Biased Bilayer Graphene Research Articles

Direct coupling of light to valley current

The coupling of circularly polarized light to local band structure extrema ("valleys”) in two dimensional semiconductors promises a new electronics based on the valley degree of freedom. Such pulses, however, couple only to valley charge and not to the valley current, precluding lightwave manipulation of this second vital element of valleytronic devices. Contradicting this established wisdom, we show that the few cycle limit of circularly polarized light is imbued with an emergent vectorial character that allows direct coupling to the valley current. The underlying physical mechanism involves the emergence of a momentum space valley dipole, the orientation and magnitude of which allows complete control over the direction and magnitude of the valley current. We demonstrate this effect via minimal tight-binding models both for the visible spectrum gaps of the transition metal dichalcogenides (generation time ~ 1 fs) as well as the infrared gaps of biased bilayer graphene ( ~ 14 fs); we further verify our findings with state-of-the-art time-dependent density functional theory incorporating transient excitonic effects. Our findings both mark a striking example of emergent physics in the ultrafast limit of light-matter coupling, as well as allowing the creation of valley currents on time scales that challenge quantum decoherence in matter.

Tunable nonlinear excitonic optical response in biased bilayer graphene

Tunable nonlinear excitonic optical response in biased bilayer graphene

Moiré excitons in biased twisted bilayer graphene under pressure

Moiré excitons in biased twisted bilayer graphene under pressure

Exciton condensation in biased bilayer graphene

Exciton condensation in biased bilayer graphene

Triplet superconductivity and spin density wave in biased AB bilayer graphene

Triplet superconductivity and spin density wave in biased AB bilayer graphene

Dynamical screening and excitonic bound states in biased bilayer graphene

Excitonic bound states are characterized by a binding energy ${\ensuremath{\epsilon}}_{b}$ and a single-particle band gap ${\mathrm{\ensuremath{\Delta}}}_{b}$. This work provides a theoretical description for both strong (${\ensuremath{\epsilon}}_{b}\ensuremath{\sim}{\mathrm{\ensuremath{\Delta}}}_{b}$) and weak (${\ensuremath{\epsilon}}_{b}\ensuremath{\ll}{\mathrm{\ensuremath{\Delta}}}_{b}$) excitonic bound states, with particular application to biased bilayer graphene. Standard description of excitons is based on a wave function that is determined by a Schr\"odinger-like equation with screened attractive potential. The wave function approach is valid only in the weak-binding regime ${\ensuremath{\epsilon}}_{b}\ensuremath{\ll}{\mathrm{\ensuremath{\Delta}}}_{b}$. The screening depends on frequency, i.e., dynamical screening, and this implies retardation. In the case of strong binding, ${\ensuremath{\epsilon}}_{b}\ensuremath{\sim}{\mathrm{\ensuremath{\Delta}}}_{b}$, a wave function description is not possible due to the retardation. Instead we appeal to the Bethe-Salpeter equation, written in terms of the electron-hole Green's function, to solve the problem. So far only the weak-binding regime has been achieved experimentally. Our analysis demonstrates that the strong-binding regime is also possible and we specify conditions in which it can be achieved for the prototypical example of biased bilayer graphene. The conditions concern the bias, the configuration of gates, and the substrate material. To verify the accuracy of our analysis we compare with available data for the weak-binding regime. We anticipate applying the developed dynamical screening Bethe-Salpeter techniques to various 2D materials with strong binding.

Orientation dependence of even-order harmonics generation in biased bilayer graphene

We theoretically study the orientation dependence of even-order harmonics in biased bilayer graphene (BLG) by numerically solving the semiconductor Bloch equations in the velocity gauge. It is shown that the yield of even-order harmonics has a perfect periodicity of ${60}^{\ensuremath{\circ}}$ with the rotation of the crystal orientation. The even-harmonic intensity reaches the maximum when the laser field is polarized along with the nearest-neighbor atom. By investigating the crystal orientation dependence for the parallel and perpendicular components of even harmonics, it is found that the Berry curvature plays an insignificant role in the even-harmonic generation of biased BLG. Further analysis reveals that the asymmetric electron density between in-plane adjacent atoms caused by polarization is responsible for the generation of even harmonics in biased BLG. Additionally, we study the ellipticity dependence of even harmonics in biased BLG when the elliptical principal axis of the laser pulse is along with the in-plane nearest-neighbor atoms. As expected, the yield of even harmonics decreases with the ellipticity. Our findings give access to understanding deeply the mechanism of the orientation dependence of even harmonics in biased BLG.

Theoretical Methods for Excitonic Physics in 2D Materials

In this Perspective article, the reader is introduced to several theoretical methods of determining the exciton wave functions and the corresponding eigenenergies. The methods covered are either analytical, semianalytical, or numeric. All the details associated with the different methods are made explicit, thus allowing newcomers to do research on their own, without experiencing a steep learning curve. The Perspective starts with a variational method and ends with a simple semianalytical approach to solve the Bethe–Salpeter equation (BSE) in gapped 2D materials. For the first methods addressed in this Perspective, the authors focus on a single layer of hexagonal boron nitride (hBN) and of transition metal dichalcogenide (TMD), as these are exemplary materials in the field of 2D excitons. For explaining the Bethe–Salpeter method, the biased bilayer graphene, which presents a tunable bandgap is chosen. The system has the right amount of complexity (without being excessive). This allows the presentation of the solution in a context that can be easily generalized to more complex systems or to apply it to simpler models.

Exciton absorption, band structure, and optical emission in biased bilayer graphene

Biased bilayer graphene (BBG) is a variable band gap semiconductor, with a strongly field-dependent band gap of up to $300 \, \text{meV}$, making it of particular interest for graphene-based nano-electronic and -photonic devices. The optical properties of BBG are dominated by strongly bound excitons. We perform ab initio density-functional-theory+Bethe-Salpeter-equation modelling of excitons in BBG and calculate the exciton band structures and optical matrix elements for field strengths in the range $30-300 \, \text{mV}/{\unicode{x212B}}$. The exciton properties prove to have a strong field dependence, with both energy ordering and dipole alignment varying significantly between the low and high field regions. Namely, at low fields we find a mostly dark ground state exciton, as opposed to high fields, where the lowest exciton is bright. Also, excitons preferentially align with a dipole moment opposite the field, due to the field-induced charge transfer in the ground state of BBG. However, in stronger fields, this alignment becomes energetically less favorable. Additionally, the bright excitons show particle- and light-like bands similar to monolayer transition metal dichalchogenides. Finally, we model the radiative lifetimes and emission properties of BBG, which prove to be strongly dependent on temperature in addition to field strength.

Absorption and optical selection rules of tunable excitons in biased bilayer graphene

Biased bilayer graphene, with its easily tunable band gap, presents itself as the ideal system to explore the excitonic effect in graphene-based systems. In this paper we study the excitonic optical response of such a system by combining a tight-binding model with the solution of the Bethe-Salpeter equation, the latter being solved in a semianalytical manner, requiring a single numerical quadrature, thus allowing for a transparent calculation. With our approach we start by analytically obtaining the optical selection rules, followed by the computation of the absorption spectrum for the case of a biased bilayer encapsulated in hexagonal boron nitride, a system which has been the subject of a recent experimental study. Excellent agreement is seen when we compare our theoretical prediction with the experimental data.

Plasmon modes in double-layer biased bilayer graphene

We investigate zero-temperature plasmon modes in a double-layer bilayer graphene structure under a perpendicular electrostatic bias. The numerical results demonstrate that there exist two collective modes which are undamped in the long wavelength limit. The finite potential bias decreases remarkably the plasmon energy in a wide range of wave-vector and makes plasmon branches become Landau damped at a higher wave-vector as compared to unbiased case. We find that the dependence of plasmon dispersions on the system parameters such as the inter-layer separation and carrier density is similar in two cases with and without electrostatic bias.

Corrugation effect, Dirac cone splitting, and plasmon properties of biased twisted bilayer graphene

The unconventional behaviors observed in twisted bilayer graphene (TBG) at special ``magic angles'' characterized by the vanishing Fermi velocity make TBG an intriguing platform for the study of correlated phenomena. Here, on the basis of an effective continuum model, we propose an analytic expression of the Fermi velocity based on which we demonstrate that the first magic angle of TBG is independent of the corrugation effect. We also correlate analytically the Dirac cone splitting of the biased TBG to the external electric field, twist angle, and corrugation effect. The biased TBGs exhibit unusual plasmonic responses. In the long-wavelength limit, the plasmon frequency is nearly independent of the carrier density but can be tuned by the bias voltage.

Carrier concentration independent plasmons in biased twisted bilayer graphene

We calculate the density-density response function of biased twisted bilayer graphene (BTBG) and study its plasmon dispersion within the random phase approximation (RPA). At long wavelengths ($q\ensuremath{\rightarrow}0$), plasmon dispersion shows local classical behavior $\ensuremath{\omega}={\ensuremath{\omega}}_{0}\sqrt{q}$. Unlike the situation in conventional two-dimensional electron gas (2DEG), where the density dependence of the plasmon energy is of the form ${\ensuremath{\omega}}_{0}\ensuremath{\propto}\sqrt{n}$ ($n$ is the carrier concentration), the plasmon energy ${\ensuremath{\omega}}_{0}$ is independent of the carrier concentration ($n$) in biased twisted bilayer graphene. Furthermore, the plasmon energy (${\ensuremath{\omega}}_{0}$) is also independent of the Fermi energy ($\ensuremath{\mu}$) which is decided by the carrier concentration ($n$).

Valley current generation using biased bilayer graphene dots

Intrinsic and extrinsic valley Hall effects are predicted to emerge in graphene systems with uniform or spatially-varying mass terms. Extrinsic mechanisms, mediated by the valley-dependent scattering of electrons at the Fermi surface, can be directly linked to quantum transport simulations. This is a promising route towards more complete experimental investigation of valleytronic phenomena in graphene, but a major obstacle is the difficulty in applying the sublattice-dependent potentials required. Here we show that strongly valley-dependent scattering also emerges from bilayer graphene quantum dots, where the gap size can be easily modulated using the interlayer potentials in dual-gated devices. Robust valley-dependent scattering and concomitant valley currents are observed for a range of systems, and we investigate the role of dot size, mass strength and additional potential terms. Finally, we note that a strong valley splitting of electronic current also emerges when a biased bilayer dot is embedded in a single layer of graphene, but that the effect is less robust than for a bilayer host. Our findings suggest that bilayer graphene devices with custom mass profiles provide an excellent platform for future valleytronic exploration of two-dimensional materials.

Valley polarization in biased bilayer graphene using circularly polarized light

Achieving a population imbalance between the two inequivalent valleys is a critical first step for any valleytronic device. A valley polarization can be induced in biased bilayer graphene using circularly polarized light. In this paper, we present a detailed theoretical study of valley polarization in biased bilayer graphene. We show that a nearly perfect valley polarization can be achieved with the proper choices of external bias and pulse frequency. We find that the optimal pulse frequency $\ensuremath{\omega}$ is given by $\ensuremath{\hbar}\ensuremath{\omega}=2a,$ where $2a$ is the potential energy difference between the graphene layers. We also find that the valley polarization originates not from the Dirac points themselves, but rather from a ring of states surrounding each. Intervalley scattering is found to greatly reduce the valley polarization for high-frequency pulses. Thermal populations are found to significantly reduce the valley polarization for small biases. This work provides insight into the origin of valley polarization in bilayer graphene and will aid experimentalists seeking to study valley polarization in the laboratory.

Plasmonic Dirac Cone in Twisted Bilayer Graphene.

We discuss plasmons of biased twisted bilayer graphene when the Fermi level lies inside the gap. The collective excitations are a network of chiral edge plasmons (CEP) entirely composed of excitations in the topological electronic edge states that appear at the AB-BA interfaces. The CEP form a hexagonal network with a unique energy scale ε_{p}=(e^{2})/(ε_{0}εt_{0}) with t_{0} the moiré lattice constant and ε the dielectric constant. From the dielectric matrix we obtain the plasmon spectra that has two main characteristics: (i)a diverging density of states at zero energy, and (ii)the presence of a plasmonic Dirac cone at ℏω∼ε_{p}/2 with sound velocity v_{D}=0.0075c, which is formed by zigzag and armchair current oscillations. A network model reveals that the antisymmetry of the plasmon bands implies that CEP scatter at the hexagon vertices maximally in the deflected chiral outgoing directions, with a current ratio of 4/9 into each of the deflected directions and 1/9 into the forward one. We show that scanning near-field microscopy should be able to observe the predicted plasmonic Dirac cone and its broken symmetry phases.

Anisotropic RKKY interaction in doped magnetic ordered bilayer graphene

Abstract We study exchange interaction between two magnetic impurities, i.e. (the Ruderman-Kittel-Kasuya-Yosida [RKKY]), in doped biased bilayer graphene by directly computing Green's function within full band method. Tight binding model Hamiltonian in the presence of magnetic long range ordering has been applied to describe electron dynamics. RKKY interaction as a function of distance between localized moments has been analyzed. It has been shown that a field induced ferromagnetic ordering along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. Such field induced ferromagnetic ordering is due to external magnetic field. The exchange interaction along arbitrary direction between two magnetic moments, has been obtained using the static spin susceptibilities of gapped graphene structure. The effects of spin polarization on the dependence of exchange interaction on distance between moments are investigated via calculating correlation function of spin density operators. Our results show the chemical potential impacts the spatial behavior of RKKY interaction. Moreover bias voltage effects on RKKY interaction have been investigated for both stacking types of bilayer graphene.

Spin susceptibilities of doped bilayer graphene in the presence of magnetic ordering

We study the dynamical spin susceptibilities of biased bilayer graphene due to spin polarization effects in the context of tight binding model Hamiltonian. Green's function approach has been implemented to find the behavior of dynamical spin susceptibility of bilayer graphene within linear response theory. We have found the frequency dependence of imaginary part of spin susceptibilities for different values of bias voltage. Also the dependence of both transverse and longitudinal spin susceptibilities on spin polarization has been investigated in details. The frequency position of sharp peaks in the frequency dependence of the susceptibilities introduce the collective magnetic excitation modes of itinerant electrons on bilayer system.

Nanoscale probing of thermally excited evanescent fields in an electrically biased graphene by near-field optical microscopy

This paper demonstrates nanoscale infrared thermal imaging in electrically biased bilayer graphene (BLG) by using a scattering-type scanning near-field optical microscope (s-SNOM). s-SNOM provides a noncontact technique to detect the thermally excited electromagnetic evanescent fields (∼21 THz) generated on the surface of a Joule-heated BLG. With increasing bias current, a strong near-field signal appears mainly in the sub-micrometer-sized constricted region. The temperature mapping of the graphene film can be derived from the infrared near-field signals, and shows good agreement with the finite-element simulation. Hence, we prove that s-SNOM is a potential infrared nano-thermography for the graphene device.

Perfect one-dimensional chiral states in biased twisted bilayer graphene

We theoretically study the electronic structure of small-angle twisted bilayer graphene with a large potential asymmetry between the top and bottom layers. We show that the emergent helical states known to appear on the triangular AB-BA domain boundary do not actually form a percolating network, but instead they provide independent, perfect one-dimensional channels propagating in three different directions. Using the continuum-model Hamiltonian, we demonstrate that an applied bias causes two well-defined energy windows which contain sparsely distributed one-dimensional channels. The origin of these energy windows can be understood using a two-band model of the intersecting electron and hole bands of single layer graphene. We also use the tight-binding model to implement the lattice deformations in twisted bilayer graphene, and discuss the effect of lattice relaxation on the one-dimensional channels.