Biased Bilayer Research Articles

Berry curvature and shift vector effects at high-order wave mixing in biased bilayer graphene

In this paper, we present a microscopic quantum theory that elucidates the nonlinear and nonperturbative optical response of biased bilayer graphene subjected to bichromatic strong laser fields. This response is analyzed using a four-band Hamiltonian derived from calculations. For the laser-stimulated dynamics, we employ structure gauge-invariant evolutionary equations to accurately describe the evolution of the single-particle density matrix across the entire Brillouin zone. The resonant generation of electron-hole pairs by the high-frequency component of the field, combined with the induction of high-order harmonic generation and high-order wave mixing by the strong low-frequency field component, leads to significant alterations in the resulting spectra. These changes are driven by the effects of Berry curvature and the shift vector, which modify the relative contributions of interband and intraband channels, thereby fundamentally reshaping the radiation spectra at high-order frequency multiplication. The numerical results are further supported by approximate analytical calculations, demonstrating that high-order wave mixing can be modeled using the classical trajectory analysis of electron-hole pairs, with Berry curvature and the shift vector significantly influencing the saddle-point equations. Published by the American Physical Society 2025

Dynamical Exciton Condensates in Biased Electron-Hole Bilayers.

Bilayer materials may support interlayer excitons comprised of electrons in one layer and holes in the other. In experiments, a nonzero exciton density is typically sustained by a bias chemical potential, implemented either by optical pumping or by electrical contacts connected to the two layers. We show that if charge can tunnel between the layers, the chemical potential bias means that an exciton condensate is in the dynamical regime of ac Josephson effect. It has physical consequences such as tunneling currents and the ability to tune a condensate from bright (emitting coherent photons) to dark by experimental controlling knobs. If the system is placed in an optical cavity, coupling with cavity photons favors different dynamical states depending on the bias, realizing superradiant phases.

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

Keldysh Field Theory of Dynamical Exciton Condensation Transitions in Nonequilibrium Electron-Hole Bilayers.

Recent experiments have realized steady-state electrical injection of interlayer excitons in electron-hole bilayers subject to a large bias voltage. In the ideal case in which interlayer tunneling is negligibly weak, the system is in quasiequilibrium with a reduced effective band gap. Interlayer tunneling introduces a current and drives the system out of equilibrium. In this work we derive a nonequilibrium field theory description of interlayer excitons in biased electron-hole bilayers. In the large bias limit, we find that p-wave interlayer tunneling reduces the effective band gap and increases the effective temperature for intervalley excitons. We discuss possible experimental implications for InAs/GaSb quantum wells and transition metal dichalcogenide bilayers.

Antiferromagnetic magnetostriction of IrMn detected by angular dependent exchange bias

The manipulation of Néel vector of antiferromagnetic (AFM) layer by an applied stress has attracted considerable attention due to the technical importance for AFM-based spintronic devices. Here, we fabricated CoFeB/IrMn and Ni/IrMn exchange bias (EB) bilayers on PMN-PT(011) to quantitatively study the AFM magnetostrictive behaviors of the IrMn layer. Numerical calculations based on the Stoner–Wohlfarth model show that the response of the Néel vector to compressive stress can be detected by measuring the angular dependent EB. The hysteresis loops experimentally measured with applying an electric field on PMN-PT show significantly different shape changes due to the opposite magnetostriction between CoFeB and Ni. The non-vanished EB field obtained at 90∘ indicates the rotation of Néel vector under compressive stress, suggesting the positive magnetostriction of IrMn. The numerical fitting of the angular dependent EB indicates that the Néel vectors in both samples deviate from the initial direction by the same −5∘. The AFM magnetostriction coefficient of IrMn is estimated to be 238 ppm, which is in good agreement with the theoretically predicted value.

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

Rotatable anisotropy in exchange bias bilayer and stripe domains films with uniaxial anisotropy

We report the rotatable anisotropy in three magnetic film systems, including in-plane magnetized FeNi film, FeNi/FeMn bilayer and FeNi stripe domains (SDs) structure film. Omnidirectional ferromagnetic resonance driven by rotatable anisotropy can be achieved in these films. We have found that the in-plane magnetized FeNi films have a negligible rotatable anisotropy of about 1 ∼ 2 Oe. Rotatable anisotropy fields of 6.1 Oe and 5.5 Oe are found for isotropic and anisotropic FeNi/FeMn bilayers, which comes from the exchange coupling at the interface of FM and AFM layer. This magnitude is smaller than the value found in thick FeNi film where a big rotatable anisotropy field of 87 Oe is present stemming from its domain structure. In addition, the uniaxial anisotropy could tailor the resonance frequency from 0.78 and 2.28 GHz for in-plane magnetized FeNi thin film, and 1.3 to 2.4 GHz for FeNi SDs films. Furthermore, a conclusion that a uniaxial anisotropy has no influence on rotatable anisotropy in three magnetic films systems, was yielded.

Bias-Field-Free Microwave Operation in NiFe/FeMn Exchange Biased Bilayers by Varying FeMn Thickness

Bias-Field-Free Microwave Operation in NiFe/FeMn Exchange Biased Bilayers by Varying FeMn Thickness

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.

Enhanced Electronic Thermal Conductivity and Heat Capacity of Biased Bilayer Boron Phosphide with Magnetic Field

Enhanced Electronic Thermal Conductivity and Heat Capacity of Biased Bilayer Boron Phosphide with Magnetic Field

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.

Topological Lifshitz transition and novel edge states induced by non-Abelian SU(2) gauge field on bilayer honeycomb lattice

We investigate the SU(2) gauge effects on bilayer honeycomb lattice thoroughly. We discover a topological Lifshitz transition induced by the non-Abelian gauge potential. Topological Lifshitz transitions are determined by topologies of Fermi surfaces in the momentum space. Fermi surface consists of N = 8 Dirac points at π-flux point instead of N = 4 in the trivial Abelian regimes. A local winding number is defined to classify the universality class of the gapless excitations. We also obtain the phase diagram of gauge fluxes by solving the secular equation. Furthermore, the novel edge states of biased bilayer nanoribbon with gauge fluxes are also investigated.

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.