Bernal Bilayer Graphene Research Articles

Isospin- and momentum-polarized orders in bilayer graphene

Electron bands in Bernal bilayer graphene flatten out in a transverse electric field, offering a promising platform for correlated electron physics. We discuss the spin/valley isospin magnetism resembling that seen in moir\'e bands. We predict that the isospin magnetism coexists with momentum-polarized phases occurring via a ``flocking transition'' in momentum space in which the electron distribution is spontaneously displaced in momentum space relative to the $K$ and ${K}^{\ensuremath{'}}$ valley centers. The momentum-polarized phases feature electronic nematicity manifest in the anisotropy of transport, and unusual observables such as persistent currents in the ground state. Momentum-polarized carriers ``sample'' the Berry curvature of the conduction band, resulting in a longitudinal and anomalous Hall conductivity that displays switching upon the flocking transition and other effects that do not occur in previously studied systems.

Superconductivity induced by the intervalley Coulomb scattering in a few layers of graphene

We study the intervalley scattering induced by the Coulomb repulsion as a purely electronic mechanism for the origin of superconductivity in a few layers of graphene. The pairing is strongly favored by the presence of van Hove singularities in the density of states. We consider three different heterostructures: twisted bilayer graphene, rhombohedral trilayer graphene, and Bernal bilayer graphene. We obtain trends and estimates of the superconducting critical temperature in agreement with the experimental findings, which might identify the intervalley Coulomb scattering as a universal pairing mechanism in a few layers of graphene.

Phonon-limited resistivity of multilayer graphene systems

We calculate the theoretical contribution to the doping and temperature ($T$) dependence of electrical resistivity due to scattering by acoustic phonons in Bernal bilayer graphene (BBG) and rhombohedral trilayer graphene (RTG). We focus on the role of nontrivial geometric features of the detailed, anisotropic $k\cdot p$ band structures of these systems - e.g. Van Hove singularities, Lifshitz transitions, Fermi surface anisotropy, and band curvature near the gap - whose effects on transport have not yet been systematically studied. We find that these geometric features strongly influence the temperature and doping dependencies of the resistivity. In particular, the band geometry leads to a nonlinear $T$-dependence in the high-$T$ equipartition regime, complicating the usual $T^4$ to $T$ Bloch-Gr\"{u}neisen crossover. Our focus on BBG and RTG is motivated by recent experiments in these systems that have discovered several exotic low-$T$ superconductivity proximate to complicated hierarchies of isospin-polarized phases. These interaction-driven phases are intimately related to the geometric features of the band structures, highlighting the importance of understanding the influence of band geometry on transport. While resolving the effects of the anisotropic band geometry on the scattering times requires nontrivial numerical solution, our approach is rooted in intuitive Boltzmann theory. We compare our results with recent experiment and discuss how our predictions can be used to elucidate the relative importance of various scattering mechanisms in these systems.

Electric-field-tunable band gap in commensurate twisted bilayer graphene

Bernal bilayer graphene exhibits a band gap that is tunable through the infrared with an electric field. We show that sublattice odd commensurate twisted bilayer graphene (C-TBG) exhibits a band gap that is tunable through the terahertz with an electric field. We show that from the perspective of terahertz optics the sublattice odd and even forms of C-TBG are ``inflated'' versions of Bernal and AA-stacked bilayer graphene, respectively, with energy scales reduced by a factor of 110 for the $21.{79}^{\ensuremath{\circ}}$ commensurate unit cell. This lower energy scale is accompanied by a correspondingly smaller gate voltage, which means that the strong-field regime is more easily accessible than in the Bernal case. Finally, we show that the interlayer coherence energy is a directly accessible experimental quantity through the position of a power-law divergence in the optical conductivity.

Cascade of transitions in twisted and non-twisted graphene layers within the van Hove scenario

Motivated by measurements of compressibility and STM spectra in twisted bilayer graphene, we analyze the pattern of symmetry breaking for itinerant fermions near a van Hove singularity. Making use of an approximate SU(4) symmetry of the Landau functional, we show that the structure of the spin/isospin order parameter changes with increasing filling via a cascade of transitions. We compute the feedback from different spin/isospin orders on fermions and argue that each order splits the initially 4-fold degenerate van Hove peak in a particular fashion, consistent with the STM data and compressibility measurements, providing a unified interpretation of the cascade of transitions in twisted bilayer graphene. Our results follow from a generic analysis of an SU(4)-symmetric Landau functional and are valid beyond a specific underlying fermionic model. We argue that an analogous van Hove scenario explains the cascade of phase transitions in non-twisted Bernal bilayer and rhombohedral trilayer graphene.

Enhanced superconductivity through virtual tunneling in Bernal bilayer graphene coupled to WSe2

Motivated by a recent experiment [arXiv:2205.05087], we investigate a possible mechanism that enhances superconductivity in hole-doped Bernal bilayer graphene due to a proximate WSe$_2$ monolayer. We show that the virtual tunneling between WSe$_2$ and Bernal bilayer graphene, which is known to induce Ising spin-orbit coupling, can generate an additional attraction between two holes, providing a potential explanation for enhancing superconductivity in Bernal bilayer graphene. Using microscopic interlayer tunneling, we derive the Ising spin-orbit coupling and the effective attraction as functions of the twist angle between Bernal bilayer graphene and the WSe$_2$ monolayer. Our theory provides an intuitive and physical explanation for the intertwined relation between Ising spin-orbit coupling and superconductivity enhancement, which should motivate future studies.

Giant ferroelectric polarization in a bilayer graphene heterostructure

At the interface of van der Waals heterostructures, the crystal symmetry and the electronic structure can be reconstructed, giving rise to physical properties superior to or absent in parent materials. Here by studying a Bernal bilayer graphene moiré superlattice encapsulated by 30°-twisted boron nitride flakes, we report an unprecedented ferroelectric polarization with the areal charge density up to 1013 cm−2, which is far beyond the capacity of a moiré band. The translated polarization ~5 pC m−1 is among the highest interfacial ferroelectrics engineered by artificially stacking van der Waals crystals. The gate-specific ferroelectricity and co-occurring anomalous screening are further visualized via Landau levels, and remain robust for Fermi surfaces outside moiré bands, confirming their independence on correlated electrons. We also find that the gate-specific resistance hysteresis loops could be turned off by the other gate, providing an additional control knob. Furthermore, the ferroelectric switching can be applied to intrinsic properties such as topological valley current. Overall, the gate-specific ferroelectricity with strongly enhanced charge polarization may encourage more explorations to optimize and enrich this novel class of ferroelectricity, and promote device applications for ferroelectric switching of various quantum phenomena.

Quantum cascade of correlated phases in trigonally warped bilayer graphene.

Divergent density of states offersan opportunity to explore a wide variety of correlated electron physics. In the thinnest limit, this has been predicted and verified in the ultraflat bands of magic-angle twisted bilayer graphene1-5, the band touching points of few-layer rhombohedral graphite6-8 and the lightly doped rhombohedral trilayer graphene9-11. The simpler and seemingly better understood Bernal bilayer graphene is also susceptible to orbital magnetism at charge neutrality7 leading to layer antiferromagnetic states12 or quantum anomalous Hallstates13. Here we report the observation of a cascade of correlated phases in the vicinity of electric-field-controlled Lifshitz transitions14,15 and van Hove singularities16 in Bernal bilayer graphene. We provide evidence for the observation of Stoner ferromagnets in the form of half and quarter metals10,11. Furthermore, we identify signatures consistent with a topologically non-trivial Wigner-Hall crystal17 at zero magnetic field and its transition to a trivial Wigner crystal, as well as two correlated metals whose behaviour deviates from that of standard Fermi liquids. Our results in this reproducible, tunable, simple systemopen up new horizons for studying strongly correlated electrons.

Acoustic-phonon-mediated superconductivity in moiréless graphene multilayers

We investigate the competition between acoustic-phonon-mediated superconductivity and the long-range Coulomb interaction in moir\'eless graphene multilayers, specifically, Bernal bilayer graphene, rhombohedral trilayer graphene, and ABCA-stacked tetralayer graphene. In these graphene multilayers, the acoustic phonons can realize, through electron-phonon coupling, both spin-singlet and spin-triplet pairings, and the intra-sublattice pairings ($s$-wave spin-singlet and $f$-wave spin-triplet) are the dominant channels. Our theory naturally explains the distinct recent experimental findings in Bernal bilayer graphene and rhombohedral trilayer graphene, and we further predict existence of superconductivity in ABCA tetralayer graphene arising from electron-phonon interactions. In particular, we demonstrate that the acoustic-phonon-mediated superconductivity prevails over a wide range of doping in rhombohedral trilayer graphene and ABCA tetralayer graphene while superconductivity exists only in a narrow range of doping near the Van Hove singularity in Bernal bilayer graphene. Key features of our theory are the inclusion of realistic band structures with the appropriate Van Hove singularities and Coulomb repulsion effects (the so-called "$\mu^*$ effect") opposing the phonon-induced superconducting pairing. We also discuss how intervalley scatterings can suppress the spin-triplet spin-polarized superconductivity. Our work provides detailed prediction based on electron-acoustic-phonon-interaction-induced graphene superconductivity, which should be investigated in future experiments.

Generalized Peierls substitution for the tight-binding model of twisted graphene systems in a magnetic field

This work aims at addressing an important advanced methodology for twisted graphene in the presence of applied magnetic field, which is the Bloch-basis tight-binding model (TBM) in conjunction with the generalized Peierls substitution. We investigate extensively the band structures, Landau levels (LLs), and quantum Hall conductivity (QHC) of twisted bilayer graphene and twisted double-bilayer graphene, as well as their dependence on the twist angle. Comparison between these crucial properties of monolayer graphene, Bernal bilayer graphene, and the twisted systems is carefully made to highlight the roles played by twisting. The unique selection rules of inter-LL transition, which is crucial for achieving a deep understanding of the step structures of QHC, are identified through the properties of LL wave functions. The effective TBM is combined with the generalized Peierls substitution to investigate the magnetic quantization of twisted graphene systems at magic angle. Our theoretical model opens up an opportunity for comprehension of the interplay between an applied magnetic field and the twisting effect associated with layered graphene. The proposed method is expected to be applicable for the calculation of magnetic quantization problems of other complex systems.

Competing orders and cascade of degeneracy lifting in doped Bernal bilayer graphene

Motivated by recent experiments [H. Zhou et al., Science 375, 774 (2022) and S. C. de la Barrera et al., arXiv:2110.13907], here we propose a general mechanism for valley and/or spin degeneracy lifting of the electronic bands in doped Bernal bilayer graphene, subject to electric displacement ($D$) fields. A $D$-field induced layer polarization (LP), when accompanied by a Hubbard repulsion-driven layer antiferromagnet (LAF) and next-nearest-neighbor repulsion-driven quantum anomalous Hall (QAH) orders, lifts the fourfold degeneracy of electronic bands, yielding a quarter metal for small doping, as also observed in ABC trilayer graphene. With the disappearance of the QAH order, electronic bands recover twofold valley degeneracy, thereby forming a conventional or compensated (with majority and minority carriers) half metal at moderate doping, depending on the relative strength of LP and LAF. At even higher doping and for a weak $D$ field only LAF survives and the Fermi surface recovers fourfold degeneracy. We also show that a pure repulsive electronic interaction mediated triplet $f$-wave pairing emerges from a parent correlated nematic liquid or compensated half metal when an in-plane magnetic field is applied to the system.

Acoustic-phonon-mediated superconductivity in Bernal bilayer graphene

We present a systematic theory of acoustic-phonon-mediated superconductivity, which incorporates Coulomb repulsion, explaining the recent experiment in Bernal bilayer graphene under a large displacement field. The acoustic-phonon mechanism predicts that $s$-wave spin-singlet and $f$-wave spin-triplet pairings are degenerate and dominant. Assuming a spin-polarized valley-unpolarized normal state, we obtain $f$-wave spin-triplet superconductivity with a $T_c\sim 20$ mK near $n_e=-0.6\times 10^{12}$ cm$^{-2}$ for hole doping, in approximate agreement with the experiment. We further predict the existence of superconductivity for larger doping in both electron-doped and hole-doped regimes. Our results indicate that the observed spin-triplet superconductivity in Bernal bilayer graphene arises from acoustic phonons.

Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene.

In conventional superconductors, Cooper pairing occurs between electrons of opposite spin. We observe spin-polarized superconductivity in Bernal bilayer graphene when doped to a saddle-point van Hove singularity generated by large applied perpendicular electric field. We observe a cascade of electrostatic gate-tuned transitions between electronic phases distinguished by their polarization within the isospin space defined by the combination of the spin and momentum-space valley degrees of freedom. Although all of these phases are metallic at zero magnetic field, we observe a transition to a superconducting state at finite B‖ ≈ 150mT applied parallel to the two-dimensional sheet. Superconductivity occurs near a symmetry breaking transition, and exists exclusively above the B‖-limit expected of a paramagnetic superconductor with the observed transition temperature TC ≈ 30mK, consistent with a spin-triplet order parameter.

Electronic transport properties and quantum localization effects monitored by selective functionalization in Bernal bilayer graphene

Monitoring electronic properties of 2D materials is an essential step to open a way for applications such as electronic devices and sensors. From this perspective, Bernal bilayer graphene (BLG) is a fairly simple system that offers great possibilities for tuning electronic gap and charge carriers' mobility by selective functionalization (adsorptions of atoms or molecules). Here, we present a detailed numerical study of BLG electronic properties when two types of adsorption site are present simultaneously. We focus on realistic cases that could be realized experimentally with adsorbate concentration c varying from 0.25% to 5%. For a given value of c, when the electronic doping is lower than c we show that quantum effects, which are ignored in usual semi-classical calculations, strongly affect the electronic structure and the transport properties. A wide range of behaviors is indeed found, such as gap opening, metallic behavior or abnormal conductivity, which depend on the adsorbate positions, the c value, the doping, and eventually the coupling between midgap states which can create a midgap band. These behaviors are understood by simple arguments based on the fact that BLG lattice is bipartite. We also analyze the conductivity at low temperature, where multiple scattering effects cannot be ignored. Moreover, when the Fermi energy lies in the band of midgap states, the average velocity of charge carriers cancels but conduction is still possible thanks to quantum fluctuations of the velocity.

Superconductivity and other phases in graphene multilayers, without twists

1. Isospin magnetism and spin-triplet superconductivity in Bernal bilayer graphene Authors: Haoxin Zhou, Yu Saito, Liam Cohen, William Huynh, Caitlin L. Patterson, Fangyuan Yang, Takashi Taniguchi, Kenji Watanabe, and Andrea F. Young arXiv:2110.11317 2. Superconductivity in rhombohedral trilayer graphene Authors: Haoxin Zhou, Tian Xie, Takashi Taniguchi, Kenji Watanabe, and Andrea F. Young Nature 598, 434–438 […]

Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders

Performing a leading-order renormalization group analysis, here we compute the effects of generic local or short-range electronic interactions in monolayer and Bernal bilayer graphene. Respectively in these two systems chiral quasiparticles display linear and biquadratic band touching, leading to linearly vanishing and constant DOS. Consequently, the former system remains stable for weak enough local interactions, and supports a variety of ordered phases only beyond a critical strength of interactions. By contrast, ordered phases can nucleate for sufficiently weak interactions in bilayer graphene. By tuning the strength of all symmetry allowed local interactions, we construct various cuts of the phase diagram at zero and finite temperature and chemical doping. Typically, at zero doping insulating phases (such as charge-density-wave, antiferromagnet, quantum anomalous and spin Hall insulators) prevail at the lowest temperature, while gapless nematic or smectic liquids stabilize at higher temperatures. On the other hand, at finite doping the lowest temperature ordered phase is occupied by a superconductor. Besides anchoring such an organizing principle among the candidate ordered phases, we also establish a selection rule between them and the interaction channel responsible for the breakdown of linear or biquadrtic chiral nodal Fermi liquid. In addition, we also demonstrate the role of the normal state band structure in selecting the pattern of symmetry breaking from a soup of preselected incipient competing orders. As a direct consequence of the selection rule, while an antiferromagnetic phase develops in undoped monolayer and bilayer graphene, the linear (biquadratic) band dispersion favors condensation of a spin-singlet nematic (translational symmetry breaking Kekul\'e) superconductor in doped monolayer (bilayer) graphene, when the on site Hubbard repulsion dominates in these systems.

Spectroscopy of a tunable moir\xe9 system with a correlated and topological flat band

Moiré superlattices created by the twisted stacking of two-dimensional crystals can host electronic bands with flat energy dispersion in which enhanced interactions promote correlated electron states. The twisted double bilayer graphene (TDBG), where two Bernal bilayer graphene are stacked with a twist angle, is such a moiré system with tunable flat bands. Here, we use gate-tuned scanning tunneling spectroscopy to directly demonstrate the tunability of the band structure of TDBG with an electric field and to show spectroscopic signatures of electronic correlations and topology for its flat band. Our spectroscopic experiments are in agreement with a continuum model of TDBG band structure and reveal signatures of a correlated insulator gap at partial filling of its isolated flat band. The topological properties of this flat band are probed with the application of a magnetic field, which leads to valley polarization and the splitting of Chern bands with a large effective g-factor.

Twisted monolayer and bilayer graphene for vertical tunneling transistors

We prepare twist-controlled resonant tunneling transistors consisting of monolayer and Bernal bilayer graphene electrodes separated by a thin layer of hexagonal boron nitride. The resonant conditions are achieved by closely aligning the crystallographic orientation of graphene electrodes, which leads to momentum conservation for tunneling electrons at certain bias voltages. Under such conditions, negative differential conductance can be achieved. Application of in-plane magnetic field leads to electrons acquiring additional momentum during the tunneling process, which allows control over the resonant conditions.

Movable Valley Switch Driven by Berry Phase in Bilayer-Graphene Resonators.

Berry phase, the geometric phase accumulated over a closed loop in parameter space during an adiabatic cyclic evolution, has been demonstrated to play an important role in many quantum systems since its discovery. In gapped Bernal bilayer graphene, the Berry phase can be continuously tuned from zero to 2π, which offers a unique opportunity to explore the tunable Berry phase on physical phenomena. Here, we report experimental observation of Berry-phase-induced valley splitting and crossing in movable bilayer-graphene p-n junction resonators. In our experiment, the resonators are generated by combining the electric field of a scanning tunneling microscope tip with the gap of bilayer graphene. A perpendicular magnetic field changes the Berry phase of the confined bound states in the resonators from zero to 2π continuously and leads to the Berry phase difference for the two inequivalent valleys in the bilayer graphene. As a consequence, we observe giant valley splitting and unusual valley crossing of the lowest bound states. Our results indicate that the bilayer-graphene resonators can be used to manipulate the valley degree of freedom in valleytronics.

Interplay of orbital hopping and perpendicular magnetic field in anisotropic phase transitions for Bernal bilayer graphene and hexagonal boron-nitride.

We theoretically address the perpendicular magnetic field effects on the electronic phase of Bernal bilayer graphene and hexagonal boron-nitride (h-BN) taking into account the total and orbital-projected electronic bands using the tight-binding parameters in the Harrison model, followed by the Green's function method. First, we confirm that our model is computationally efficient and accurate for calculating the magneto-orbital electronic phase transition by reproducing the semimetallic and insulating treatments of pristine Bernal bilayer graphene and h-BN, respectively. In our model, the magnetic field couples only to the electron spin degrees of freedom (with the same contributions for spin-up and spin-down) due to the low dimension of the systems. Here, the main features of the phase transitions are characterized by the electronic density of states (DOS). We found that sp2-hybridization is destroyed when the systems are immersed in the magnetic field, leading to a phase transition to metal for both systems at strong magnetic fields. While there is no phase transition for bilayer graphene at weak magnetic fields, for the case of bilayer h-BN, an insulator to semiconductor phase transition can be viewed, making h-BN more applicable in industry. In bilayer graphene, the anisotropic phase transition appears as insulator-semiconductor, insulator-metal, and semimetal-metal for s-, {px + py}-, and pz-orbitals, respectively, whereas in the case of bilayer h-BN, one observes the same transitions for {s,pz}-orbitals but insulator-semiconductor for {px + py} orbitals. Generically, our findings highlight that the applied magnetic field manipulates the band structure of bilayer graphene and h-BN, and gives ideas to experimentalists for tuning the electro-optical properties of these materials.