Bernal-stacked Bilayer Graphene Research Articles

High-Mobility Compensated Semimetals, Orbital Magnetization, and Umklapp Scattering in Bilayer Graphene Moiré Superlattices.

Twist-controlled moiré superlattices (MSs) have emerged as a versatile platform for realizing artificial systems with complex electronic spectra. The combination of Bernal-stacked bilayer graphene (BLG) and hexagonal boron nitride (hBN) can give rise to an interesting MS, which has recently featured a set of unexpected behaviors, such as unconventional ferroelectricity and the electronic ratchet effect. Yet, the understanding of the electronic properties of BLG/hBN MS has, at present, remained fairly limited. Here, we combine magneto-transport and low-energy sub-THz excitation to gain insights into the properties of this MS. We demonstrate that the alignment between BLG and hBN crystal lattices results in the emergence of compensated semimetals at some integer fillings of the moiré bands, separated by van Hove singularities where the Lifshitz transition occurs. A particularly pronounced semimetal develops when eight holes reside in the moiré unit cell, where coexisting high-mobility electron and hole systems feature strong magnetoresistance reaching 2350% already at B = 0.25 T. Next, by measuring the THz-driven Nernst effect in remote bands, we observe valley splitting, indicating an orbital magnetization characterized by a strongly enhanced effective gv-factor of 340. Finally, using THz photoresistance measurements, we show that the high-temperature conductivity of the BLG/hBN MS is limited by electron-electron umklapp processes. Our multifaceted analysis introduces THz-driven magnetotransport as a convenient tool to probe the band structure and interaction effects in van der Waals materials and provides a comprehensive understanding of the BLG/hBN MS.

Direct observation of a magnetic-field-induced Wigner crystal.

Wigner predicted that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice1. A variety of two-dimensional systems have shown evidence for Wigner crystals2-11 (WCs). However, a spontaneously formed classical or quantum WC has never been directly visualized. Neither the identification of the WC symmetry nor direct investigation of its melting has been accomplished. Here we use high-resolution scanning tunnelling microscopy measurements to directly image a magnetic-field-induced electron WC in Bernal-stacked bilayer graphene and examine its structural properties as a function of electron density, magnetic field and temperature. At high fields and the lowest temperature, we observe a triangular lattice electron WC in the lowest Landau level. The WC possesses the expected lattice constant and is robust between filling factor ν ≈ 0.13 and ν ≈ 0.38 except near fillings where it competes with fractional quantum Hall states. Increasing the density or temperature results in the melting of the WC into a liquid phase that is isotropic but has a modulated structure characterized by the Bragg wavevector of the WC. At low magnetic fields, the WC unexpectedly transitions into an anisotropic stripe phase, which has been commonly anticipated to form in higher Landau levels. Analysis of individual lattice sites shows signatures that may be related to the quantum zero-point motion of electrons in the WC lattice.

Spontaneous charge-ordered state in Bernal-stacked bilayer graphene

Spontaneous charge-ordered state in Bernal-stacked bilayer graphene

Quasi-freestanding AA-stacked bilayer graphene induced by calcium intercalation of the graphene-silicon carbide interface

We study quasi-freestanding bilayer graphene on silicon carbide intercalated by calcium. The intercalation, and subsequent changes to the system, were investigated by low-energy electron diffraction, angle-resolved photoemission spectroscopy (ARPES) and density-functional theory (DFT). Calcium is found to intercalate only at the graphene-SiC interface, completely displacing the hydrogen terminating SiC. As a consequence, the system becomes highly n-doped. Comparison to DFT calculations shows that the band dispersion, as determined by ARPES, deviates from the band structure expected for Bernal-stacked bilayer graphene. Instead, the electronic structure closely matches AA-stacked bilayer graphene on calcium-terminated SiC, indicating a spontaneous transition from AB- to AA-stacked bilayer graphene following calcium intercalation of the underlying graphene-SiC interface.

Flavor symmetry breaking in spin-orbit coupled bilayer graphene

Recent experimental discovery of flavor symmetry breaking metallic phases in Bernal-stacked bilayer graphene points to the strongly interacting nature of electrons near the top (bottom) of its valence (conduction) band. Superconductivity was also observed in between these symmetry breaking phases when the graphene bilayer is placed under a small in-plane magnetic field or in close proximity to a monolayer WSe$_2$ substrate. Here we address the correlated nature of the band edge electrons and obtain the quantum phase diagram of their many-body ground states incorporating the effect of proximity induced spin-orbit coupling. We find that in addition to the spin/valley flavor polarized half and quarter metallic states, two types of intervalley coherent phases emerge near the phase boundaries between the flavor polarized metals. Both spin-orbit coupling and in-plane magnetic field disfavor the spin-unpolarized valley coherent phase. Our findings suggest possible competition between intervalley coherence and superconducting orders, arising from the intriguing correlation effects in bilayer graphene in the presence of spin-orbit coupling.

Multilayer graphene with a superlattice potential

Bernal stacked bilayer graphene subject to a superlattice potential can realize topological and stacked flat bands [Ghorashi et al., Phys. Rev. Lett. 130, 196201 (2023)]. In the present work, we extend the study of a superlattice potential on graphene heterostructures to trilayer and quadrilayer graphene. Comparing Bernal- and chirally stacked multilayers reveals that the latter are more suitable for realizing stacks of many flat bands. On the other hand, Bernal-stacked graphene heterostructures can realize topological flat bands. Imposing two simultaneous superlattice potentials enhances the viability of both regimes.

Unconventional correlated insulator in CrOCl-interfaced Bernal bilayer graphene

The realization of graphene gapped states with large on/off ratios over wide doping ranges remains challenging. Here, we investigate heterostructures based on Bernal-stacked bilayer graphene (BLG) atop few-layered CrOCl, exhibiting an over-1-GΩ-resistance insulating state in a widely accessible gate voltage range. The insulating state could be switched into a metallic state with an on/off ratio up to 107 by applying an in-plane electric field, heating, or gating. We tentatively associate the observed behavior to the formation of a surface state in CrOCl under vertical electric fields, promoting electron–electron (e–e) interactions in BLG via long-range Coulomb coupling. Consequently, at the charge neutrality point, a crossover from single particle insulating behavior to an unconventional correlated insulator is enabled, below an onset temperature. We demonstrate the application of the insulating state for the realization of a logic inverter operating at low temperatures. Our findings pave the way for future engineering of quantum electronic states based on interfacial charge coupling.

Graphene Formation through Spontaneous Exfoliation of Graphite by Chlorosulfonic Acid: A DFT Study

Using exfoliating agents is one of the most promising ways for large-scale production of liquid dispersed graphenic materials from graphite. Therefore, it is crucial to know the reason why some molecules have a larger exfoliating power than others. The highest reported experimental yield for the liquid phase single-surfactant spontaneous exfoliation of graphite, i.e., without sonication, has been obtained using chlorosulfonic acid. The ability of this acid to disperse graphite is studied within the framework of Density Functional Theory (DFT). Equilibrium configurations, electron transfers, binding energies, and densities of states are presented for two acid concentrations and for two situations: adsorption (on monolayer and bilayer graphene) and intercalation (in between simple hexagonal and Bernal-stacked bilayer graphene). Experimental exfoliation power and dispersion stability are explained in terms of charge transfer—the largest found among several studied exfoliating and surfactant agents—facilitated by the good geometrical matching of chlorosulfonic acid molecules to constituent carbon rings of graphene. This matching is in the origin of the tendency toward adsorption of chlorosulfonic acid molecules on graphene monolayers when they separate, originating the charging of the monolayers that precludes their reaggregation.

Electrical switching of a bistable moiré superconductor.

Electrical control of superconductivity is critical for nanoscale superconducting circuits including cryogenic memory elements1-4, superconducting field-effect transistors (FETs)5-7 and gate-tunable qubits8-10. Superconducting FETs operate through continuous tuning of carrier density, but no bistable superconducting FET, which could serve as a new type of cryogenic memory element, has been reported. Recently, gate hysteresis and resultant bistability in Bernal-stacked bilayer graphene aligned to its insulating hexagonal boron nitride gate dielectrics were discovered11,12. Here we report the observation of this same hysteresis in magic-angle twisted bilayer graphene (MATBG) with aligned boron nitride layers. This bistable behaviour coexists alongside the strongly correlated electron system of MATBG without disrupting its correlated insulator or superconducting states. This all-van der Waals platform enables configurable switching between different electronic states of this rich system. To illustrate this new approach, we demonstrate reproducible bistable switching between the superconducting, metallic and correlated insulator states of MATBG using gate voltage or electric displacement field. These experiments unlock the potential to broadly incorporate this new switchable moiré superconductor into highly tunable superconducting electronics.

Enhanced superconductivity in spin-orbit proximitized bilayer graphene.

In the presence of a large perpendicular electric field, Bernal-stacked bilayer graphene (BLG) features several broken-symmetry metallic phases1-3 as well as magnetic-field-induced superconductivity1. The superconducting state is quite fragile, however, appearing only in a narrow window of density and with a maximum critical temperature Tc ≈ 30 mK. Here we show that placing monolayer tungsten diselenide (WSe2) on BLG promotes Cooper pairing to an extraordinary degree: superconductivity appears at zero magnetic field, exhibits an order of magnitude enhancement in Tc and occurs over a density range that is wider by a factor of eight. By mapping quantum oscillations in BLG-WSe2 as a function of electric field and doping, we establish that superconductivity emerges throughout a region for which the normal state is polarized, with two out of four spin-valley flavours predominantly populated. In-plane magnetic field measurements further reveal that superconductivity in BLG-WSe2 can exhibit striking dependence of the critical field on doping, with the Chandrasekhar-Clogston (Pauli) limit roughly obeyed on one end of the superconducting dome, yet sharply violated on the other. Moreover, the superconductivity arises only for perpendicular electric fields that push BLG hole wavefunctions towards WSe2, indicating that proximity-induced (Ising) spin-orbit coupling plays a key role in stabilizing the pairing. Our results pave the way for engineering robust, highly tunable and ultra-clean graphene-based superconductors.

Aharonov–Bohm Oscillations in Bilayer Graphene Quantum Hall Edge State Fabry–Pérot Interferometers

Bernal-stacked bilayer graphene exhibits a wealth of interaction-driven phenomena, including robust even-denominator fractional quantum Hall states. We construct Fabry-Pérot interferometers using a split-gate design and present measurements of the Aharonov-Bohm oscillations. The edge state velocity is found to be approximately 6 × 104 m/s at filling factor ν = 2 and decreases with increasing filling factor. The dc bias and temperature dependence of the interference point to electron-electron interaction induced decoherence mechanisms. These results pave the way for the quest of fractional and non-Abelian braiding statistics in this promising device platform.

Spontaneous time-reversal symmetry breaking in twisted double bilayer graphene

Twisted double bilayer graphene (tDBG) comprises two Bernal-stacked bilayer graphene sheets with a twist between them. Gate voltages applied to top and back gates of a tDBG device tune both the flatness and topology of the electronic bands, enabling an unusual level of experimental control. Metallic states with broken spin and valley symmetries have been observed in tDBG devices with twist angles in the range 1.2–1.3°, but the topologies and order parameters of these states have remained unclear. We report the observation of an anomalous Hall effect in the correlated metal state of tDBG, with hysteresis loops spanning hundreds of mT in out-of-plane magnetic field (B⊥) that demonstrate spontaneously broken time-reversal symmetry. The B⊥ hysteresis persists for in-plane fields up to several Tesla, suggesting valley (orbital) ferromagnetism. At the same time, the resistivity is strongly affected by even mT-scale values of in-plane magnetic field, pointing to spin-valley coupling or to a direct orbital coupling between in-plane field and the valley degree of freedom.

Proximity-induced diversified magnetic states and electrically controllable spin polarization in bilayer graphene: Towards layered spintronics

Compared to monolayer graphene, electrons in Bernal-stacked bilayer graphene (BLG) have an additional layer degree of freedom, offering a platform for developing layered spintronics with the help of proximity-induced magnetism. Based on an effective phenomenological model, we systematically study the effect of this magnetism on the spin-dependent band structure near the Fermi energy and identify the magnetic phases induced in BLG by proximity with magnets. We show that spin polarization can develop in BLG due to this proximity effect. This spin polarization depends strongly on the layer distribution of magnetism, and can always be controlled by gate voltage which shifts spin-dependent band edges and modifies the total band gap. We further show that the band spin polarization can be modified by the proximity-induced staggered sublattice potential. By taking full advantage of layer-dependent magnetism in BLG, we propose that spintronic devices such as a spin filter, a giant magnetoresistance device, and a spin diode can operate under fully electric control, which is easier than the common magnetic field control.

Hofstadter butterflies in magnetically modulated graphene bilayer: An algebraic approach

It has been shown that Bernal stacked bilayer graphene (BLG) in a uniform magnetic field demonstrates integer quantum Hall effect with a zero Landau-level anomaly \cite{Geimbilayer}. In this article we consider such system in a two dimensional periodic magnetic modulation with square lattice symmetry. It is shown algebraically that the resulting Hofstadter spectrum can be expressed in terms of the corresponding spectrum of monolayer graphene in a similar magnetic modulation. In the weak-field limit, using the tight-binding model, we also derive the Harper-Hofstadter equation for such BLG system in a periodic magnetic modulation. We further demonstrate the topological quantisation of Hall conductivity in such system and point out that the quantised Hall plateaus are equally spaced for all quantum numbers for the quantised Hall conductivity.

Nearly flat bands in twisted triple bilayer graphene

We investigate the electronic structure of alternating-twist triple Bernal-stacked bilayer graphene (t3BG) as a function of interlayer coupling $\omega$, twist angle $\theta$, interlayer potential difference $\Delta$, and top-bottom bilayers sliding vector $\boldsymbol{\tau}$ for three possible configurations AB/AB/AB, AB/BA/AB, and AB/AB/BA. The parabolic low-energy band dispersions in a Bernal-stacked bilayer and gap-opening through a finite interlayer potential difference $\Delta$ allows the flattening of bands in t3BG down to $\sim 20$~meV for twist angles $\theta \lesssim 2^{\circ}$ regardless of the stacking types. The easier isolation of the flat bands and associated reduction of Coulomb screening thanks to the intrinsic gaps of bilayer graphene for finite $\Delta$ facilitate the formation of correlation-driven gaps when it is compared to the metallic phases of twisted trilayer graphene under electric fields. We obtain the stacking dependent Coulomb energy versus bandwidth $U/W \gtrsim 1$ ratios in the $\theta$ and $\Delta$ parameter space. We also present the expected $K$-valley Chern numbers for the lowest-energy nearly flat bands.

Cascade of isospin phase transitions in Bernal-stacked bilayer graphene at zero magnetic field

Emergent phenomena arising from the collective behaviour of electrons is expected when Coulomb interactions dominate over the kinetic energy, and one way to create this situation is to reduce the electronic bandwidth. Bernal-stacked bilayer graphene intrinsically supports saddle points in the band structure that are predicted to host a variety of spontaneous symmetry-broken states1,2,3,4,5,6,7. Here we show that bilayer graphene displays a cascade of symmetry-broken states with spontaneous spin and valley isospin ordering at zero magnetic field. We independently tune the carrier density and electric displacement field to explore the phase space of isospin order. Itinerant ferromagnetic states emerge near the conduction and valence band edges with complete spin and valley polarization. At larger hole densities, twofold degenerate quantum oscillations manifest in an additional symmetry-broken state that is enhanced by the application of an in-plane magnetic field. Both symmetry-broken states display enhanced layer polarization, suggesting a coupling to the layer degree of freedom1,7. These states occur in the absence of a moiré superlattice and are intrinsic to natural graphene bilayers. Therefore, we demonstrate that bilayer graphene represents a related but distinct approach to produce collective behaviour from flat dispersion, complementary to engineered moiré structures.

Realizing Valley-Polarized Energy Spectra in Bilayer Graphene Quantum Dots via Continuously Tunable Berry Phases.

The Berry phase plays an important role in determining many physical properties of quantum systems. However, tuning the energy spectrum of a quantum system via Berry phase is comparatively rare because the Berry phase is usually a fixed constant. Here, we report the realization of an unusual valley-polarized energy spectra via continuously tunable Berry phases in Bernal-stacked bilayer graphene quantum dots. In our experiment, the Berry phase of electron orbital states is continuously tuned from about π to 2π by perpendicular magnetic fields. When the Berry phase equals π or 2π, the electron states in the two inequivalent valleys are energetically degenerate. By altering the Berry phase to noninteger multiples of π, large and continuously tunable valley-polarized energy spectra are realized. Our result reveals the Berry phase's essential role in valleytronics and the observed valley splitting, on the order of 10meV at a magnetic field of 1T, is about 100 times larger than Zeeman splitting for spin, shedding light on graphene-based valleytronics.

Manipulating electron waves in graphene using carbon nanotube gating

Graphene with its dispersion relation resembling that of photons offers ample opportunities for applications in electron optics. The spacial variation of carrier density by external gates can be used to create electron waveguides, in analogy to optical fiber, with additional confinement of the carriers in bipolar junctions leading to the formation of few transverse guiding modes. We show that waveguides created by gating graphene with carbon nanotubes (CNTs) allow obtaining sharp conductance plateaus, and propose applications in the Aharonov-Bohm and two-path interferometers, and a pointlike source for injection of carriers in graphene. Other applications can be extended to Bernal-stacked or twisted bilayer graphene or two-dimensional electron gas. Thanks to their versatility, CNT-induced waveguides open various possibilities for electron manipulation in graphene-based devices.

Holes distribution in bilayer graphene

Layer-resolved charge distribution in bilayer graphene is crucial for understanding new physics in van der Waals stacked 2D crystals and related electronics applications. Here, we report the hole distribution in Bernal-stacked and twisted bilayer graphene (AB-BLG and t-BLG) labeled by carbon isotopes prepared by chemical vapor deposition. Raman spectroscopy identifies the isotope components and stacking orientation and further characterizes the hole concentration (nh) by monitoring the shift of ωG and ω2D. This study reveals that, for both AB-BLG and t-BLG, the nh in the top and bottom layers are close, leaving negligible differences smaller than their standard deviation of experimental data. The redshift of ωG in each layer of BLG relative to that of single-layer graphene implies the extra layer reduces the degree of charge exchange at the graphene/dopant interface. Moreover, the hole distribution behavior is rotational-angle independent despite a distinct electronically coupling degree between AB-BLG and t-BLG.

Fractional Chern insulators in magic-angle twisted bilayer graphene

Fractional Chern insulators (FCIs) are lattice analogues of fractional quantum Hall states that may provide a new avenue towards manipulating non-Abelian excitations. Early theoretical studies1–7 have predicted their existence in systems with flat Chern bands and highlighted the critical role of a particular quantum geometry. However, FCI states have been observed only in Bernal-stacked bilayer graphene (BLG) aligned with hexagonal boron nitride (hBN)8, in which a very large magnetic field is responsible for the existence of the Chern bands, precluding the realization of FCIs at zero field. By contrast, magic-angle twisted BLG9–12 supports flat Chern bands at zero magnetic field13–17, and therefore offers a promising route towards stabilizing zero-field FCIs. Here we report the observation of eight FCI states at low magnetic field in magic-angle twisted BLG enabled by high-resolution local compressibility measurements. The first of these states emerge at 5 T, and their appearance is accompanied by the simultaneous disappearance of nearby topologically trivial charge density wave states. We demonstrate that, unlike the case of the BLG/hBN platform, the principal role of the weak magnetic field is merely to redistribute the Berry curvature of the native Chern bands and thereby realize a quantum geometry favourable for the emergence of FCIs. Our findings strongly suggest that FCIs may be realized at zero magnetic field and pave the way for the exploration and manipulation of anyonic excitations in flat moiré Chern bands.