Evidence for Dirac flat band superconductivity enabled by quantum geometry.

In a flat band superconductor, the charge carriers' group velocity vF is extremely slow. Superconductivity therein is particularly intriguing, being related to the long-standing mysteries of high-temperature superconductors1 and heavy-fermion systems2. Yet the emergence of superconductivity in flat bands would appear paradoxical, as a small vF in the conventional Bardeen-Cooper-Schrieffer theory implies vanishing coherence length, superfluid stiffness and critical current. Here, using twisted bilayer graphene3-7, we explore the profound effect of vanishingly small velocity in a superconducting Dirac flat band system8-13. Using Schwinger-limited non-linear transport studies14,15, we demonstrate an extremely slow normal state drift velocity vn ≈ 1,000 m s-1 for filling fraction ν between -1/2 and -3/4 of the moiré superlattice. In the superconducting state, the same velocity limit constitutes a new limiting mechanism for the critical current, analogous to a relativistic superfluid16. Importantly, our measurement of superfluid stiffness, which controls the superconductor's electrodynamic response, shows that it is not dominated by the kinetic energy but instead by the interaction-driven superconducting gap, consistent with recent theories on a quantum geometric contribution8-12. We find evidence for small Cooper pairs, characteristic of the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover17-19, with an unprecedented ratio of the superconducting transition temperature to the Fermi temperature exceeding unity and discuss how this arises for ultra-strong coupling superconductivity in ultra-flat Dirac bands.

Reproducibility in the fabrication and physics of moiré materials.

Overlaying two atomic layers with a slight lattice mismatch or at a small rotation angle creates a moiré superlattice, which has properties that are markedly modified from (and at times entirely absent in) the 'parent' materials. Such moiré materials have progressed the study and engineering of strongly correlated phenomena and topological systems in reduced dimensions. The fundamental understanding of the electronic phases, such as superconductivity, requires a precise control of the challenging fabrication process, involving the rotational alignment of two atomically thin layers with an angular precision below 0.1 degrees. Here we review the essential properties of moiré materials and discuss their fabrication and physics from a reproducibility perspective.

Gate-Tunable Magnetism and Giant Magnetoresistance in Suspended Rhombohedral-Stacked Few-Layer Graphene.

Conventionally, magnetism arises from the strong exchange interaction among the magnetic moments of d- or f-shell electrons. It can also emerge in perfect lattices from nonmagnetic elements, such as that exemplified by the Stoner criterion. Here we report tunable magnetism in suspended rhombohedral-stacked few-layer graphene (r-FLG) devices with flat bands. At small doping levels (n ∼ 1011 cm-2), we observe prominent conductance hysteresis and giant magnetoconductance that exceeds 1000% as a function of magnetic fields. Both phenomena are tunable by density and temperature and disappear at n > 1012 cm-2 or T > 5 K. These results are confirmed by first-principles calculations, which indicate the formation of a half-metallic state in doped r-FLG, in which the magnetization is tunable by electric field. Our combined experimental and theoretical work demonstrate that magnetism and spin polarization, arising from the strong electronic interactions in flat bands, emerge in a system composed entirely of carbon atoms.

Enhancing Perpendicular Magnetic Anisotropy in Garnet Ferrimagnet by Interfacing with Few-Layer WTe2.

Engineering magnetic anisotropy in a ferro- or ferrimagnetic (FM) thin film is crucial in a spintronic device. One way to modify the magnetic anisotropy is through the surface of the FM thin film. Here, we report the emergence of a perpendicular magnetic anisotropy (PMA) induced by interfacial interactions in a heterostructure comprised of a garnet ferrimagnet, Y3Fe5O12 (YIG), and a low-symmetry, high spin-orbit coupling (SOC) transition metal dichalcogenide, WTe2. At the same time, we also observed an enhancement in Gilbert damping in the WTe2-covered YIG area. Both the magnitude of interface-induced PMA and the Gilbert damping enhancement have no observable WTe2 thickness dependence down to a single quadruple layer, indicating that the interfacial interaction plays a critical role. The ability of WTe2 to enhance the PMA in FM thin film, combined with its previously reported capability to generate out-of-plane damping like spin torque, makes it desirable for magnetic memory applications.

Gate-Tunable Transport in Quasi-One-Dimensional α-Bi4I4 Field Effect Transistors.

Bi4I4 belongs to a novel family of quasi-one-dimensional (1D) topological insulators (TIs). While its ß phase was demonstrated to be a prototypical weak TI, the α phase, long thought to be a trivial insulator, was recently predicted to be a rare higher order TI. Here, we report the first gate tunable transport together with evidence for unconventional band topology in exfoliated α-Bi4I4 field effect transistors. We observe a Dirac-like longitudinal resistance peak and a sign change in the Hall resistance; their temperature dependences suggest competing transport mechanisms: a hole-doped insulating bulk and one or more gate-tunable ambipolar boundary channels. Our combined transport, photoemission, and theoretical results indicate that the gate-tunable channels likely arise from novel gapped side surface states, two-dimensional (2D) TI in the bottommost layer, and/or helical hinge states of the upper layers. Markedly, a gate-tunable supercurrent is observed in an α-Bi4I4 Josephson junction, underscoring the potential of these boundary channels to mediate topological superconductivity.

Unprecedented Charge State Control in Graphene Quantum Dots.

High-quality double quantum dots in bilayer graphene are realized with controlled charge down to one electron. These devices provide a promising basis for spin-based qubits with long spin lifetimes.

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.

Quantum Hall Effect Measurement of Spin-Orbit Coupling Strengths in Ultraclean Bilayer Graphene/WSe2 Heterostructures.

We study proximity-induced spin-orbit coupling (SOC) in bilayer graphene/few-layer WSe2 heterostructure devices. Contact mode atomic force microscopy (AFM) cleaning yields ultraclean interfaces and high-mobility devices. In a perpendicular magnetic field, we measure the quantum Hall effect to determine the Landau level structure in the presence of out-of-plane Ising and in-plane Rashba SOC. A distinct Landau level crossing pattern emerges when tuning the charge density and displacement field independently with dual gates, originating from a layer-selective SOC proximity effect. Analyzing the Landau level crossings and measured inter-Landau level energy gaps yields the proximity-induced SOC energy scale. The Ising SOC is ∼2.2 meV, 100 times higher than the intrinsic SOC in graphene, whereas its sign is consistent with theories predicting a dependence of SOC on interlayer twist angle. The Rashba SOC is ∼15 meV. Finally, we infer the magnetic field dependence of the inter-Landau level Coulomb interactions. These ultraclean bilayer graphene/WSe2 heterostructures provide a high mobility system with the potential to realize novel topological electronic states and manipulate spins in nanostructures.

Fractional and Symmetry-Broken Chern Insulators in Tunable Moiré Superlattices.

We study dual-gated graphene bilayer/hBN moiré superlattices. Under zero magnetic field, we observe additional resistance peaks as the charge density varies. The peaks' resistivities vary approximately quadratically with an applied perpendicular displacement field D. Data fit to a continuum model yield a bilayer/hBN interaction energy scale ∼30 ± 10 meV. Under a perpendicular magnetic field, we observe Hofstadter butterfly spectra as well as symmetry-broken and fractional Chern insulator states. Their topology and lattice symmetry breaking is D-tunable, enabling the realization of new topological states in this system.

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.

Electron liquids and solids in one dimension.

Even though bulk metallic systems contain a very large number of strongly interacting electrons, their properties are well described within Landau's Fermi liquid theory of non-interacting quasiparticles. Although many higher-dimensional systems can be successfully understood on the basis of such non-interacting theories, this is not possible for one-dimensional systems. When confined to narrow channels, electron interaction gives rise to such exotic phenomena as spin-charge separation and the emergence of correlated-electron insulators. Such strongly correlated electronic behaviour has recently been seen in experiments on one-dimensional carbon nanotubes and nanowires, and this behaviour challenges the theoretical description of such systems.

Superior Current Carrying Capacity of Boron Nitride Encapsulated Carbon Nanotubes with Zero-Dimensional Contacts.

We report fabrication and characterization of hexagonal boron nitride (hBN)-encapsulated carbon nanotube (CNT) field effect transistors, which are coupled to electrical leads via zero-dimensional contacts. Device quality is attested by the ohmic contacts and observation of Coulomb blockade with a single periodicity in small bandgap semiconducing nanotubes. Surprisingly, hBN-encapsulated CNT devices demonstrate significantly enhanced current carrying capacity; a single-walled CNT can sustain >180 µA current or, equivalently, a current density of ∼2 × 10(10) A/cm(2), which is a factor of 6-7 higher than devices supported on SiO2 substrates. Such dramatic enhancement of current carrying capacity arises from the high thermal conductivity of hBN and lower hBN-CNT interfacial thermal resistance and has implications for carbon electronic applications.

Topological Winding Number Change and Broken Inversion Symmetry in a Hofstadter's Butterfly.

Graphene's quantum Hall features are associated with a π Berry's phase due to its odd topological pseudospin winding number. In nearly aligned graphene-hexagonal BN heterostructures, the lattice and orientation mismatch produce a superlattice potential, yielding secondary Dirac points in graphene's electronic spectrum, and under a magnetic field, a Hofstadter butterfly-like energy spectrum. Here we report an additional π Berry's phase shift when tuning the Fermi level past the secondary Dirac points, originating from a change in topological winding number from odd to even when the Fermi-surface electron orbit begins to enclose the secondary Dirac points. At large hole doping inversion symmetry breaking generates a distinct hexagonal pattern in the longitudinal resistivity versus magnetic field and charge density. Major Hofstadter butterfly features persist up to ∼100 K, demonstrating the robustness of the fractal energy spectrum in these systems.

Evidence for a spontaneous gapped state in ultraclean bilayer graphene.

At the charge neutrality point, bilayer graphene (BLG) is strongly susceptible to electronic interactions and is expected to undergo a phase transition to a state with spontaneously broken symmetries. By systematically investigating a large number of single-and double-gated BLG devices, we observe a bimodal distribution of minimum conductivities at the charge neutrality point. Although σ(min) is often approximately 2-3 e(2)/h (where e is the electron charge and h is Planck's constant), it is several orders of magnitude smaller in BLG devices that have both high mobility and low extrinsic doping. The insulating state in the latter samples appears below a transition temperature T(c) of approximately 5 K and has a T = 0 energy gap of approximately 3 meV. Transitions between these different states can be tuned by adjusting disorder or carrier density.

Graphene nanoelectromechanical systems as stochastic-frequency oscillators.

We measure the quality factor Q of electrically driven few-layer graphene drumhead resonators, providing an experimental demonstration that Q ∼ 1/T, where T is the temperature. We develop a model that includes intermodal coupling and tensioned graphene resonators. Because the resonators are atomically thin, out-of-plane fluctuations are large. As a result, Q is mainly determined by stochastic frequency broadening rather than frictional damping, in analogy to nuclear magnetic resonance. This model is in good agreement with experiment. Additionally, at larger drives the resonance line width is enhanced by nonlinear damping, in qualitative agreement with recent theory of damping by radiation of in-plane phonons. Parametric amplification produced by periodic thermal expansion from the ac drive voltage yields an anomalously large line width at the largest drives. Our results contribute toward a general framework for understanding the mechanisms of dissipation and spectral line broadening in atomically thin membrane resonators.

Transport measurement of Landau level gaps in bilayer graphene with layer polarization control.

Landau level (LL) gaps are important parameters for understanding electronic interactions and symmetry-broken processes in bilayer graphene (BLG). Here we present transport spectroscopy measurements of LL gaps in double-gated suspended BLG with high mobilities in the quantum Hall regime. By using bias as a spectroscopic tool, we measure the gap Δ for the quantum Hall (QH) state at filling factors ν = ±4 and -2. The single-particle Δ(ν=4) scales linearly with magnetic field B and is independent of the out-of-plane electric field E⊥. For the symmetry-broken ν = -2 state, the measured values of Δ(ν=-2) are ∼1.1 meV/T and 0.17 meV/T for singly gated geometry and dual-gated geometry at E⊥ = 0, respectively. The difference between the two values arises from the E⊥. dependence of Δ(ν=-2), suggesting that the ν = -2 state is layer polarized. Our studies provide the first measurements of the gaps of the broken symmetry QH states in BLG with well-controlled E⊥ and establish a robust method that can be implemented for studying similar states in other layered materials.

Graphene-graphite oxide field-effect transistors.

Graphene's high mobility and two-dimensional nature make it an attractive material for field-effect transistors. Previous efforts in this area have used bulk gate dielectric materials such as SiO(2) or HfO(2). In contrast, we have studied the use of an ultrathin layered material, graphene's insulating analogue, graphite oxide. We have fabricated transistors comprising single or bilayer graphene channels, graphite oxide gate insulators, and metal top-gates. The graphite oxide layers show relatively minimal leakage at room temperature. The breakdown electric field of graphite oxide was found to be comparable to SiO(2), typically ~1-3 × 10(8) V/m, while its dielectric constant is slightly higher, κ ≈ 4.3.

DNA-linker-induced surface assembly of ultra dense parallel single walled carbon nanotube arrays.

Ultrathin film preparations of single-walled carbon nanotube (SWNT) allow economical utilization of nanotube properties in electronics applications. Recent advances have enabled production of micrometer scale SWNT transistors and sensors but scaling these devices down to the nanoscale, and improving the coupling of SWNTs to other nanoscale components, may require techniques that can generate a greater degree of nanoscale geometric order than has thus far been achieved. Here, we introduce linker-induced surface assembly, a new technique that uses small structured DNA linkers to assemble solution dispersed nanotubes into parallel arrays on charged surfaces. Parts of our linkers act as spacers to precisely control the internanotube separation distance down to <3 nm and can serve as scaffolds to position components such as proteins between adjacent parallel nanotubes. The resulting arrays can then be stamped onto other substrates. Our results demonstrate a new paradigm for the self-assembly of anisotropic colloidal nanomaterials into ordered structures and provide a potentially simple, low cost, and scalable route for preparation of exquisitely structured parallel SWNT films with applications in high-performance nanoscale switches, sensors, and meta-materials.

Visualizing electrical breakdown and ON/OFF states in electrically switchable suspended graphene break junctions.

Narrow gaps are formed in suspended single- to few-layer graphene devices using a pulsed electrical breakdown technique. The conductance of the resulting devices can be programmed by the application of voltage pulses, with voltages of 2.5 to ~4.5 V, corresponding to an ON pulse, and ~8 V, corresponding to an OFF pulse. Electron microscope imaging of the devices shows that the graphene sheets typically remain suspended and that the device conductance tends to zero when the observed gap is large. The switching rate is strongly temperature dependent, which rules out a purely electromechanical switching mechanism. This observed switching in suspended graphene devices strongly suggests a switching mechanism via atomic movement and/or chemical rearrangement and underscores the potential of all-carbon devices for integration with graphene electronics.

Quantum transport and field-induced insulating states in bilayer graphene pnp junctions.

We perform transport measurements in high quality bilayer graphene pnp junctions with suspended top gates. At a magnetic field B = 0, we demonstrate band gap opening by an applied perpendicular electric field with an On/Off ratio up to 20,000 at 260 mK. Within the band gap, the conductance decreases exponentially by 3 orders of magnitude with increasing electric field and can be accounted for by variable range hopping with a gate-tunable density of states, effective mass, and localization length. At large B, we observe quantum Hall conductance with fractional values, which arise from equilibration of edge states between differentially doped regions, and the presence of an insulating state at filling factor v = 0. Our work underscores the importance of bilayer graphene for both fundamental interest and technological applications.