Recently the small-twist-angle (< 2°) bilayer graphene has received extraordinary attentions due to its exciting physical properties. Compared with monolayer graphene, the Brillouin zone folding in twisted bilayer graphene (TBG) leads to the formation of superlattice bandgap and significant modification of density of states. However, these emerging properties have rarely been leveraged for the realization of new optoelectronic devices. Here we demonstrate the strong, gate-tunable photoresponse in mid-infrared wavelength range of 5 to 12 um. A maximum extrinsic photoresponsivity of 26 mA/W has been achieved at 12 um when the Fermi level in a 1.81° TBG is tuned to its superlattice bandgap. Moreover, the strong photoresponse critically depends on the formation of superlattice bandgap, and it vanishes in the gapless case with ultrasmall twist angle (< 0.5°). Our demonstration reveals the promising optical properties of TBG and provides an alternative material platform for tunable mid-infrared optoelectronics.
Nanoscale mapping of stacking-dependent work function and local photoresponse in CVD-grown MoS2 bilayers by KPFM
Nanomagnetism and Microscopy Laboratory, Department of Physics, Indian Institute of Technology Hyderabad（印度理工学院海得拉巴分校物理系纳米磁学与显微镜实验室）；Department of Physics, Indian Institute of Technology Bombay（印度理工学院孟买分校物理系）
Nonlinear intensity dependence of photogalvanics and photoconductance induced by terahertz laser radiation in twisted bilayer graphene close to magic angle
University of Regensburg（雷根斯堡大学）；ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（巴塞罗那科学和技术研究所光子科学研究所）；National Institute for Materials Science（国立材料研究所）；Institute of High Pressure Physics, Polish Academy of Sciences（波兰科学院高压物理研究所）
MoS2 monolayers exhibit excellent light absorption and large thermoelectric power, which are, however, accompanied with very strong exciton binding energy - resulting in complex photoresponse characteristics. We study the electrical response to scanning photo-excitation on MoS2 monolayer (1L) and bilayer (2L) devices, and also on monolayer/bilayer (1L/2L) planar heterojunction and monolayer/few-layer/multi-layer (1L/FL/ML) planar double heterojunction devices to unveil the intrinsic mechanisms responsible for photocurrent generation in these materials and junctions. Strong photoresponse modula…
Graphene-based moiré superlattices have recently emerged as a unique class of tuneable solid-state systems that exhibit significant optoelectronic activity. Local probing at length scales of the superlattice should provide deeper insight into the microscopic mechanisms of photoresponse and the exact role of the moiré lattice. Here, we employ a nanoscale probe to study photoresponse within a single moiré unit cell of minimally twisted bilayer graphene. Our measurements reveal a spatially rich photoresponse, whose sign and magnitude are governed by the fine structure of the moiré lattice and its…
Moiré materials, and in particular twisted bilayer graphene (TBG), exhibit a range of fascinating phenomena, that emerge from the interplay of band topology and interactions. We show that the non-linear second-order photoresponse is an appealing probe of this rich interplay. A dominant part of the photoresponse is the shift-current, which is determined by the geometry of the electronic wavefunctions and carrier properties, and thus becomes strongly modified by electron-electron interactions. We analyze its dependence on the twist angle and doping, and investigate the role of interactions. In t…
The photovoltaic and bolometric photoresponse in gapped bilayer graphene was investigated by optical and transport measurements. A pulse coincidence technique at 1.5 um was used to measure the response times as a function of temperature. The bolometric and photovoltaic response times were found to be identical implying that the photovoltaic response is also governed by hot electron thermal relaxation. Response times of tau ~ 100 - 20 ps were found for temperatures from 3 - 100 K. Above 10 K, the relaxation time was observed to be tau = 25 +/- 5 ps, independent of temperature within noise.
Graphene is a new material showing high promise in optoelectronics, photonics, and energy-harvesting applications. However, the underlying physical mechanism of optoelectronic response has not been established. Here, we report on the intrinsic optoelectronic response of high-quality dual-gated monolayer and bilayer graphene p-n junction devices. Local laser excitation at the p-n interface leads to striking six-fold photovoltage patterns as a function of bottom- and top-gate voltages. These patterns, together with the measured spatial and density dependence of the photoresponse, provide strong …
We measure microwave photocurrent in devices made from InAs/GaInSb bilayers where both insulating bulk state and conducting edge state were observed in the inverted-band regime, consistent with the theoretical prediction for a quantum spin Hall (QSH) insulator. It has been theoretically proposed that microwave photocurrent could be a unique probe in studying the properties of QSH edge states. To distinguish possible photoresponse between bulk state and helical edge state, we prepare Hall bar and Corbino disk from the same wafer. Results show that the Corbino disk samples have a negligible phot…
Twisted bilayer graphenes with magical angle exhibit strongly correlated electronic properties because of the isolated flat band at the Fermi level. We studied the twisted bilayer graphene with substrates on both layers. The substrate induce Kekul$\acute{e}$ distortion for each graphene layer. The systems are investigated by both continuous Dirac Fermion model and tight binding model. The two investigations give similar conclusion that isolated flat band with ultra-narrow bandwidth could appear.
Near a magic twist angle, bilayer graphene transforms from a weakly correlated Fermi liquid to a strongly correlated two-dimensional electron system with properties that are extraordinarily sensitive to carrier density and to controllable environmental factors such as the proximity of nearby gates and twist-angle variation. Among other phenomena magic-angle twisted bilayer graphene hosts superconductivity, interaction induced insulating states, magnetism, electronic nematicity, linear-in-T low-temperature resistivity, and quantized anomalous Hall states. We highlight some key research results …
Twistronic has recently attracted tremendous attention because the twisting can engineer the bilayer graphene-like materials into varying types of strongly correlated phases. In this paper, we study the twisting of bilayer graphene (BLG) quantum dots (QDs) with hexagonal shape and zigzag edges. In the untwisted BLG-QDs, the zigzag edges of graphene host spontaneous magnetism with varying magnetic configurations. As a BLG-QD being adiabatically twisted, the quantum state evolves as a function of the twisting angle. If the twisting angle changes across certain critical value, the magnetic config…
Angle disorder is an intrinsic feature of twisted bilayer graphene and other moiré materials. Here, we discuss electron transport in twisted bilayer graphene in the presence of angle disorder. We compute the local density of states and the Landauer-Büttiker transmission through an angle disorder barrier of width comparable to the moiré period, using a decimation technique based on a real space description. We find that barriers which separate regions where the width of the bands differ by 50% or more lead to a minor suppression of the transmission, and that the transmission is close to one for…
We study the edge states of twisted bilayer graphene and their topological origin. We show that the twisted bilayer graphene has special edge states associated with the moiré pattern, and the emergence of these moiré edge states is linked with the sliding Chern number, which describes topological charge pumping caused by relative interlayer sliding. When one layer of the twisted bilayer is relatively slid with respect to the other layer, the edge states are transferred from a single band to another across the band gap, and the number of the edge states pumped in a sliding cycle is shown to be …
We show that the twisted graphene bilayer can reveal unusual topological properties at low energies, as a consequence of a Dirac-point splitting. These features rely on a symmetry analysis of the electron hopping between the two layers of graphene and we derive a simplified effective low-energy Hamiltonian which captures the essential topological properties of twisted bilayer graphene. The corresponding Landau levels peculiarly reveal a degenerate zero-energy mode which cannot be lifted by strong magnetic fields.
Twisted bilayer graphene provides a new two-dimensional platform for studying electron interaction phenomena and flat band properties such as correlated insulator transition, superconductivity and ferromagnetism at certain magic angles. Here, we present strong evidence of correlated insulator states and superconductivity signatures in p-type twisted double-bilayer WSe$_2$. Enhanced interlayer interactions are observed when the twist angle decreases to a few degrees as reflected by the high-order satellites in the electron diffraction patterns taken from the 2H/3R-stacked domains reconstructed …
We introduce a minimum tight-binding model with only three parameters extracted from graphene and untwisted bilayer graphene. This model reproduces quantitatively the electronic structure of not only these two systems and bulk graphite near the Fermi level, but also that of twisted bilayer graphene including the value of the magic angle, at which bands at $E_F$ flatten without overlap and two gaps open, one above and one below $E_F$. The Hamiltonian is sufficiently transparent and flexible to be adopted to other twisted layered systems.
Twisted bilayer graphene with tiny rotation angles have drawn significant attention due to the observation of the unconventional superconducting and correlated insulating behaviors. In this paper, we employ a full tight-binding model to investigate collective excitations in twisted bilayer graphene near magic angle. The polarization function is obtained from the tight-binding propagation method without diagonalization of the Hamiltonian matrix. With the atomic relaxation considered in the simulation, damped and undamped interband plasmon modes are discovered near magic angle under both room te…
Flatbands with extremely narrow bandwidths on the order of a few mili-electron volts can appear in twisted multilayer graphene systems for appropriate system parameters. Here we investigate the electronic structure of a twisted bi-bilayer graphene, or twisted double bilayer graphene, to find the parameter space where isolated flatbands can emerge as a function of twist angle, vertical pressure, and interlayer potential differences. We find that in twisted bi-bilayer graphene the bandwidth is generally flatter than in twisted bilayer graphene by roughly up to a factor of two in the same paramet…
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…
We investigate the gap in the single-electron spectrum of twisted bilayer graphene. In a perfect infinite lattice of a twisted bilayer, the gap varies exponentially in response to weak changes of the twist angle. Such a large sensitivity makes theoretical predictions of the gap nearly impossible, since experimentally the twist angle is always known with finite accuracy. To address this issue, we numerically study finite clusters of twisted bilayer graphene. For finite systems, changing the twist angle causes a gradual crossover between gapless and gapped regimes. The crossover occurs when the …
We investigate the band structure of twisted monolayer-bilayer graphene (tMBG), or twisted graphene on bilayer graphene (tGBG), as a function of twist angles and perpendicular electric fields in search of optimum conditions for achieving isolated nearly flat bands. Narrow bandwidths comparable or smaller than the effective Coulomb energies satisfying $U_{\textrm{eff}} /W \gtrsim 1$ are expected for twist angles in the range of $0.3^{\circ} \sim 1.5^{\circ}$, more specifically in islands around $θ\sim 0.5^{\circ}, \, 0.85^{\circ}, \,1.3^{\circ}$ for appropriate perpendicular electric field magn…
Moiré superlattice created by twist stacking has multiple physical properties. These physical properties depend on the twist angle, hence investigation of the twist angle dependency is important for the deep understanding of physical phenomena in moiré superlattice. In this work, negative magnetoresistance owing to weak localization (WL) was investigated in twisted double bilayer graphene (TDBG) as a function of the twist angle. The ratio of the intervalley scattering time to the intravalley scattering time, estimated using the WL formula for bilayer graphene, tended to decrease as the twist a…
Theory predicts that the application of an electric field breaks the inversion symmetry of AB and BA stacked domains in twisted bilayer graphene, resulting in the formation of a triangular network of one-dimensional valley-protected helical states. This two-dimensional network of one-dimensional states has been observed in several studies, but direct experimental evidence that the electronic transport in these one-dimensional states is valley-protected is still lacking. In this study, we report the existence of the network in small-angle twisted bilayer graphene at room temperature. Moreover, …
Recently, the twist angle between adjacent sheets of stacked van der Waals materials emerged as a new knob to engineer correlated states of matter in two-dimensional heterostructures in a controlled manner, giving rise to emergent phenomena such as superconductivity or correlated insulating states. Here,we use an ab initio based approach to characterize the electronic properties of twisted bilayer MoS2. We report that, in marked contrast to twisted bilayer graphene, slightly hole-doped MoS2 realizes a strongly asymmetric px-py Hubbard model on the honeycomb lattice, with two almost entirely di…
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…
The transport properties of a twisted bilayer graphene barrier are investigated for various twist angles. Remarkably, for small twist angles around the magic angle $θ_m \sim 1.05^{\circ}$, the local currents around the AA-stacked regions are strongly enhanced compared to the injected electron rate. Furthermore, the total and counterflow (magnetic) current patterns show high correlations in these regions, given rise to well-defined magnetic moments that form a magnetic Moiré superlattice. The orientation and magnitude of these magnetic moments changes as function of the gate voltage and possibl…
We investigate the electronic structure of alternating-twist triple Bernal-stacked bilayer graphene (t3BG) as a function of interlayer coupling $ω$, twist angle $θ$, interlayer potential difference $Δ$, and top-bottom bilayers sliding vector $\boldsymbolτ$ 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 $Δ$ allows the flattening of bands in t3BG down to $\sim 20$~meV for twist angles $θ\lesssim 2^{\circ}$ regardless of the stacking types. Th…
Incommensurately twisted graphene bilayers are described by long-wavelength theories, but to date such theories exist only at small angles of interlayer rotation. We construct a long wavelength theory without such a restriction, instead requiring nearness to commensuration. The theory inherits its energy scale from the exactly commensurate bilayer that it is close to. It is a spatial interpolation between the low-energy theories of commensurate structures with the two possible sublattice exchange (SE) symmetries: SE even and SE odd. In addition to generalizing existing theories, our theory bri…
We propose a new kind of geometric effective theory based on curved space-time single valley Dirac theory with spin connection for twisted bilayer graphene under generic twist angle. This model can reproduce the nearly flat bands with particle-hole symmetry around the first magic angle. The band width is near the former results given by Bistritzer-MacDonald model or density matrix renormalization group. Even more, such geometric formalism allows one to predict the properties of rotating bilayer graphene which cannot be accessed by former theories. As an example, we investigate the Bott index o…
The large surface-to-volume ratio in atomically thin 2D materials allows to efficiently tune their properties through modifications of their environment. Artificial stacking of two monolayers into a bilayer leads to an overlap of layer-localized wave functions giving rise to a twist angle-dependent hybridization of excitonic states. In this joint theory-experiment study, we demonstrate the impact of interlayer hybridization on bright and momentum-dark excitons in twisted WSe$_2$ bilayers. In particular, we show that the strong hybridization of electrons at the $Λ$ point leads to a drastic reds…
We develop a general theory of the layer circular photogalvanic effect (LCPGE) in quasi two-dimensional chiral bilayers, which refers to the appearance of a polarization-dependent, out-of-plane dipole moment induced by circularly polarized light. We elucidate the geometric origin of the LCPGE as two types of interlayer coordinate shift weighted by the quantum metric tensor and the Berry curvature, respectively. As a concrete example, we calculate the LCPGE in twisted bilayer graphene, and find that it exhibits a resonance peak whose frequency can be tuned from visible to infrared as the twisti…
We construct an analytic continuum model to describe the electronic structure and the electron-phonon interaction in twisted bilayer graphenes with arbitrary lattice deformation. Starting from the tight-binding model, we derive the interlayer Hamiltonian in the presence of general lattice displacement, and obtain a long-wavelength continuum expression for smooth deformation. We show that the continuum model correctly describes the band structures of the lattice-relaxed twisted bilayer graphenes. We apply the formula to the phonon vibration, and derive an explicit expression of the electron-pho…
We study the transport properties of a twisted bilayer graphene flake contacted by two monolayer nanoribbons which act as leads. We analyze the conductance in terms of the spectra of the bilayer nanoribbon and the monolayer contacts. The low-energy transport properties are governed by the edge states with AB stacking. Remarkably, the electronic conductance in this energy region does not depend much on the relative position of the leads, in contrast with that of bilayer flakes with more symmetric stackings. We attribute this feature to the localization of these low-energy states in the AB edge …
We derive a simple formula for the real-space chirality of twisted bilayer graphene that can be related to the cross-product of its sheet currents. This quantity shows well-defined plateaus for the first remote band as function of the gate voltage which are approximately quantized for commensurate twist angles. The zeroth plateau corresponds to the first magic angle where a sign change occurs due to an emergent $C_6$-symmetry. Our observation offers a new definition of the magic angle based on a macroscopic observable which is accessible in typical transport experiments.
We identify a mapping between two-dimensional (2D) electron transport in a minimally twisted graphene bilayer and a 1D quantum walk, where one spatial dimension plays the role of time. In this mapping a magnetic field B perpendicular to the bilayer maps onto an electric field. Bloch oscillations due to the periodic motion in a 1D Bloch band can then be observed in purely DC transport as magnetoconductance oscillations with periodicity set by the Bloch frequency.
Twistronic van der Waals heterostrutures offer exciting opportunities for engineering optoelectronic properties of nanomaterials. Here, we use multiscale modeling to study trapping of charge carriers and excitons by ferroelectric polarisation and piezoelectric charges by domain structures in twistronic WX$_2$/MoX$_2$ bilayers (X=S,Se). For almost aligned 2H-type bilayers, we find that holes and electrons are trapped in the opposite -- WMo and XX (tungsten over molybdenum {\it versus} overlaying chalcogens) -- corners of the honeycomb domain wall network, swapping their position at a twist angl…
Selection rules and interference effects in angle resolved photoemission spectra from twisted graphene bilayers are studied within a long wavelength theory for the electronic structure. Using a generic model for the interlayer coupling, we identify features in the calculated ARPES momentum distributions that are controlled by the singularities and topological character of its long wavelength spectrum. We distinguish spectral features that are controlled by single-layer singularities in the spectrum, their modification by gauge potentials in each layer generated by the interlayer coupling, and …
We show that a sliding motion between the two layers of a \moire superlattice induces an electric current and realizes a two-dimensional version of the topological Thouless pump when the Fermi energy lies in one of the minigaps. Interestingly, a chiral charge pump, namely, a transverse current induced by the sliding motion, is possible in twisted homobilayers. This result is confirmed by a concrete calculation of the adiabatic current in twisted bilayer graphene. Our work reveals an interesting link between mechanical motion and electricity unique to \moire superlattices, and may find applicat…
The mechanisms of optical activity and quantum transport of twisted bilayer graphene are studied. The formation of unique electron states in the bilayer systems is studied using an effective continuum model. Such states are shown to support the correlation of transverse motions of electrons in two graphene layers. Because of the chiral structure of the atomic lattices, the contribution of such drag correlations is incompletely cancelled, thus resulting in a drag term of the optical conductivity tensor. We show that the drag term of the conductivity is the manifestation of the spatial dispersio…
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 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 charge susceptibility of twisted bilayer graphene is investigated in the Dirac cone, respectively random-phase approximation. For small enough twist angles $θ\lesssim 2^\circ$ we find weakly Landau damped interband plasmons, i.~e., collective excitonic modes which exist in the undoped material, with an almost constant energy dispersion. In this regime, the loss function can be described as a Fano resonance and we argue that these excitations arise from the interaction of quasi-localised states with the incident light field. These predictions can be tested by nano-infrared imaging and possi…
We consider twisted bilayer and trilayer graphene in the presence of Rashba spin-orbit coupling and explore the physics of Moiré spintronics. The electronic charge density has a sharp step right at the magic angles $θ_m$. As a result, local spin observables (polarization and equilibrium spin currents) have sharp peaks (of width about a small fraction of 1$^\circ$) as a function of the twist angle $θ$, and abrupt sign reversals at $θ_m$. Thereby, the magic angle can be determined in an unprecedented accuracy. In the first chiral limit, the spin currents vanish, but the peculiar pattern of the p…
Lattice reconstruction in twisted transition-metal dichalcogenide (TMD) bilayers gives rise to piezo- and ferroelectric moiré potentials for electrons and holes, as well as a modulation of the hybridisation across the bilayer. Here, we develop hybrid $\mathbf{k}\cdot \mathbf{p}$ tight-binding models to describe electrons and holes in the relevant valleys of twisted TMD homobilayers with parallel (P) and anti-parallel (AP) orientations of the monolayer unit cells. We apply these models to describe moiré superlattice effects in twisted WSe${}_2$ bilayers, in conjunction with microscopic \emph{ab…
Control over minivalley polarization and interlayer coupling is demonstrated in double bilayer graphene twisted with an angle of 2.37$^\circ$. This intermediate angle is small enough for the minibands to form and large enough such that the charge carrier gases in the layers can be tuned independently. Using a dual-gated geometry we identify and control all possible combinations of minivalley polarization via the population of the two bilayers. An applied displacement field opens a band gap in either of the two bilayers, allowing us to even obtain full minivalley polarization. In addition, the …
We introduce a new approach that allows one complete control over the modulation of the effective twist angle change in few-layer van der Waals heterostructures by irradiating them with longitudinal waves of light at the end of a waveguide. As a specific application, we consider twisted bilayer graphene and show that one can tune the magic angles to be either larger or smaller, allowing in-situ experimental control of the phase diagram of this and other related materials. A waveguide allows one to circumvent the free-space constraints on the absence of longitudinal electric field components of…
Currently there is a lively discussion concerning Fermi velocity renormalization in twisted bilayers and several contradicted experimental results are reported. Here we study electronic structures of the twisted bilayers by scanning tunneling microscopy (STM) and spectroscopy (STS). The interlayer coupling strengths between the adjacent bilayers are measured according to energy separations of two pronounced low-energy van Hove singularities (VHSs) in the STS spectra. We demonstrate that there is a large range of values for the interlayer interaction in different twisted bilayers. Below the VHS…
