An intuitive picture is given for the carrier trajectories in response to the optical-field polarization state. We note that the peculiar interplay between optical fields and charge carriers in graphene may also apply to surface states in topological insulators with similar Dirac cone dispersion relations.
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Conversion of electric current into heat involves microscopic processes that operate on nanometer length scales and release minute amounts of power. Although central to our understanding of the electrical properties of materials, individual mediators of energy dissipation have so far eluded direct observation. Using scanning nanothermometry with submicrokelvin sensitivity, we visualized and controlled phonon emission from individual atomic-scale defects in graphene. The inferred electron-phonon "cooling power spectrum" exhibits sharp peaks when the Fermi level comes into resonance with electronic quasi-bound states at such defects. Rare in the bulk but abundant at graphene's edges, switchable atomic-scale phonon emitters provide the dominant dissipation mechanism. Our work offers insights for addressing key materials challenges in modern electronics and enables control of dissipation at the nanoscale.
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Electron surface states in solids are typically confined to the outermost atomic layers and, due to surface disorder, have negligible impact on electronic transport. Here, we demonstrate a very different behavior for surface states in graphene. We probe the wavelike character of these states by Fabry-Perot (FP) interferometry and find that, in contrast to theoretical predictions, these states can propagate ballistically over micron-scale distances. This is achieved by embedding a graphene resonator formed by gate-defined p-n junctions within a graphene superconductor-normal-superconductor structure. By combining superconducting Aharanov-Bohm interferometry with Fourier methods, we visualize spatially resolved current flow and image FP resonances due to p-n-p cavity modes. The coherence of the standing-wave edge states is revealed by observing a new family of FP resonances, which coexist with the bulk resonances. The edge resonances have periodicity distinct from that of the bulk states manifest in a repeated spatial redistribution of current on and off the FP resonances. This behavior is accompanied by a modulation of the multiple Andreev reflection amplitude on-and-off resonance, indicating that electrons propagate ballistically in a fully coherent fashion. These results, which were not anticipated by theory, provide a practical route to developing electron analog of optical FP resonators at the graphene edge.
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The phase of a quantum state may not return to its original value after the system's parameters cycle around a closed path; instead, the wave function may acquire a measurable phase difference called the Berry phase. Berry phases typically have been accessed through interference experiments. Here, we demonstrate an unusual Berry phase-induced spectroscopic feature: a sudden and large increase in the energy of angular-momentum states in circular graphene p-n junction resonators when a relatively small critical magnetic field is reached. This behavior results from turning on a π Berry phase associated with the topological properties of Dirac fermions in graphene. The Berry phase can be switched on and off with small magnetic field changes on the order of 10 millitesla, potentially enabling a variety of optoelectronic graphene device applications.
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Strongly interacting electrons can move in a neatly coordinated way, reminiscent of the movement of viscous fluids. Here, we show that in viscous flows, interactions facilitate transport, allowing conductance to exceed the fundamental Landauer's ballistic limit [Formula: see text] The effect is particularly striking for the flow through a viscous point contact, a constriction exhibiting the quantum mechanical ballistic transport at [Formula: see text] but governed by electron hydrodynamics at elevated temperatures. We develop a theory of the ballistic-to-viscous crossover using an approach based on quasi-hydrodynamic variables. Conductance is found to obey an additive relation [Formula: see text], where the viscous contribution [Formula: see text] dominates over [Formula: see text] in the hydrodynamic limit. The superballistic, low-dissipation transport is a generic feature of viscous electronics.
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Recently studied hyperbolic materials host unique phonon-polariton (PP) modes. The ultrashort wavelengths of these modes, as well as their low damping, hold promise for extreme subdiffraction nanophotonics schemes. Polar hyperbolic materials such as hexagonal boron nitride can be used to realize long-range coupling between PP modes and extraneous charge degrees of freedom. The latter, in turn, can be used to control and probe PP modes. Here we analyze coupling between PP modes and plasmons in an adjacent graphene sheet, which opens the door to accessing PP modes by angle-resolved photoemission spectroscopy (ARPES). A rich structure in the graphene ARPES spectrum due to PP modes is predicted, providing a new probe of PP modes and their coupling to graphene plasmons.
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We outline a designer approach to endow widely available plain materials with topological properties by stacking them atop other nontopological materials. The approach is illustrated with a model system comprising graphene stacked atop hexagonal boron nitride. In this case, the Berry curvature of the electron Bloch bands is highly sensitive to the stacking configuration. As a result, electron topology can be controlled by crystal axes alignment, granting a practical route to designer topological materials. Berry curvature manifests itself in transport via the valley Hall effect and long-range chargeless valley currents. The nonlocal electrical response mediated by such currents provides diagnostics for band topology.
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Gapped 2D Dirac materials, in which inversion symmetry is broken by a gap-opening perturbation, feature a unique valley transport regime. Topological valley currents in such materials are dominated by bulk currents produced by electronic states just beneath the gap rather than by edge modes. The system ground state hosts dissipationless persistent valley currents existing even when topologically protected edge modes are absent. Valley currents induced by an external bias are characterized by a quantized half-integer valley Hall conductivity. The undergap currents dominate magnetization and the charge Hall effect in a light-induced valley-polarized state.
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The design of high-finesse resonant cavities for electronic waves faces challenges due to short electron coherence lengths in solids. Complementing previous approaches to confine electronic waves by carefully positioned adatoms at clean metallic surfaces, we demonstrate an approach inspired by the peculiar acoustic phenomena in whispering galleries. Taking advantage of graphene's gate-tunable light-like carriers, we create whispering-gallery mode (WGM) resonators defined by circular pn junctions, induced by a scanning tunneling probe. We can tune the resonator size and the carrier concentration under the probe in a back-gated graphene device over a wide range. The WGM-type confinement and associated resonances are a new addition to the quantum electron-optics toolbox, paving the way to develop electronic lenses and resonators.
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Long lifetimes of hot carriers can lead to qualitatively new types of responses in materials. The magnitude and time scales for these responses reflect the mechanisms governing energy flows. We examine the microscopics of two processes which are key for energy transport, focusing on the unusual behavior arising due to graphene's unique combination of material properties. One is hot carrier generation in its photoexcitation dynamics, where hot carriers multiply through an Auger type carrier-carrier scattering cascade. The hot-carrier generation manifests itself through elevated electronic temperatures which can be accessed in a variety of ways, in particular optical conductivity measurements. Another process of high interest is electron-lattice cooling. We survey different cooling pathways and discuss the cooling bottleneck arising for the momentum-conserving electron-phonon scattering pathway. We show how this bottleneck can be relieved by higher-order collisionssupercollisionsand examine the variety of supercollision processes that can occur in graphene.
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Transport in photoactive graphene heterostructures, originating from the dynamics of photogenerated hot carriers, is governed by the processes of thermionic emission, electron-lattice thermal imbalance, and cooling. These processes give rise to interesting photoresponse effects, in particular negative differential resistance (NDR) arising in the hot-carrier regime. The NDR effect stems from a strong dependence of electron-lattice cooling on the carrier density, which results in the carrier temperature dropping precipitously upon increasing bias. The ON-OFF switching between the NDR regime and the conventional cold emission regime, as well as the gate-controlled closed-circuit current that is present at zero bias voltage, can serve as signatures of hot-carrier dominated transport.
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Massless Dirac fermions in graphene at charge neutrality form a strongly interacting system in which both charged and neutral (energy) modes play an important role. These modes are essentially decoupled in the absence of a magnetic field, but become strongly coupled when the field is applied. We show that this regime is characterized by strong magnetodrag and Hall drag, originating from long-range energy currents and spatial temperature gradients. The energy-driven effects arise in a wide temperature range, and feature an unusually strong dependence on field and carrier density. We argue that this mechanism accounts for the recently observed giant magnetodrag and Hall drag occurring at classically weak fields.