Terahertz conductivity of twisted bilayer graphene

Optical properties and plasmons in moiré structures

The discoveries of numerous exciting phenomena in twisted bilayer graphene (TBG) are stimulating significant investigations on moiré structures that possess a tunable moiré potential. Optical response can provide insights into the electronic structures and transport phenomena of non-twisted and twisted moiré structures. In this article, we review both experimental and theoretical studies of optical properties such as optical conductivity, dielectric function, non-linear optical response, and plasmons in moiré structures composed of graphene, hexagonal boron nitride (hBN), and/or transition metal dichalcogenides. Firstly, a comprehensive introduction to the widely employed methodology on optical properties is presented. After, moiré potential induced optical conductivity and plasmons in non-twisted structures are reviewed, such as single layer graphene-hBN, bilayer graphene-hBN and graphene-metal moiré heterostructures. Next, recent investigations of twist-angle dependent optical response and plasmons are addressed in twisted moiré structures. Additionally, we discuss how optical properties and plasmons could contribute to the understanding of the many-body effects and superconductivity observed in moiré structures.

Temperature-dependent charge carrier behavior in phosphorene quantum dots probed by terahertz time-domain spectroscopy

Although phosphorene quantum dots (PQDs) have gained significant attention in optoelectronics and physics due to their unique optical responses, the low-frequency electromagnetic properties of PQDs and the effects of temperature still remain largely unexplored. Herein, we investigate the temperature-dependent terahertz (THz) response of PQDs by using THz time-domain spectroscopy. Effective THz conductivity of the PQD sample is extracted based on THz measurements to analyze the charge carrier behavior. It is shown that the carriers in the PQDs can be approximated as a weakly confined Drude gas of classical and noninteracting charge particles, which are described by the modified Drude-Smith formula. Then, we also obtain the temperature dependences of the effective characteristic parameters for the charge carriers. As the temperature increases, the plasma frequency linearly enhances whereas both of the carrier diffusion time and the momentum scattering time decrease, which are akin to conventional semiconductors to a large extent. In addition, the confinement factor is closed to 1 and nearly insensitive to temperature. These results are helpful to gain an in-depth understanding of the low-frequency electromagnetic response of charge carriers in PQDs and to explore new applications in photonics and optoelectronics.

Controlled light energy and perfect absorption in twisted bilayer graphene

We theoretically study the components of the dynamical optical conductivity tensor and associated finite-frequency dielectric response of bilayer graphene (BLG), where one graphene layer can slide in-plane or commensurably twist on top of the other. Our results reveal that even slight deviations from the conventional AA, AB, or AC stacking orders yield a finite transverse conductivity. Upon calculating the optical conductivity of the BLG at any arbitrary interlayer displacement, Δ, and chemical potential, µ, it is utilized for a layered device with an epsilon-near-zero (ENZ) insert and metallic back plate. We find that both Δ and µ can effectively control the polarization, energy flow direction, and absorptivity of linearly polarized incident light. By appropriately tailoring Δ and µ, near-perfect absorption and tunable dissipation can be accessible through particular angles of incidence and a broad range of ENZ layer thicknesses. Our findings can be applied to the design of programmable optoelectronics devices.

Optical tuning of the terahertz response of black phosphorus quantum dots: effects of weak carrier confinement

In contrast to few-layer black phosphorus (BP) with a relatively larger area, BP quantum dots (BP-QDs) are expected to have distinctive electromagnetic response and carrier behaviors, especially in low-frequency range such as in the THz regime. Herein, we experimentally investigate the THz properties of BP-QDs as well as the optical control of these properties. It is demonstrated that the effects of weak carrier confinement, which is associated with diffusive restoring current in each BP-QD, contribute significantly to the effective THz conductivity of BP-QDs. Instead, spectral features of discretely spaced energy levels as shown for many kinds of semiconductor QDs in UV-visible range are not observed in the THz regime. This indicates an insignificant contribution of strong quantum confinement here. Based on the modified Drude-Smith formula, we show that the optical excitation/pump of a CW laser can induce photogenerated carriers and enhance the effects of weak carrier confinement in BP-QDs. Thus, a nonlinear enhancement of THz absorption can be observed by increasing the power of the excitation laser. These results not only deepen our understanding of the fundamental physics of BP nanomaterials but also provide an alternative approach to realize active control of BP-based THz devices.

Terahertz charge transport dynamics in 3D graphene networks with localization and band regimes

Terahertz steady-state and time-resolved conductivity and permittivity spectra were measured in 3D graphene networks assembled in free-standing covalently cross-linked graphene aerogels. Investigation of a transition between reduced-graphene oxide and graphene controlled by means of high-temperature annealing allowed us to elucidate the role of defects in the charge carrier transport in the materials. The THz spectra reveal increasing conductivity and decreasing permittivity with frequency. This contrasts with the Drude- or Lorentz-like conductivity typically observed in various 2D graphene samples, suggesting a significant contribution of a relaxational mechanism to the conductivity in 3D graphene percolated networks. The charge transport in the graphene aerogels exhibits an interplay between the carrier hopping among localized states and a Drude contribution of conduction-band carriers. Upon photoexcitation, carriers are injected into the conduction band and their dynamics reveals picosecond lifetime and femtosecond dephasing time. Our findings provide important insight into the charge transport in complex graphene structures.

Moiré metasurfaces for dynamic beamforming

Recent advances in digitally programmable metamaterials have accelerated the development of reconfigurable intelligent surfaces (RIS). However, the excessive use of active components (e.g., pin diodes and varactor diodes) leads to high costs, especially for those operating at millimeter-wave frequencies, impeding their large-scale deployments in RIS. Here, we introduce an entirely different approach-moiré metasurfaces-to implement dynamic beamforming through mutual twists of two closely stacked metasurfaces. The superposition of two high-spatial-frequency patterns produces a low-spatial-frequency moiré pattern through the moiré effect, which provides the surface impedance profiles to generate desired radiation patterns. We demonstrate experimentally that the direction of the radiated beams can continuously sweep over the entire reflection space along predesigned trajectories by simply adjusting the twist angle and the overall orientation. Our work opens previously unexplored directions for synthesizing far-field scattering through the direct contact of mutually twisted metallic patterns with different plane symmetry groups.

Twist dependent magneto-optical response in twisted bilayer graphene

By employing a linearised Boltzmann equation, we calculate the magneto-optical properties of twisted bilayer graphene using non-magnetic wave functions. Both transverse and longitudinal responses are calculated up to the second order in applied magnetic field with their twist angle and Fermi level dependence examined. We find that increasing the twist angle increases the transverse metallic response so long as the Fermi level remains below the upper conduction band. Interlayer transitions provide an appreciable enhancement when the Fermi level traverses the gap between the two conduction bands. Interlayer transitions are also responsible for a nonzero anomalous Hall conductivity in this model. As the Fermi level moves towards zero, the longitudinal response begins to dominate and a highly anisotropic negative magneto-resistance is observed.

Controllable Growth of Graphene on Liquid Surfaces

Controllable fabrication of graphene is necessary for its practical application. Chemical vapor deposition (CVD) approaches based on solid metal substrates with morphology-rich surfaces, such as copper (Cu) and nickel (Ni), suffer from the drawbacks of inhomogeneous nucleation and uncontrollable carbon precipitation. Liquid substrates offer a quasiatomically smooth surface, which enables the growth of uniform graphene layers. The fast surface diffusion rates also lead to unique growth and etching kinetics for achieving graphene grains with novel morphologies. The rheological surface endows the graphene grains with self-adjusted rotation, alignment, and movement that are driven by specific interactions. The intermediary-free transfer or the direct growth of graphene on insulated substrates is demonstrated using liquid metals. Here, the controllable growth process of graphene on a liquid surface to promote the development of attractive liquid CVD strategies is in focus. The exciting progress in controlled growth, etching, self-assembly, and delivery of graphene on a liquid surface is presented and discussed in depth. In addition, prospects and further developments in these exciting fields of graphene growth on a liquid surface are discussed.

Active multifunctional terahertz modulator based on plasmonic metasurface

An active multifunctional terahertz modulator based on plasmon-induced transparency (PIT) metasurface under the effect of external infrared light was investigated theoretically and experimentally. A distinct transparency window, which resulted from the near-field coupling between two resonators, could be observed in the transmission spectra. Experimental results showed a phenomenon infrared light induced blue shift on the both resonator with increasing optical powers. When the optical power was tuned from 0 mW to 400 mW, the amplitude tunability of transmission at transparency window reached to 34.01%, much larger than that at the two resonance frequencies. Moreover, the phase tunability of the transmission at 0.98 THz reached to 31.35%. Meanwhile, the amplitude variation was limited to 10%. Furthermore, a coupled Lorentz oscillator model was adopted to analyze the near-field interaction of the resonances. Experimental results were in good agreement with the analytical fitting results.

Terahertz Time-Domain Spectroscopy of Graphene Nanoflakes Embedded in Polymer Matrix

The terahertz time-domain spectroscopy (THz-TDS) technique has been used to obtain transmission THz-radiation spectra of polymer nanocomposites containing a controlled amount of exfoliated graphene. Graphene nanocomposites (1 wt%) that were used in this work were based on poly(ethylene terephthalate-ethylene dilinoleate) (PET-DLA) matrix and were prepared via a kilo-scale (suitable for research and development, and prototyping) in-situ polymerization. This was followed by compression molding into 0.3-mm-thick and 0.9-mm-thick foils. Transmission electron microscopy (TEM) and Raman studies were used to confirm that the graphene nanoflakes dispersed in a polymer matrix consisted of a few-layer graphene. The THz-radiation transients were generated and detected using a low-temperature–grown GaAs photoconductive emitter and detector, both excited by 100-fs-wide, 800-nm-wavelength optical pulses, generated at a 76-MHz repetition rate by a Ti:Sapphire laser. Time-domain signals transmitted through the nitrogen, neat polymer reference, and 1-wt% graphene-polymer nanocomposite samples were recorded and subsequently converted into the spectral domain by means of a fast Fourier transformation. The spectral range of our spectrometer was up to 4 THz, and measurements were taken at room temperature in a dry nitrogen environment. We collected a family of spectra and, based on Fresnel equations, performed a numerical analysis, that allowed us to extract the THz-frequency-range refractive index and absorption coefficient and their dependences on the sample composition and graphene content. Using the Clausius-Mossotti relation, we also managed to estimate the graphene effective dielectric constant to be equal to ~7 ± 2. Finally, we extracted from our experimental data complex conductivity spectra of graphene nanocomposites and successfully fitted them to the Drude-Smith model, demonstrating that our graphene nanoflakes were isolated in their polymer matrix and exhibited highly localized electron backscattering with a femtosecond relaxation time. Our results shed new light on how the incorporation of exfoliated graphene nanoflakes modifies polymer electrical properties in the THz-frequency range. Importantly, they demonstrate that the complex conductivity analysis is a very efficient, macroscopic and non-destructive (contrary to TEM) tool for the characterization of the dispersion of a graphene nanofiller within a copolyester matrix.

Real-Space Imaging of the Tailored Plasmons in Twisted Bilayer Graphene

We report a systematic plasmonic study of twisted bilayer graphene (TBLG)-two graphene layers stacked with a twist angle. Through real-space nanoimaging of TBLG single crystals with a wide distribution of twist angles, we find that TBLG supports confined infrared plasmons that are sensitively dependent on the twist angle. At small twist angles, TBLG has a plasmon wavelength comparable to that of single-layer graphene. At larger twist angles, the plasmon wavelength of TBLG increases significantly with apparently lower damping. Further analysis and modeling indicate that the observed twist-angle dependence of TBLG plasmons in the Dirac linear regime is mainly due to the Fermi-velocity renormalization, a direct consequence of interlayer electronic coupling. Our work unveils the tailored plasmonic characteristics of TBLG and deepens our understanding of the intriguing nano-optical physics in novel van der Waals coupled two-dimensional materials.

Epitaxial strain driven crossover from Drude to Drude-Smith terahertz conductivity dynamics in LaNiO3 thin films

We investigate the hetero-epitaxial strain driven low-energy charge dynamics in compressive and tensile strained LaNiO₃ thin films employing terahertz (THz) time-domain spectroscopy. The complex THz conductivity exhibits a crossover from Drude type metallic behavior for the compressive film to a Drude-Smith type disordered behavior for the tensile film. This demonstration of strain driven crossover in THz conductivity dynamics, while the two films have qualitatively similar dc conductivities, (i) brings out the potential of THz technology in distinguishing between similar dc electronic phases and (ii) suggests that LaNiO₃ under compressive strain is a better candidate for applications as electrodes in oxides electronics.

Optically controlled terahertz modulator by liquid-exfoliated multilayer WS2 nanosheets

Lack of efficient routes to modulate the propagation properties of the terahertz (THz) wave is a major barrier for the further development of THz technology. In recent years, two dimensional transition metal dichalcogenides (2D TMDCs) were applied to the design of effective THz modulator by forming heterostructure with Si. Here, we experimentally demonstrate an optical controlled THz modulator consisting of liquid-exfoliated WS₂ nanosheets and a silicon substrate (WS₂-Si). By innovatively depositing liquid-exfoliated WS₂ nanosheets on the Si instead of growing by chemical vapor deposition (CVD) method, both of the size and the thickness of WS₂ film is controlled. The WS₂-Si sample presents a flat modulation depth from 0.2 THz to 1.6 THz. The modulation depth reaches 56.7% under a 50 mW pumping power, which is over 5 times enhanced compared with that of the Si substrate. With the increase of illumination power, the modulation depth continues to increase, finally reaching up to 94.8% under 470 mW. Besides, the WS₂-Si sample also achieves ~80% modulation depth under 450 nm illumination, indicating its ability to operate under either of wavelength in visible spectra. Moreover, we compare the sample to the reported modulators including CVD growth TMDCs-Si ones and find our sample has comparable modulation effects while is much easy to be prepared. Therefore, we believe our work is meaningful to provide an alternative route to achieve effective modulation of THz waves by adopting liquid-exfoliated 2D materials.

Dielectric properties of a CsPbBr3 quantum dot solution in the terahertz region

In recent years, CsPbBr₃ quantum dots (QDs) have attracted much attention due to their bright prospects in solar cell studies. Dielectric properties are important for the fabrication of optoelectronic devices. Here, the dielectric properties of a CsPbBr₃ QD solution are investigated between 0.1 and 2.0 THz by terahertz time-domain spectroscopy. The measured frequency-dependent transmitted ratio is found to decrease from 0.96 to 0.80 in this range. By comparing different concentrations of the QD solution, the frequency-averaged absorption is linearly increased with the increase in QD concentration. After that, the frequency-dependent dielectric constant, including the complex refractive index, complex dielectric constant, and conductivity, is extracted by Fourier transform of the time-domain spectrum. An effective medium approach method is adopted to extract the complex dielectric constant of a CsPbBr₃ QD inclusion, and a slight peak around 0.4 THz is found in the imaginary part of the dielectric constant. The result of Drude-Lorentz fitting shows that the phonon plays a dominant role in the dielectric properties of a CsPbBr₃ QD solution. Moreover, the THz response of a CsPbBr₃ QD is found to be unchanged when the test is conducted under illumination. We attribute this phenomenon to the discrete energy level of excitons in CsPbBr₃ QDs due to quantum confinement, and design a comparative experiment to validate it. This study is significant for its deeper insight into the dielectric properties of CsPbBr₃ QDs, and thus is helpful through its applications in optoelectronics.

Phonon Mode Transformation Across the Orthohombic-Tetragonal Phase Transition in a Lead Iodide Perovskite CH3NH3PbI3: A Terahertz Time-Domain Spectroscopy Approach

We study the temperature-dependent phonon modes of the organometallic lead iodide perovskite CH3NH3PbI3 thin film across the terahertz (0.5-3 THz) and temperature (20-300 K) ranges. These modes are related to the vibration of the Pb-I bonds. We found that two phonon modes in the tetragonal phase at room temperature split into four modes in the low-temperature orthorhombic phase. By use of the Lorentz model fitting, we analyze the critical behavior of this phase transition. The carrier mobility values calculated from the low-temperature phonon mode frequencies, via two theoretical approaches, are found to agree reasonably with the experimental value (∼2000 cm(2) V(-1) s(-1)) from a previous time-resolved THz spectroscopy work. Thus, we have established a possible link between terahertz phonon modes and the transport properties of perovskite-based solar cells.

New insights into the diverse electronic phases of a novel vanadium dioxide polymorph: a terahertz spectroscopy study

A remarkable feature of vanadium dioxide is that it can be synthesized in a number of polymorphs. The conductivity mechanism in the metastable layered polymorph VO2(B) thin films has been investigated by terahertz time-domain spectroscopy (THz-TDS). In VO2(B), a critical temperature of 240 K marks the appearance of a non-zero Drude term in the observed complex conductivity, indicating the evolution from a pure insulating state towards a metallic state. In contrast, the THz conductivity of the well-known VO2(M1) is well fitted only by a modification of the Drude model to include backscattering. We also identified two different THz conductivity regimes separated by temperature in these two polymorphs. The electronic phase diagram is constructed, revealing that the width and onset of the metal-insulator transition in the B phase develop differently from the M1 phase.

Revealing the interactions between pentagon–octagon–pentagon defect graphene and organic donor/acceptor molecules: a theoretical study

The cyano group interacts strongly with 5–8–5 defect graphene, changes the bands near the Fermi level and enhances the infrared light absorption.

Layer-stacking growth and electrical transport of hierarchical graphene architectures

Hierarchical graphene architectures (HGAs) that grow by stacking of layers are produced on a liquid copper surface using chemical vapor deposition. The stacking mode--for example hexagonal-hexagonal-hexagonal or hexagonal-snowflake-dendritic--can be simply controlled. Measurements of the electrical properties of HGAs indicate that hierarchical stacking of graphene may be a simple and effective way of tailoring their properties without degrading them.

Bilayer Phosphorene: Effect of Stacking Order on Bandgap and Its Potential Applications in Thin-Film Solar Cells

Phosphorene, a monolayer of black phosphorus, is promising for nanoelectronic applications not only because it is a natural p-type semiconductor but also because it possesses a layer-number-dependent direct bandgap (in the range of 0.3 to 1.5 eV). On basis of the density functional theory calculations, we investigate electronic properties of the bilayer phosphorene with different stacking orders. We find that the direct bandgap of the bilayers can vary from 0.78 to 1.04 eV with three different stacking orders. In addition, a vertical electric field can further reduce the bandgap to 0.56 eV (at the field strength 0.5 V/Å). More importantly, we find that when a monolayer of MoS2 is superimposed with the p-type AA- or AB-stacked bilayer phosphorene, the combined trilayer can be an effective solar-cell material with type-II heterojunction alignment. The power conversion efficiency is predicted to be ∼18 or 16% with AA- or AB-stacked bilayer phosphorene, higher than reported efficiencies of the state-of-the-art trilayer graphene/transition metal dichalcogenide solar cells.

Large hexagonal bi- and trilayer graphene single crystals with varied interlayer rotations

Bi- and trilayer graphene have attracted intensive interest due to their rich electronic and optical properties, which are dependent on interlayer rotations. However, the synthesis of high-quality large-size bi- and trilayer graphene single crystals still remains a challenge. Here, the synthesis of 100 μm pyramid-like hexagonal bi- and trilayer graphene single-crystal domains on Cu foils using chemical vapor deposition is reported. The as-produced graphene domains show almost exclusively either 0° or 30° interlayer rotations. Raman spectroscopy, transmission electron microscopy, and Fourier-transformed infrared spectroscopy were used to demonstrate that bilayer graphene domains with 0° interlayer stacking angles were Bernal stacked. Based on first-principle calculations, it is proposed that rotations originate from the graphene nucleation at the Cu step, which explains the origin of the interlayer rotations and agrees well with the experimental observations.

Terahertz conductivity of topological surface states in Bi₁.₅Sb₀.₅Te₁.₈Se₁.₂

Topological insulators are electronic materials with an insulating bulk and conducting surface. However, due to free carriers in the bulk, the properties of the metallic surface are difficult to detect and characterize in most topological insulator materials. Recently, a new topological insulator Bi_1.5Sb_0.5Te_1.7Se_1.3 (BSTS) was found, showing high bulk resistivities of 1–10 Ω.cm and greater contrast between the bulk and surface resistivities compared to other Bi-based topological insulators. Using Terahertz Time-Domain Spectroscopy (THz-TDS), we present complex conductivity of BSTS single crystals, disentangling the surface and bulk contributions. We find that the Drude spectral weight is 1–2 orders of magnitude smaller than in other Bi-based topological insulators, and similar to that of Bi₂Se₃ thin films, suggesting a significant contribution of the topological surface states to the conductivity of the BSTS sample. Moreover, an impurity band is present about 30 meV below the Fermi level, and the surface and bulk carrier densities agree with those obtained from transport data. Furthermore, from the surface Drude contribution, we obtain a ~98% transmission through one surface layer — this is consistent with the transmission through single-layer or bilayer graphene, which shares a common Dirac-cone feature in the band structure.