Untying the insulating and superconducting orders in magic-angle graphene.

The coexistence of superconducting and correlated insulating states in magic-angle twisted bilayer graphene1-11 prompts fascinating questions about their relationship. Independent control of the microscopic mechanisms that govern these phases could help uncover their individual roles and shed light on their intricate interplay. Here we report on direct tuning of electronic interactions in this system by changing the separation distance between the graphene and a metallic screening layer12,13. We observe quenching of correlated insulators in devices with screening layer separations that are smaller than the typical Wannier orbital size of 15 nanometres and with twist angles that deviate slightly from the magic angle of 1.10 ± 0.05 degrees. Upon extinction of the insulating orders, the vacated phase space is taken over by superconducting domes that feature critical temperatures comparable to those in devices with strong insulators. In addition, we find that insulators at half-filling can reappear in small out-of-plane magnetic fields of 0.4 tesla, giving rise to quantized Hall states with a Chern number of 2. Our study suggests re-examination of the often-assumed 'parent-and-child' relation between the insulating and superconducting phases in moiré graphene, and suggests a way of directly probing the microscopic mechanisms of superconductivity in strongly correlated systems.

Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene.

Superconductivity can occur under conditions approaching broken-symmetry parent states1. In bilayer graphene, the twisting of one layer with respect to the other at 'magic' twist angles of around 1 degree leads to the emergence of ultra-flat moiré superlattice minibands. Such bands are a rich and highly tunable source of strong-correlation physics2-5, notably superconductivity, which emerges close to interaction-induced insulating states6,7. Here we report the fabrication of magic-angle twisted bilayer graphene devices with highly uniform twist angles. The reduction in twist-angle disorder reveals the presence of insulating states at all integer occupancies of the fourfold spin-valley degenerate flat conduction and valence bands-that is, at moiré band filling factors ν = 0, ±1, ±2, ±3. At ν ≈ -2, superconductivity is observed below critical temperatures of up to 3 kelvin. We also observe three new superconducting domes at much lower temperatures, close to the ν = 0 and ν = ±1 insulating states. Notably, at ν = ± 1 we find states with non-zero Chern numbers. For ν = -1 the insulating state exhibits a sharp hysteretic resistance enhancement when a perpendicular magnetic field greater than 3.6 tesla is applied, which is consistent with a field-driven phase transition. Our study shows that broken-symmetry states, interaction-driven insulators, orbital magnets, states with non-zero Chern numbers and superconducting domes occur frequently across a wide range of moiré flat band fillings, including close to charge neutrality. This study provides a more detailed view of the phenomenology of magic-angle twisted bilayer graphene, adding to our evolving understanding of its emergent properties.

Quantum parity Hall effect in Bernal-stacked trilayer graphene.

The quantum Hall effect has recently been generalized from transport of conserved charges to include transport of other approximately conserved-state variables, including spin and valley, via spin- or valley-polarized boundary states with different chiralities. Here, we report a class of quantum Hall effect in Bernal- or ABA-stacked trilayer graphene (TLG), the quantum parity Hall (QPH) effect, in which boundary channels are distinguished by even or odd parity under the system's mirror reflection symmetry. At the charge neutrality point, the longitudinal conductance [Formula: see text] is first quantized to [Formula: see text] at a small perpendicular magnetic field [Formula: see text], establishing the presence of four edge channels. As [Formula: see text] increases, [Formula: see text] first decreases to [Formula: see text], indicating spin-polarized counterpropagating edge states, and then, to approximately zero. These behaviors arise from level crossings between even- and odd-parity bulk Landau levels driven by exchange interactions with the underlying Fermi sea, which favor an ordinary insulator ground state in the strong [Formula: see text] limit and a spin-polarized state at intermediate fields. The transitions between spin-polarized and -unpolarized states can be tuned by varying Zeeman energy. Our findings demonstrate a topological phase that is protected by a gate-controllable symmetry and sensitive to Coulomb interactions.

Competing Zero-Field Chern Insulators in Superconducting Twisted Bilayer Graphene.

The discovery of magic angle twisted bilayer graphene has unveiled a rich variety of superconducting, magnetic, and topologically nontrivial phases. Here, we show that the zero-field states at odd integer filling factors in h-BN nonaligned devices are consistent with symmetry broken Chern insulators, as is evidenced by the observation of the anomalous Hall effect near moiré cell filling factor ν=+1. The corresponding Chern insulator has a Chern number C=±1 and a relatively high Curie temperature of T_{c}≈4.5 K. In a perpendicular magnetic field above B>0.5 T we observe a transition of the ν=+1 Chern insulator from Chern number C=±1 to C=3, characterized by a quantized Hall plateau with R_{yx}=h/3e^{2}. These observations demonstrate that interaction-induced symmetry breaking leads to zero-field ground states that include almost degenerate and closely competing Chern insulators, and that states with larger Chern numbers couple most strongly to the B field. In addition, the device reveals strong superconducting phases with critical temperatures of up to T_{c}≈3.5 K. By providing the first demonstration of a system that allows gate-induced transitions between magnetic and superconducting phases, our observations mark a major milestone in the creation of a new generation of quantum electronics.

Exciton-Exciton Interaction beyond the Hydrogenic Picture in a MoSe_{2} Monolayer in the Strong Light-Matter Coupling Regime.

In transition metal dichalcogenides' layers of atomic-scale thickness, the electron-hole Coulomb interaction potential is strongly influenced by the sharp discontinuity of the dielectric function across the layer plane. This feature results in peculiar nonhydrogenic excitonic states in which exciton-mediated optical nonlinearities are predicted to be enhanced compared to their hydrogenic counterparts. To demonstrate this enhancement, we perform optical transmission spectroscopy of a MoSe_{2} monolayer placed in the strong coupling regime with the mode of an optical microcavity and analyze the results quantitatively with a nonlinear input-output theory. We find an enhancement of both the exciton-exciton interaction and of the excitonic fermionic saturation with respect to realistic values expected in the hydrogenic picture. Such results demonstrate that unconventional excitons in MoSe_{2} are highly favorable for the implementation of large exciton-mediated optical nonlinearities, potentially working up to room temperature.

Magic-Angle Bilayer Graphene Nanocalorimeters: Toward Broadband, Energy-Resolving Single Photon Detection.

Because of the ultralow photon energies at mid-infrared and terahertz frequencies, in these bands photodetectors are notoriously underdeveloped, and broadband single photon detectors (SPDs) are nonexistent. Advanced SPDs exploit thermal effects in nanostructured superconductors, and their performance is currently limited to the more energetic near-infrared photons due to their high electronic heat capacity. Here, we demonstrate a superconducting magic-angle bilayer graphene (MAG) device that is theoretically capable of detecting single photons of ultralow energies by utilizing its record-low heat capacity and sharp superconducting transition. We theoretically quantify its calorimetric photoresponse and estimate its detection limits. This device allows the detection of ultrabroad range single photons from the visible to sub-terahertz with a response time around 4 ns and energy resolution better than 1 THz. These attributes position MAG as an exceptional material for long-wavelength single photon sensing, which could revolutionize such disparate fields as quantum information processing and radio astronomy.

Substrate-Dependent Band Structures in Trilayer Graphene/h-BN Heterostructures.

The tight-binding model has been spectacularly successful in elucidating the electronic and optical properties of a vast number of materials. Within the tight-binding model, the hopping parameters that determine much of the band structure are often taken as constants. Here, using ABA-stacked trilayer graphene as the model system, we show that, contrary to conventional wisdom, the hopping parameters and therefore band structures are not constants, but are systematically variable depending on their relative alignment angle between h-BN. Moreover, the addition or removal of the h-BN substrate results in an inversion of the K and K^{'} valley in trilayer graphene's lowest Landau level. Our work illustrates the oft-ignored and rather surprising impact of the substrates on band structures of 2D materials.

All-Optical Mapping of the Position of Quantum Dots Embedded in a Nanowire Antenna.

Nanowire antennas embedding single quantum dots (QDs) have recently emerged as a versatile solid-state platform for quantum optics. Within the nanowire section, the emitter position simultaneously determines the strength of the light-matter interaction, as well as the coupling to potential decoherence channels. Therefore, to quantitatively understand device performance and guide future optimization, it is highly desirable to map the emitter position with an accuracy much smaller than the waveguide diameter, on the order of a few hundreds of nanometers. We introduce here a nondestructive, all-optical mapping technique that exploits the QD emission into two guided modes with different transverse profiles. These two modes are fed by the same emitter and thus interfere. The resulting intensity pattern, which is highly sensitive to the emitter position, is resolved in the far-field using Fourier microscopy. We demonstrate this technique on a standard microphotoluminescence setup and map the position of individual QDs in a nanowire antenna with a spatial resolution of ±10 nm. This work opens important perspectives for the future development of light-matter interfaces based on nanowire antennas. Beyond single-QD devices, it will also provide a valuable tool for the investigation of collective effects that imply several emitters coupled to an optical waveguide.

Integer and Fractional Quantum Hall effect in Ultrahigh Quality Few-layer Black Phosphorus Transistors.

As a high mobility two-dimensional semiconductor with strong structural and electronic anisotropy, atomically thin black phosphorus (BP) provides a new playground for investigating the quantum Hall (QH) effect, including outstanding questions such as the functional dependence of Landau level (LL) gaps on magnetic field B, and possible anisotropic fractional QH states. Using encapsulated few-layer BP transistors with mobility up to 55 000 cm2/(V s), we extracted LL gaps over an exceptionally wide range of B for QH states at filling factors -1 to -4, which are determined to be linear in B, thus resolving a controversy raised by its anisotropy. Furthermore, a fractional QH state at ν ≈ -4/3 and an additional feature at -0.56 ± 0.1 are observed, underscoring BP as a tunable 2D platform for exploring electron interactions.

Raman Spectroscopy, Photocatalytic Degradation, and Stabilization of Atomically Thin Chromium Tri-iodide.

As a 2D ferromagnetic semiconductor with magnetic ordering, atomically thin chromium tri-iodide is the latest addition to the family of two-dimensional (2D) materials. However, realistic exploration of CrI3-based devices and heterostructures is challenging due to its extreme instability under ambient conditions. Here, we present Raman characterization of CrI3 and demonstrate that the main degradation pathway of CrI3 is the photocatalytic substitution of iodine by water. While simple encapsulation by Al2O3, PMMA, and hexagonal BN (hBN) only leads to modest reduction in degradation rate, minimizing light exposure markedly improves stability, and CrI3 sheets sandwiched between hBN layers are air-stable for >10 days. By monitoring the transfer characteristics of the CrI3/graphene heterostructure over the course of degradation, we show that the aquachromium solution hole-dopes graphene.

Thermal Decoherence of a Nonequilibrium Polariton Fluid.

Exciton polaritons constitute a unique realization of a quantum fluid interacting with its environment. Using selenide-based microcavities, we exploit this feature to warm up a polariton condensate in a controlled way and monitor its spatial coherence. We determine directly the amount of heat picked up by the condensate by measuring the phonon-polariton scattering rate and comparing it with the loss rate. We find that, upon increasing the heating rate, the spatial coherence length decreases markedly, while localized phase structures vanish, in good agreement with a stochastic mean-field theory. From the thermodynamical point of view, this regime is unique, as it involves a nonequilibrium quantum fluid with no well-defined temperature but which is nevertheless able to pick up heat with dramatic effects on the order parameter.

Large and Uniform Optical Emission Shifts in Quantum Dots Strained along Their Growth Axis.

We introduce a calibration method to quantify the impact of external mechanical stress on the emission wavelength of distinct quantum dots (QDs). Specifically, these emitters are integrated in a cross-section of a semiconductor core wire and experience a longitudinal strain that is induced by an amorphous capping shell. Detailed numerical simulations show that, thanks to the shell mechanical isotropy, the strain in the core is uniform, which enables a direct comparison of the QD responses. Moreover, the core strain is determined in situ by an optical measurement, yielding reliable values for the QD emission tuning slope. This calibration technique is applied to self-assembled InAs QDs submitted to incremental elongation along their growth axis. In contrast to recent studies conducted on similar QDs submitted to a uniaxial stress perpendicular to the growth direction, optical spectroscopy reveals up to ten times larger tuning slopes, with a moderate dispersion. These results highlight the importance of the stress direction to optimize the QD optical shift, with general implications, both in static and dynamic regimes. As such, they are in particular relevant for the development of wavelength-tunable single-photon sources or hybrid QD opto-mechanical systems.

Energy Gaps and Layer Polarization of Integer and Fractional Quantum Hall States in Bilayer Graphene.

Owing to the spin, valley, and orbital symmetries, the lowest Landau level in bilayer graphene exhibits multicomponent quantum Hall ferromagnetism. Using transport spectroscopy, we investigate the energy gaps of integer and fractional quantum Hall (QH) states in bilayer graphene with controlled layer polarization. The state at filling factor ν=1 has two distinct phases: a layer polarized state that has a larger energy gap and is stabilized by high electric field, and a hitherto unobserved interlayer coherent state with a smaller gap that is stabilized by large magnetic field. In contrast, the ν=2/3 quantum Hall state and a feature at ν=1/2 are only resolved at finite electric field and large magnetic field. These results underscore the importance of controlling layer polarization in understanding the competing symmetries in the unusual QH system of BLG.

Tunable Symmetries of Integer and Fractional Quantum Hall Phases in Heterostructures with Multiple Dirac Bands.

The copresence of multiple Dirac bands in few-layer graphene leads to a rich phase diagram in the quantum Hall regime. Using transport measurements, we map the phase diagram of BN-encapsulated ABA-stacked trilayer graphene as a function charge density n, magnetic field B, and interlayer displacement field D, and observe transitions among states with different spin, valley, orbital, and parity polarizations. Such a rich pattern arises from crossings between Landau levels from different subbands, which reflect the evolving symmetries that are tunable in situ. At D=0, we observe fractional quantum Hall (FQH) states at filling factors 2/3 and -11/3. Unlike those in bilayer graphene, these FQH states are destabilized by a small interlayer potential that hybridizes the different Dirac bands.

Ionic Liquid Gating of Suspended MoS2 Field Effect Transistor Devices.

We demonstrate ionic liquid (IL) gating of suspended few-layer MoS2 transistors, where ions can accumulate on both exposed surfaces. Upon application of IL, all free-standing samples consistently display more significant improvement in conductance than substrate-supported devices. The measured IL gate coupling efficiency is up to 4.6 × 10(13) cm(-2) V(-1). Electrical transport data reveal contact-dominated electrical transport properties and the Schottky emission as the underlying mechanism. By modulating IL gate voltage, the suspended MoS2 devices display metal-insulator transition. Our results demonstrate that more efficient charge induction can be achieved in suspended two-dimensional (2D) materials, which with further optimization, may enable extremely high charge density and novel phase transition.

Annealing and transport studies of suspended molybdenum disulfide devices.

We fabricate suspended molybdenum disulfide (MoS2) field effect transistor devices and develop an effective gas annealing technique that significantly improves device quality and increases conductance by 3-4 orders of magnitude. Mobility of the suspended devices ranges from 0.01 to 46 cm(2) V(-1) s(-1) before annealing, and from 0.5 to 105 cm(2) V(-1) s(-1) after annealing. Temperature dependence measurements reveal two transport mechanisms: electron-phonon scattering at high temperatures and thermal activation over a gate-tunable barrier height at low temperatures. Our results suggest that transport in these devices is not limited by the substrates, but likely by defects, charge impurities and/or Schottky barriers at the metal-MoS2 interfaces. Finally, this suspended MoS2 device structure provides a versatile platform for other research areas, such as thermal, optical and mechanical studies.

Layer- and gate-tunable spin-orbit coupling in a high-mobility few-layer semiconductor.

Spin-orbit coupling (SOC) is a relativistic effect, where an electron moving in an electric field experiences an effective magnetic field in its rest frame. In crystals without inversion symmetry, it lifts the spin degeneracy and leads to many magnetic, spintronic, and topological phenomena and applications. In bulk materials, SOC strength is a constant. Here, we demonstrate SOC and intrinsic spin splitting in atomically thin InSe, which can be modified over a broad range. From quantum oscillations, we establish that the SOC parameter α is thickness dependent; it can be continuously modulated by an out-of-plane electric field, achieving intrinsic spin splitting tunable between 0 and 20 meV. Unexpectedly, α could be enhanced by an order of magnitude in some devices, suggesting that SOC can be further manipulated. Our work highlights the extraordinary tunability of SOC in 2D materials, which can be harnessed for in operando spintronic and topological devices and applications.

Dispersion relation of the collective excitations in a resonantly driven polariton fluid.

Exciton-polaritons in semiconductor microcavities constitute the archetypal realization of a quantum fluid of light. Under coherent optical drive, remarkable effects such as superfluidity, dark solitons or the nucleation of vortices have been observed, and can be all understood as specific manifestations of the condensate collective excitations. In this work, we perform a Brillouin scattering experiment to measure their dispersion relation [Formula: see text] directly. The results, such as a speed of sound which is apparently twice too low, cannot be explained upon considering the polariton condensate alone. In a combined theoretical and experimental analysis, we demonstrate that the presence of an excitonic reservoir alongside the polariton condensate has a dramatic influence on the characteristics of the quantum fluid, and explains our measurement quantitatively. This work clarifies the role of such a reservoir in polariton quantum hydrodynamics. It also provides an unambiguous tool to determine the condensate-to-reservoir fraction in the quantum fluid, and sets an accurate framework to approach ideas for polariton-based quantum-optical applications.

Optical valley Hall effect for highly valley-coherent exciton-polaritons in an atomically thin semiconductor.

Spin-orbit coupling is a fundamental mechanism that connects the spin of a charge carrier with its momentum. In the optical domain, an analogous synthetic spin-orbit coupling is accessible by engineering optical anisotropies in photonic materials. Both yield the possibility of creating devices that directly harness spin and polarization as information carriers. Atomically thin transition metal dichalcogenides promise intrinsic spin-valley Hall features for free carriers, excitons and photons. Here we demonstrate spin- and valley-selective propagation of exciton-polaritons in a monolayer of MoSe2 that is strongly coupled to a microcavity photon mode. In a wire-like device we trace the flow and helicity of exciton-polaritons expanding along its channel. By exciting a coherent superposition of K and K' tagged polaritons, we observe valley-selective expansion of the polariton cloud without either an external magnetic field or coherent Rayleigh scattering. The observed optical valley Hall effect occurs on a macroscopic scale, offering the potential for applications in spin-valley-locked photonic devices.