The gapless energy band spectra make the structures based on graphene and graphene bilayers with the population inversion created by optical or injection pumping to be promising media for the interband terahertz (THz) lasing. However, a strong intraband absorption at THz frequencies still poses a challenge for efficient THz lasing. In this paper, we show that in the pumped graphene bilayer structures, the indirect interband radiative transitions accompanied by scattering of carriers caused by disorder can provide a substantial negative contribution to the THz conductivity (together with the direct interband transitions).
In the graphene bilayer structures on high-$κ$ substrates with point charged defects, these transitions almost fully compensate the losses due to the intraband (Drude) absorption. We also demonstrate that the indirect interband contribution to the THz conductivity in a graphene bilayer with the extended defects (such as the charged impurity clusters, surface corrugation, and nanoholes) can surpass by several times the fundamental limit associated with the direct interband transitions and the Drude conductivity. These predictions can affect the strategy of the graphene-based THz laser implementation.
We reveal that there exists a class of graphene structures (a sub-class of bilayer graphene nanoribbons) which has unusually strong optical response in the terahertz (THz) and far infrared (FIR) regime. The peak conductance of terahertz/FIR active bilayer ribbons is around two orders of magnitude higher than the universal conductance of $e^2/4\hbar$ observed in graphene sheets. The criterion for the terahertz/FIR active sub-class is a bilayer graphene nanoribbon with one-dimensional massless Dirac Fermion energy dispersion near the $Γ$ point. Our results overcome a significant obstacle that hi…
Injection or optical generation of electrons and holes in graphene bilayers (GBLs) can result in the interband population inversion enabling the terahertz (THz) radiation lasing. The intraband radiative processes compete with the interband transitions. We demonstrate that remote doping enhances the indirect interband generation of photons in the proposed GBL heterostructures. Therefore such remote doping helps surpassing the intraband (Drude) absorption and results in large absolute values of the negative dynamic THz conductivity in a wide range of frequencies at elevated (including room) temp…
A density-matrix formalism within the length gauge is developed for the purpose of calculating the nonlinear response of intrinsic bilayer graphene at terahertz frequencies. Employing a tight-binding model, we find that interplay between the interband and intraband dynamics leads to strong harmonic generation at moderate field amplitudes. Specifically, we find that at low temperature (10 K), the reflected field of undoped suspended bilayer graphene exhibits a third harmonic amplitude that is 30% of the fundamental in the reflected field for an incident 1 THz single-cycle pulse with a field amp…
We describe studies on the nanoscale transport dynamics of carriers in strained AlN/GaN/AlN quantum wells: an electron-hole bilayer charge system with large difference in transport properties between the two charge layers. From electronic band diagram analysis, the presence of spatially separated two-dimensional electron and hole charge layers is predicted at opposite interfaces. Since these charge layers exhibit distinct spectral signatures at terahertz frequencies, a combination of terahertz and far-infrared spectroscopy enables us to extract (a) individual contributions to the total conduct…
We report bilayer-graphene field effect transistors operating as THz broadband photodetectors based on plasma-waves excitation. By employing wide-gate geometries or buried gate configurations, we achieve a responsivity $\sim 1.2V/W (1.3 mA/W)$ and a noise equivalent power $\sim 2\times 10^{-9} W/Hz^{-1/2}$ in the 0.29-0.38 THz range, in photovoltage and photocurrent mode. The potential of this technology for scalability to higher frequencies and the development of flexible devices makes our approach competitive for a future generation of THz detection systems.
High-order terahertz (THz) sideband generation (HSG) in semiconductors is a phenomenon with physics similar to high-order harmonic generation but in a much lower frequency regime. It was found that the electron-hole pairs excited by a weak optical laser can accumulate Berry phases along a cyclic path under the driving of a strong THz field. The Berry phases appear as the Faraday rotation angles of the emission signal under short-pulse excitation in monolayer MoS$_2$. In this paper, the theory of Berry phase in THz extreme nonlinear optics is applied to biased bilayer graphene with Bernal stack…
Terahertz nanoscopy of quantum-geometric photovoltaics in bilayer graphene
University of Notre Dame（圣母大学）；Stavropoulos Center for Complex Quantum Matter, University of Notre Dame（圣母大学斯塔夫罗普洛斯复杂量子物质中心）；University of Texas at Dallas（德克萨斯大学达拉斯分校）；National Institute for Materials Science（国立研究开发法人物质·材料研究机构）；Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST（加泰罗尼亚纳米科学与技术研究所（ICN2），西班牙国家研究委员会与巴塞罗那科学技术研究院）
We investigate intra-Landau-level collective excitations in a bilayer disordered two-dimensional electron system exposed to a perpendicular magnetic field. The energy spectrum is calculated within the random phase approximation by taking into account electron-impurity scattering in the self-consistent Born approximation which includes consistent vertex corrections. Signatures of these bilayer excitations in drag and collective excitation measurements are identified.
We investigate the intraband nonlinear dynamics in doped bilayer graphene in the presence of strong, linearly-polarized, in-plane terahertz fields. We perform degenerate pump-probe experiments with 3.4 THz fields on doped bilayer graphene at low temperature (12 K) and find that when the pump is co-polarized with the probe beam, the differential pump-probe signal is almost double that found in the cross-polarized case. We show that the origin of this pump-induced anisotropy is the difference in the average electron effective mass in the probe direction when carriers are displaced in k-space by …
We study the effects of disorder on the interlayer transport properties of disordered semiconductor bilayers outside of the quantum Hall regime by performing self-consistent quantum transport calculations. We find that the addition of material disorder to the system affects interlayer interactions leading to significant deviations in the interlayer transfer characteristics. In particular, we find that disorder decreases and broadens the tunneling peak, effectively reducing the interacting system to the non-interacting system, when the mean-free path for the electrons becomes shorter than the s…
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）
We report anomalous quantum transport features in bilayer graphene in presence of a random distribution of structural vacancies. By using an efficient real-space Kubo-Greenwood transport methodology, the impact of a varying density of dimer versus non-dimer vacancies is investigated in very large scale disordered models. While non-dimer vacancies are shown to induce localization regimes, dimer vacancies result in an unexpected ballistic regime whose energy window surprisingly enlarges with increasing impurity density. Such counterintuitive phenomenon is explained by the formation of an effecti…
Using terahertz time-domain spectroscopy, the real part of optical conductivity [$σ_{1}(ω)$] of twisted bilayer graphene was obtained at different temperatures (10 -- 300 K) in the frequency range 0.3 -- 3 THz. On top of a Drude-like response, we see a strong peak in $σ_{1} (ω)$ at $\sim$2.7 THz. We analyze the overall Drude-like response using a disorder-dependent (unitary scattering) model, then attribute the peak at 2.7 THz to an enhanced density of states at that energy, that is caused by the presence of a van Hove singularity arising from a commensurate twisting of the two graphene layers…
The inhomogenous real-space electronic structure of gapless and gapped disordered bilayer graphene is calculated in the presence of quenched charge impurities. For gapped bilayer graphene we find that for current experimental conditions the amplitude of the fluctuations of the screened disorder potential is of the order of (or often larger than) the intrinsic gap $Δ$ induced by the application of a perpendicular electric field. We calculate the crossover chemical potential, $Δ_{\rm cr}$, separating the insulating regime from a percolative regime in which less than half of the area of the bilay…
Photoconductivity of novel materials is the key property of interest for design of photodetectors, optical modulators, and switches. Despite the photoconductivity of most novel 2d materials has been studied both theoretically and experimentally, the same is not true for 2d p-n junctions that are necessary blocks of most electronic devices. Here, we study the sub-terahertz photocoductivity of gapped bilayer graphene with electrically-induced p-n junctions. We find a strong positive contribution from junctions to resistance, temperature resistance coefficient and photo-resistivity at cryogenic t…
Metallic bilayer structures have been shown to emit strong terahertz (THz) pulses. We present a predictive multiscale mode that simulates optically induced spin-currents in a Fe/Pt-heterostructure and the emitted electric field. Electronic effects are treated on the nano scale using the Boltzmann transport equation for the dynamics of out-of-equilibrium charge carriers, numerically solved with a particle-in-cell code. The optical effects are simulated with a formalism that bridges the nanometer scale of the structure to the micrometer scale of the emitted waves. The approach helps to understan…
A density-matrix formalism within the length gauge is developed to calculate the nonlinear response of both doped and undoped biased bilayer graphene (BBLG) at terahertz frequencies. Employing a tight-binding model, we derive an effective two-band Hamiltonian with which we calculate the conduction and valence band dispersion, as well as their respective Bloch states. We then solve for the dynamic equations of the density matrix elements, allowing for the calculation of the intraband and interband current densities and the transmitted and reflected terahertz fields. We find that for undoped BBL…
A graphene bilayer phototransistor (GBL-PT) is proposed and analyzed. The GBL-PT under consideration has the structure of a field-effect transistor with a GBL as the channel and the back and top gates. The positive bias of the back gate results in the formation of conducting source and drain sections in the channel, while the negatively biased top gate provides the potential barrier which is controlled by the charge of the photogenerated holes. The features of the GBL-PT operation are associated with the variations of both the potential distribution and the energy gap in different sections of …
We present and solve a model for the vortex configuration of a disordered quantum Hall bilayer in the limit of strong and smooth disorder. We argue that there is a characteristic disorder strength below which vortices will be rare, and above which they proliferate. We predict that this can be observed tuning the electron density in a given sample. The ground state in the strong-disorder regime can be understood as an emulsion of vortex-antivortex crystals. Its signatures include a suppression of the spatial decay of counterflow currents. We find an increase of at least an order of magnitude in…
We report on the observation of photogalvanic effects in twisted bilayer graphene (tBLG) with a twist angle of 0.6°. We show that excitation of tBLG bulk causes a photocurrent, whose sign and magnitude are controlled by orientation of the radiation electric field and the photon helicity. The observed photocurrent provides evidence for the reduction of the point group symmetry in low twist-angle tBLG to the lowest possible one. The developed theory shows that the current is formed by asymmetric scattering in gyrotropic tBLG. We also detected the photogalvanic current formed in the vicinity of t…
Terahertz emission spectroscopy (TES) has recently played an important role in unveiling the spin dynamics at a terahertz (THz) frequency range. So far, ferromagnetic (FM)/nonmagnetic (NM) heterostructures have been intensively studied as THz sources. Compensated magnets such as a ferrimagnet (FIM) and antiferromagnet (AFM) are other types of magnetic materials with interesting spin dynamics. In this work, we study TES from compensated magnetic heterostructures including CoGd FIM alloy or IrMn AFM layers. Systematic measurements on composition and temperature dependences of THz emission from C…
The electron gas hosted in a two-dimensional solid-state matrix, such as a quantum well or a two-dimensional van der Waals heterostructure, supports the propagation of plasma waves. Nonlinear interactions between plasma waves, due to charge conservation and current convection, generate a constant density gradient which can be detected as a dc potential signal at the boundaries of the system. This phenomenon is at the heart of a plasma-wave photodetection scheme which was first introduced by Dyakonov and Shur for electronic systems with a parabolic dispersion and then extended to the massless D…
Based on a multi-scale calculations, combining ab-initio methods with spin dynamics simulations, we perform a detailed study of the magnetic behavior of Ni2MnAl/Fe bilayers. Our simulations show that such a bilayer exhibits a small exchange bias effect when the Ni2MnAl Heusler alloy is in a disordered B2 phase. Additionally, we present an effective way to control the magnetic structure of the Ni2MnAl antiferromagnet, in the pseudo-ordered B2-I as well as the disordered B2 phases, via a spin-flop coupling to the Fe layer.
The quantum theory of multiphoton stimulated bremsstrahlung of charged carriers on an arbitrary electrostatic potential of impurity ion in doped bilayer graphene at the presence of coherent electromagnetic radiation is developed. A terahertz wave field is considered exactly, while the electrostatic potential of doped ions as a perturbation. The essentially nonlinear response of bilayer graphene to a pump wave and significant differences from the case of a single layer graphene are shown, which can be associated to nonlinear parabolic dispersion. The latter opens new way to manipulate with the …
Employing the Kernel Polynomial method (KPM), we study the electronic properties of the graphene bilayers in the presence of diagonal disorder, within the tight-binding approximation. The KPM method enables us to calculate local density of states (LDOS) without need to exactly diagonalize the Hamiltonian. We use the geometrical averaging of the LDOS's at different lattice sites as a criterion to distinguish the localized states from extended ones. We find that bilayer graphene undergoes Anderson metal-insulator transition at a critical value of disorder strength.
Nonlinear intensity dependence of ratchet currents induced by terahertz laser radiation in bilayer graphene with asymmetric periodic grating gates
University of Regensburg（雷根斯堡大学）；CENTERA Laboratories, Institute of High Pressure Physics, Polish Academy of Sciences（波兰科学院高压物理研究所 CENTERA 实验室）；Ioffe Institute（约费研究所）；National Institute for Materials Science（日本国立材料研究所）
We present a theory for the regime of coherent interlayer tunneling in a disordered quantum Hall bilayer at total filling factor one, allowing for the effect of static vortices. We find that the system consists of domains of polarized superfluid phase. Injected currents introduce phase slips between the polarized domains which are pinned by disorder. We present a model of saturated tunneling domains that predicts a critical current for the breakdown of coherent tunneling that is extensive in the system size. This theory is supported by numerical results from a disordered phase model in two dim…
We use an exact solution of the relaxation-time Boltzmann equation in a uniform AC electric field to describe the nonlinear optical response of graphene in the terahertz (THz). The cases of monolayer, bilayer and ABA-stacked trilayer graphene are considered, and the monolayer species is shown to be the most appropriate one to exploit the nonlinear free electron response. We find that a single layer of monolayer graphene shows an optical bistability in the THz range, within the electromagnetic power range attainable in practice. The current associated with the third harmonic generation is also …
We propose a device for the generation of valley polarized electronic current in bilayer graphene. By analyzing the response of this material to intense terahertz frequency light in the presence of a transverse electric field, we demonstrate that dynamical states are induced in the gapped energy region, and if the system parameters are properly tuned, these states exist only in one valley. The valley polarized states can then be used to filter an arbitrary electron current, so generating a valley polarized current.
We study collective plasmon excitations and screening of disordered single- and bilayer black phosphorus beyond the low energy continuum approximation. The dynamical polarizability of phosphorene is computed using a tight-binding model that properly accounts for the band structure in a wide energy range. Electron-electron interaction is considered within the Random Phase Approximation. Damping of the plasmon modes due to different kinds of disorder, such as resonant scatterers and long-range disorder potentials, is analyzed. We further show that an electric field applied perpendicular to bilay…
In bilayers consisting of a normal metal (N) with spin-orbit coupling and a ferromagnet (F), the combination of the spin-Hall effect, the spin-transfer torque, and the inverse spin-Hall effect gives a small correction to the in-plane conductivity of N, which is referred to as spin-Hall magnetoresistance (SMR). We here present a theory of the SMR and the associated off-diagonal conductivity corrections for frequencies up to the terahertz regime. We show that the SMR signal has pronounced singularities at the spin-wave frequencies of F, which identifies it as a potential tool for all-electric sp…
Weakly disordered bilayer quantum Hall systems at filling factor $ν=1$ show spontaneous interlayer phase coherence if the layers are sufficiently close together. We study the collective modes in the system, the current-voltage characteristics and their evolution with an in-plane magnetic field in the phase-coherent regime.
The recent demonstration of saturable absorption and negative optical conductivity in the Terahertz range in graphene has opened up new opportunities for optoelectronic applications based on this and other low dimensional materials. Recently, population inversion across the Dirac point has been observed directly by time- and angle-resolved photoemission spectroscopy (tr-ARPES), revealing a relaxation time of only ~ 130 femtoseconds. This severely limits the applicability of single layer graphene to, for example, Terahertz light amplification. Here we use tr-ARPES to demonstrate long-lived popu…
The microscopic quantum theory of nonlinear stimulated scattering of chiral particles in doped $AB$ stacked bilayer graphene on Coulomb field of charged impurities in the presence of strong coherent electromagnetic radiation is presented. The Liouville-von Neumann equation for the density matrix is solved analytically. Here the interaction of electrons with the scattering potential is taken into account as a perturbation. The absorption rate of nonlinear inverse-bremsstrahlung for a grand canonical ensemble of fermionic chiral particles is calculated using the obtained solution. The analysis o…
We report on generation of pulsed broadband terahertz radiation utilizing the inverse spin Hall effect in Fe/Pt bilayers on MgO and sapphire substrates. The emitter was optimized with respect to layer thickness, growth parameters, substrates and geometrical arrangement. The experimentally determined optimum layer thicknesses were in qualitative agreement with simulations of the spin current induced in the ferromagnetic layer. Our model takes into account generation of spin polarization, spin diffusion and accumulation in Fe and Pt and electrical as well as optical properties of the bilayer sam…
We present a detailed numerical study of the electronic transport properties of bilayer and trilayer graphene within a framework of single-electron tight-binding model. Various types of disorder are considered, such as resonant (hydrogen) impurities, vacancies, short- or long-range Gaussian random potentials, and Gaussian random nearest neighbor hopping. The algorithms are based on the numerical solution of the time-dependent Schr ödinger equation and applied to calculate the density of states and conductivities (via the Kubo formula) of large samples containing millions of atoms. In the cases…
Spintronic ferromagnetic/non-magnetic heterostructures are novel sources for the generation of THz radiation based on spin-to-charge conversion in the layers. The key technological and scientific challenge of THz spintronic emitters is to increase their intensity and frequency bandwidth. Our work reveals the factors to engineer spintronic Terahertz generation by introducing the scattering lifetime and the interface transmission for spin polarized, non-equilibrium electrons. We clarify the influence of the electron-defect scattering lifetime on the spectral shape and the interface transmission …
We report on a tunable - by magnetic field and gate voltage - conversion of terahertz radiation into a dc current in spatially modulated bilayer graphene. We experimentally demonstrate that the underlying physics is related to the so-called ratchet effect. Our key findings are the direct observation of a sharp cyclotron resonance in the photocurrent and the demonstration of two effects caused by electron-electron interaction: the plasmonic splitting of the resonance due to long-range Coulomb coupling and the partial suppression of its second harmonic due to fast interparticle collisions. We de…
We describe the gated bilayer graphene system when it is subjected to intense terahertz frequency electromagnetic radiation. We examine the electron band structure and density of states via exact diagonalization methods within Floquet theory. We find that dynamical states are induced which lead to modification of the band structure. We first examine the situation where there is no external magnetic field. In the unbiased case, dynamical gaps appear in the spectrum which manifest as dips in the density of states. For finite interlayer bias (where a static gap is present in the band structure of…
Plasmons, collective oscillations of electron systems, can efficiently couple light and electric current, and thus can be used to create sub-wavelength photodetectors, radiation mixers, and on-chip spectrometers. Despite considerable effort, it has proven challenging to implement plasmonic devices operating at terahertz frequencies. The material capable to meet this challenge is graphene as it supports long-lived electrically-tunable plasmons. Here we demonstrate plasmon-assisted resonant detection of terahertz radiation by antenna-coupled graphene transistors that act as both plasmonic Fabry-…
We report the observation of the resonant excitation of edge photocurrents in bilayer graphene subjected to terahertz radiation and a magnetic field. The resonantly excited edge photocurrent is observed for both inter-band (at low carrier densities) and intra-band (at high densities) transitions between Landau levels (LL). While the intra-band LL transitions can be traced to the classical cyclotron resonance (CR) and produce strong resonant features, the inter-band-LL resonances have quantum nature and lead to the weaker features in the measured photocurrent spectra. The magnitude and polariza…
Electronic localization is numerically studied in disordered bilayer graphene with an electric-field induced energy gap. Bilayer graphene is a zero-gap semiconductor, in which an energy gap can be opened and controlled by an external electric field perpendicular to the layer plane. We found that, in the smooth disorder potential not mixing the states in different valleys (K and K' points), the gap opening causes a phase transition at which the electronic localization length diverges. We show that this can be interpreted as the integer quantum Hall transition at each single valley, even though …
The influence of plasma etched sample edges on electrical transport and doping is studied. Through electrical transport measurements the overall doping and mobility are analyzed for mono- and bilayer graphene samples. As a result the edge contributes strongly to the overall doping of the samples. Furthermore the edge disorder can be found as the main limiting source of the mobility for narrow samples.
The rectification of electromagnetic waves to direct currents is a crucial process for energy harvesting, beyond-5G wireless communications, ultra-fast science, and observational astronomy. As the radiation frequency is raised to the sub-terahertz (THz) domain, ac-to-dc conversion by conventional electronics becomes challenging and requires alternative rectification protocols. Here we address this challenge by tunnel field-effect transistors made of bilayer graphene (BLG). Taking advantage of BLG's electrically tunable band structure, we create a lateral tunnel junction and couple it to an ant…
We report on the observation of the ratchet effect -- generation of direct electric current in response to external terahertz (THz) radiation -- in bilayer graphene, where inversion symmetry is broken by an asymmetric dual-grating gate potential. As a central result, we demonstrate that at high temperature, $T = 150~\textrm{K}$, the ratchet current decreases at high frequencies as $ \propto 1/ω^2$, while at low temperature, $T = 4.2~\textrm{K}$, the frequency dependence becomes much stronger $\propto 1/ω^6$. The developed theory shows that the frequency dependence of the ratchet current is ver…
