Magic-angle twisted bilayer graphene exhibits quasi-flat low-energy bands with Van Hove singularities close to the Fermi level. These singularities play an important role in the exotic phenomena observed in this material, such as superconductivity and magnetism, by amplifying electronic correlation effects. In this work, we study the correspondence of four-terminal conductance and the Fermi surface topology as a function of the twist angle, pressure, and energy in mesoscopic, ballistic samples of small-angle twisted bilayer graphene. We establish a correspondence between features in the wide-junction conductance and the presence of van Hove singularities in the density of states. Moreover, we identify additional transport features, such as a large, pressure-tunable minimal conductance, conductance peaks coinciding with non-singular band crossings, and unusually large conductance oscillations as a function of the system size. Our results suggest that twisted bilayer graphene close the magic angle is a unique system featuring simultaneously large conductance due to the quasi-flat bands, strong quantum nonlinearity due to the Van Hove singularities and high sensitivity to external parameters, which could be utilized in high-frequency device applications and sensitive detectors.
Magnetic impurity adsorbed on one of the carbon planes of a bilayer graphene is studied. The formation of the many-body SU(2) and SU(4) resonances close to the bandgap is analyzed within the mean field Kotliar-Ruckenstein slave boson approach. Impact of enhanced hybridization and magnetic instability of bilayer doped near the Van Hove singularity on the screening of magnetic moment is discussed.
By means of atomistic tight-binding calculations, we investigate the effects of uniaxial strain on the electronic bandstructure of twisted graphene bilayer. We find that the bandstructure is dramatically deformed and the degeneracy of the bands is broken by strain. As a conseqence, the number of Dirac cones can double and the van Hove singularity points are separated in energy. The dependence of these effects on the strength of strain, its applied direction and the twist angle is carefully clarified. As an important result, we demonstrate that the position of van Hove singularities can be modu…
In a continuous search for the energy-efficient electronic switches, a great attention is focused on tunnel field-effect transistors (TFETs) demonstrating an abrupt dependence of the source-drain current on the gate voltage. Among all TFETs, those based on one-dimensional (1D) semiconductors exhibit the steepest current switching due to the singular density of states near the band edges, though the current in 1D structures is pretty low. In this paper, we propose a TFET based on 2D graphene bilayer which demonstrates a record steep subthreshold slope enabled by van Hove singularities in the de…
Van Hove singularity-driven giant Nernst signal in twisted double bilayer graphene
Indian Institute of Science（印度科学研究所）；Tel-Aviv University（特拉维夫大学）；The Ohio State University（俄亥俄州立大学）；Weizmann Institute of Science（魏茨曼科学研究所）；National Institute of Material Science（国家材料研究所）；Tata Institute of Fundamental Research（塔塔基础研究所）
We investigate the many-body instabilities of electrons interacting near Van Hove singularities arising in monolayer and twisted bilayer graphene. We show that a pairing instability must be dominant over the tendency to magnetic order as the Fermi level is tuned to the Van Hove singularity in the conduction band of graphene. As a result of the extended character of the saddle points in the dispersion, we find that the pairing of the electrons takes place preferentially in a channel of f-wave symmetry, with an order parameter vanishing at the position of the saddle points along the Fermi line. …
We consider the electronic structure of a slightly twisted graphene bilayer and show the coexistence of van Hove singularities (VHSs) and superlattice Dirac points in a continuum approximation. The graphene-on-graphene moiré pattern gives rise to a periodic electronic potential, which leads to the emergence of the superlattice Dirac points due to the chiral nature of the charge carriers. Owning to the distinguishing real and reciprocal structures, the sublattice exchange even and odd structures of the twisted graphene bilayer (the two types of commensurate structures) result in two different s…
We report a systematic study of the optical conductivity of twisted bilayer graphene (tBLG) across a large energy range (1.2 eV to 5.6 eV) for various twist angles, combined with first-principles calculations. At previously unexplored high energies, our data show signatures of multiple van Hove singularities (vHSs) in the tBLG bands, as well as the nonlinearity of the single layer graphene bands and their electron-hole asymmetry. Our data also suggest that excitonic effects play a vital role in the optical spectra of tBLG. Including electron-hole interactions in first-principles calculations i…
The stacking and bending of graphene are trivial but extremely powerful agents of control over graphene's manifold physics. By changing the twist angle, one can drive the system over a plethora of exotic states via strong electron correlation, thanks to the moiré superlattice potentials, while the periodic or triaxial strains induce discretization of the band structure into Landau levels without the need for an external magnetic field. We fabricated a hybrid system comprising both the stacking and bending tuning knobs. We have grown the graphene monolayers by chemical vapor deposition, using $…
Topological phases, van Hove singularities, and spin texture in magic-angle twisted bilayer graphene in the presence of proximity-induced spin-orbit couplings
Recent studies show that two low-energy Van Hove singularities (VHSs) seen as two pronounced peaks in the density of states (DOS) could be induced in twisted graphene bilayer. Here, we report angle dependent VHSs of slightly twisted graphene bilayer studied by scanning tunneling microscopy and spectroscopy. We show that energy difference of the two VHSs follows \DeltaEvhs ~ \hbarνF\DeltaK between 1.0^{\circ} and 3.0^{\circ} (here νF ~ 1.1\times106 m/s is the Fermi velocity of monolayer graphene, \DeltaK = 2Ksin(θ/2) is the shift between the corresponding Dirac points of the twisted graphene bi…
We numerically investigate the electronic transport properties between two mesoscopic graphene disks with a twist by employing the density functional theory coupled with non-equilibrium Green's function technique. By attaching two graphene leads to upper and lower graphene layers separately, we explore systematically the dependence of electronic transport on the twist angle, Fermi energy, system size, layer stacking order and twist axis. When choose different twist axes for either AA- or AB-stacked bilayer graphene, we find that the dependence of conductance on twist angle displays qualitative…
The creation of van der Waals heterostructures based on a graphene monolayer and other two-dimensional crystals has attracted great interest because atomic registry of the two-dimensional crystals can modify the electronic spectra and properties of graphene. Twisted graphene bilayer can be viewed as a special van der Waals structure composed of two mutual misoriented graphene layers, where the sublayer graphene not only plays the role of a substrate, but also acts as an equivalent role as the top graphene layer in the structure. Here we report the electronic spectra of slightly twisted graphen…
Twisted graphene bilayers (TGBs) have low-energy van Hove singularities (VHSs) that are strongly localized around AA-stacked regions of the moire pattern. Therefore, they exhibit novel many-body electronic states, such as Mott-like insulator and unconventional superconductivity. Unfortunately, these strongly correlated states were only observed in magic angle TGBs with the twist angle theta~1.1°, requiring a precisely tuned structure. Is it possible to realize exotic quantum phases in the TGBs not limited at the magic angle? Here we studied electronic properties of a TGB with theta~1.64° and d…
The possibility of triggering correlated phenomena by placing a singularity of the density of states near the Fermi energy remains an intriguing avenue towards engineering the properties of quantum materials. Twisted bilayer graphene is a key material in this regard because the superlattice produced by the rotated graphene layers introduces a van Hove singularity and flat bands near the Fermi energy that cause the emergence of numerous correlated phases, including superconductivity. While the twist angle-dependence of these properties has been explored, direct demonstration of electrostatic co…
Moiré patterns on Highly Oriented Pyrolytic Graphite surfaces due to dislocated graphene layers were studied. We observed that the apparent corrugations of the moiré patterns in scanning tunnelling microscopy images change as a function of tunnel junction bias. A simple geometric investigation of the atomic structure of the graphene layers generating moiré patterns revealed that different atomic arrangements due to different twist angles can result in similar geometric moiré periods such that, only a small fraction of the observed moiré periodicities may coincide with the real atomic periodici…
The electronic band structure of twisted bilayer graphene develops van Hove singularities whose energy depends on the twist angle between the two layers. Using Raman spectroscopy, we monitor the evolution of the electronic band structure upon doping using the G peak area which is enhanced when the laser photon energy is resonant with the energy separation of the van Hove singularities. Upon charge doping, the Raman G peak area initially increases for twist angles larger than a critical angle and decreases for smaller angles. To explain this behavior with twist angle, the energy of separation o…
Van Hove singularities (VHS's) in the density of states play an outstanding and diverse role for the electronic and thermodynamic properties of crystalline solids. At the critical point the Fermi surface connectivity changes and topological properties undergo a transition. Opportunities to systematically pass a VHS at the turn of a voltage knob and study its diverse impact are however rare. With the advent of van der Waals heterostructures, control over the atomic registry of neigbouring graphene layers offers an unprecedented tool to generate a low energy VHS easily accessible with convention…
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 compressibi…
Extensive scanning tunnelling microscopy and spectroscopy experiments complemented by first principles and parameterized tight binding calculations provide a clear answer to the existence, origin and robustness of van Hove singularities (vHs) in twisted graphene layers. Our results are conclusive: vHs due to interlayer coupling are ubiquitously present in a broad range (from 1° to 10°) of rotation angles in our graphene on 6H-SiC(000-1) samples. From the variation of the energy separation of the vHs with rotation angle we are able to recover the Fermi velocity of a graphene monolayer as well a…
We theoretically calculate the impurity-scattering induced resistivity of twisted bilayer graphene at low twist angles where the graphene Fermi velocity is strongly suppressed. We consider, as a function of carrier density, twist angle, and temperature, both long-ranged Coulomb scattering and short-ranged defect scattering within a Boltzmann theory relaxation time approach. For experimentally relevant disorder, impurity scattering contributes a resistivity comparable to (much larger than) the phonon scattering contribution at high (low) temperatures. Decreasing twist angle leads to larger resi…
We consider Friedel oscillation in the two-dimensional Dirac materials when Fermi level is near the van Hove singularity. Twisted graphene bilayer and the surface state of topological crystalline insulator are the representative materials which show low-energy saddle points that are feasible to probe by gating. We approximate the Fermi surface near saddle point with a hyperbola and calculate the static Lindhard response function. Employing a theorem of Lighthill, the induced charge density $δn$ due to an impurity is obtained and the algebraic decay of $δn$ is determined by the singularity of t…
Relativistic Mott transition and high-order van Hove singularity in twisted double bilayer WSe${}_2$: mean-field and functional renormalization group study
We analyze the orbital magnetic susceptibility from the band structure of twisted bilayer graphene. Close to charge neutrality, the out-of-plane susceptibility inherits the strong diamagnetic response from graphene. Increasing the doping, a crossover from diamagnetism to paramagnetism is obtained and a logarithmic divergence develops at the van Hove singularity of the Moiré lattice in the first band. The enhanced paramagnetism at the van Hove singularity is stronger for relatively large angle but gets suppressed by the flat spectrum towards the vicinity of the first magic angle. A diverging pa…
Rotated graphene multilayers form a new class of graphene related systems with electronic properties that drastically depend on the rotation angles. It has been shown that bilayers behave like two isolated graphene planes for large rotation angles. For smaller angles, states in the Dirac cones belonging to the two layers interact resulting in the appearance of two van Hove singularities. States become localised as the rotation angle decreases and the two van Hove singularities merge into one peak at the Dirac energy. Here we go further and consider bilayers with very small rotation angles. In …
Isolating the natural edges of bilayer graphene in gate-defined mesoscopic devices
University of Basel（巴塞尔大学）；Advanced Materials Laboratory, National Institute for Materials Science（国家材料科学研究所先进材料实验室）；Solid State Physics Laboratory, ETH Zürich（苏黎世联邦理工学院固体物理实验室）；Swiss Nanoscience Institute（瑞士纳米科学研究所）
We numerically calculate the optical conductivity of twisted graphene bilayers within the continuum model. To obtain the imaginary part, we employ the regularized Kramers-Kronig relation allowing us to discuss arbitrary twist angles, chemical potential and temperature. We find that the Drude weight $D$ as function of the chemical potential $μ$ closely follows the shell structure of twisted bilayer displayed by the density of states. For certain angles, this results in a transport gap D=0 at finite $μ$. We also discuss the loss function which, for low doping, is characterized by acoustic interb…
Recent experiments have observed possible spin- and valley-polarized insulators and spin-triplet superconductivity in twisted double bilayer graphene, a moire structure consisting of a pair of Bernal-stacked bilayer graphene. Besides the continuously tunable band widths controlled by an applied displacement field and twist angle, these moire bands also possess van Hove singularities near the Fermi surface and a field-dependent nesting which is far from perfect. Here we carry out a perturbative renormalization group analysis to unbiasedly study the competition among all possible instabilities i…
Employing graphene as a template, we fabricate moiré superlattices by stacking bilayer or folded bilayer-bilayer graphene (BLG or fBBLG) and hexagonal boron nitride (hBN), i.e., hBN/BLG/hBN or hBN/fBBLG/hBN stacks, with a small twist angle between the graphene and one of the two hBN layers. Because of the modulation due to the hBN, higher-generation Dirac points can emerge with a narrow bandwidth and van Hove singularities. In the moiré superlattice devices, we can therefore access the higher-generation Dirac points by in-situ gate tuning. This study is based on our previous paper (Appl. Phys.…
The experimental control over the twist angle in twisted bilayer graphene has not been reported and its realistic structure is most likely incommensurate. In this paper, we develop a tight-binding virtual crystal approximation theory to study the electronic properties in incommensurate twisted bilayer graphene. The theory yields the electronic band structure and the local density of states for any incommensurate twist angle θ between the graphene sheets. Angle dependent Van Hove singularities are observed in the numerically calculated local density of states. In accord with observations in sca…
Understanding and tuning correlated states is of great interest and significance to modern condensed matter physics. The recent discovery of unconventional superconductivity and Mott-like insulating states in magic-angle twisted bilayer graphene (tBLG) presents a unique platform to study correlation phenomena, in which the Coulomb energy dominates over the quenched kinetic energy as a result of hybridized flat bands. Extending this approach to the case of twisted multilayer graphene would allow even higher control over the band structure because of the reduced symmetry of the system. Here, we …
While it is known that the double-layer Bi$_2$Sr$_2$CaCu$_2$O$_{8+y}$ (BSCCO) cuprate superconductor exhibits a one-dimensional (1D) incommensurate superlattice (IS), the effect of IS on the electronic structure remains elusive. Following the recent shift of the interest from underdoped to optimum and overdoped phase in BSCCO by increasing the hole doping $x$, controlled by the oxygen interstitials concentration $y$, here we focus on the multiple splitting of the density of states (DOS) peaks and emergence of higher order van Hove singularities (VHS) due to the 1D incommensurate superlattice. …
Rotated graphene bilayers form an exotic class of nanomaterials with fascinating electronic properties governed by the rotation angle theta. For large rotation angles, the electron eigenstates are restricted to one layer and the bilayer behaves like two decoupled graphene layer. At intermediate angles, Dirac cones are preserved but with a lower velocity and van Hove singularities are induced at energies where the two Dirac cones intersect. At very small angles, eigenstates become localized in peculiar moire zones. We analyse here the effect of an asymmetric doping for a series of commensurate …
This article reviews the theoretical and experimental work related to the electronic properties of bilayer graphene systems. Three types of bilayer stackings are discussed: the AA, AB, and twisted bilayer graphene. This review covers single-electron properties, effects of static electric and magnetic fields, bilayer-based mesoscopic systems, spin-orbit coupling, dc transport and optical response, as well as spontaneous symmetry violation and other interaction effects. The selection of the material aims to introduce the reader to the most commonly studied topics of theoretical and experimental …
This is a numerical study of thermoelectric properties of ballistic bilayer graphene in the presence of trigonal warping term in the effective Hamiltonian. We find, in the mesoscopic samples of the length $L>10\,μ$m at sub-Kelvin temperatures, that both the Seebeck coefficient and the Lorentz number show anomalies (the additional maximum and minimum, respectively) when the electrochemical potential is close to the Lifshitz energy, which can be attributed to the presence of the van Hove singularity in a bulk density of states. At higher temperatures the anomalies vanish, but measurable quantiti…
In recent years, Chebyshev polynomial expansions of tight-binding Green's functions have been successfully applied to the study of a wide range of spectral and transport properties of materials. However, the application of the Chebyshev approach to the study of quantum transport properties of noninteracting mesoscopic systems with leads has been hampered by the lack of a suitable Chebyshev expansion of Landaeur's formula or one of its equivalent formulations in terms of Green's functions in Keldysh's perturbation theory. Here, we tackle this issue by means of a hybrid approach that combines th…
We present a theoretical study of the effects of heterostrain and lattice relaxation on the optical conductivity of twisted bilayer graphene near the magic angle, based on the band structures obtained from a continuum model. We find that heterostrain, lattice relaxation and their combination give rise to very distinctive spectroscopic features in the optical conductivity, which can be used to probe and distinguish these effects. From the spectrum at various Fermi energies, important features in the strain- and relaxation-modified band structure such as the bandgap, bandwidth and van Hove singu…
We theoretically study the optical absorption property of twisted bilayer graphenes with various stacking geometries, and demonstrate that the spectroscopic characteristics serve as a fingerprint to identify the rotation angle between two layers. We find that the absorption spectrum almost continuously evolves in changing the rotation angle, regardless of the lattice commensurability. The spectrum is characterized by series of peaks associated with the van Hove singularity, and the peak energies systematically shift with the rotation angle. We calculate the optical absorption in two different …
We present a comprehensive dynamical mean field study of the triangular lattice moiré Hubbard model, which is believed to represent the physics of moiré bilayer transition metal dichalcogenides. In these materials, important aspects of the band structure including the bandwidth and the order and location of van Hove singularities can be tuned by varying the interlayer potential. We present a magnetic and metal-insulator phase diagram and a detailed study of the dependence of the resistivity on temperature, band filling and interlayer potential. We find that transport displays Fermi liquid, str…
We calculate the finite-frequency conductivity of bilayer graphene with a relative twist between the layers. The low frequency response at zero doping shows a flat conductivity with value twice that of the monolayer case and at higher frequency a strong absorption peak occurs. For finite doping, the low frequency flat absorption is modified into a peak about zero frequency (the Drude response) accompanied by an interband edge which results from the transfer of spectral weight from interband to intraband absorption due to Pauli blocking. If the system is doped sufficiently such that the chemica…
Electronic and transport properties of bilayer heterostructure under light irradiation are of fundamental interest to improve functionality of optoelectronic devices. We theoretically study the modification of transport properties of bilayer graphene and bilayer heterostructures under a time-periodic external light field. The bulk electronic and transport properties are studied in a Landauer-type configuration by using the nonequilibrium Green's function formalism. To illustrate the behavior of the differential conductance of a bilayer contact under light illumination, we consider tight-bindin…
Weak localization and universal conductance fluctuations in large area twisted bilayer graphene
University of Pennsylvania（宾夕法尼亚大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Pohang University of Science and Technology（浦项科技大学）；Washington University in St. Louis（华盛顿大学圣路易斯分校）；National University of Singapore（新加坡国立大学）
Flat bands in twisted moire superlattices support a variety of topological and strongly correlated phenomena along with easily tunable electrical and optical properties. Here, we demonstrate the existence of tunable, long-lived, and flat intraband and interband terahertz plasmons in twisted double bilayer graphene. We show that the interband plasmons originate from the presence of a Van Hove singularity in the joint density of states and a finite Berry connection between the pair of bands involved. We find that the gapped interband plasmon mode has a universal dispersion, and the plasmon gap i…
Motivated by experiments on twisted bilayer graphene, we study the emergence of superconductivity from $\textit{weak}$ repulsive interactions in the Hubbard model on a honeycomb lattice, with both spin and orbital degeneracies, and with the filling treated as a tunable control parameter. The attraction is generated through the Kohn-Luttinger mechanism. We find, similar to old studies of single layer graphene, that the leading superconducting instability is in a $d$-wave pairing channel close to Van Hove filling, and is in an $f$-wave pairing channel away from Van Hove filling. The $d$-wave pai…
The absorption energy of atomic hydrogen at rotated graphene bilayers is studied using ab initio methods based on the density functional theory including van der Waals interactions. We find that, due to the surface corrugation induced by the underneath rotated layer and the perturbation of the electronic density of states near the Fermi energy, the atoms with an almost AA stacking are the preferential ones for hydrogen chemisorption. The adsorption energy difference between different atoms can be as large as 80 meV. In addition, we find that, due to the logarithmic van Hove singularities in th…
Twisted bilayer graphene (tBLG) forms a quasicrystal whose structural and electronic properties depend on the angle of rotation between its layers. Here we present a scanning tunneling microscopy study of gate-tunable tBLG devices supported by atomically-smooth and chemically inert hexagonal boron nitride (BN). The high quality of these tBLG devices allows identification of coexisting moiré patterns and moiré super-superlattices produced by graphene-graphene and graphene-BN interlayer interactions. Furthermore, we examine additional tBLG spectroscopic features in the local density of states be…
Divergent density of states offers the unique opportunity to explore a wide variety of correlated electron physics. In the thinnest limit, this has been predicted and verified in the ultra-flat bands of magic-angle twisted bilayer graphene, the band touching points of few-layer rhombohedral graphite, and the lightly doped rhombohedral trilayer graphene. The simpler and seemingly better understood Bernal bilayer graphene is also susceptible to orbital magnetism-driven phases at charge neutrality, such as layer antiferromagnet and quantum anomalous Hall octet. Here we report the discovery of a c…
We investigate the electronic spectra and quantum Hall effect in twisted bilayer graphenes with various rotation angles under magnetic fields, using a model rigorously including the interlayer interaction. We describe the spectral evolution from discrete Landau levels in the weak field regime to the fractal band structure in the strong field regime, and estimate the quantized Hall conductivity for each single gap. In weak magnetic fields, the low-energy conduction band of the twisted bilayer is quantized into electron-like Landau levels and hole-like Landau levels above and below the van Hove …
Magic-angle twisted bilayer graphene (MA-TBG) exhibits intriguing quantum phase transitions triggered by enhanced electron-electron interactions when its flat-bands are partially filled. However, the phases themselves and their connection to the putative non-trivial topology of the flat bands are largely unexplored. Here we report transport measurements revealing a succession of doping-induced Lifshitz transitions that are accompanied by van Hove singularities (VHS) which facilitate the emergence of correlation-induced gaps and topologically non-trivial sub-bands. In the presence of a magnetic…
Linear resistivity at low temperatures is a prominent feature of high-T$_c$ superconductors which has also been found recently in twisted bilayer graphene. We show that due to an extended van Hove singularity (vHS), the $T$-linear resistivity can be obtained from a microscopic tight-binding model for filling factors close to the vHS. The linear behavior is shown to be related to the linear energy dependence of the electron quasiparticle decay rate which implies the low-energy logarithmic attenuation of the quasiparticle weight. These are distinctive features of a marginal Fermi liquid, which w…
We show that in bilayer graphene it is possible to achieve a very restrictive confinement of the massless Dirac fermions zero-modes by using inhomogeneous magnetic fields. Specifically, we show that, using a suitable nonuniform magnetic fields, the wave function may be restricted to a specific region of the space, being forbidden all transmission probability to the contiguous regions. This allows to construct mesoscopic structures in bilayer graphene by magnetic fields configurations.
