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 hinders potential application of graphene in electronics and photonics.
We use time dependent perturbation theory to study quantum size effects on the terahertz nonlinear response of metallic graphene armchair nanoribbons of finite length under an applied electric field. Our work shows that quantization due to the finite length of the nanoribbon, the applied field profile, and the broadening of the graphene spectrum all play a significant role in the resulting nonlinear conductances. In certain cases, these effects can significantly enhance the nonlinearity over that for infinitely-long metallic armchair graphene nanoribbon.
We compute the terahertz third-order nonlinear conductance of metallic armchair graphene nanoribbons using time-dependent perturbation theory. Significant enhancement of the intrinsic third-order conductance over the result for instrinsic 2D single-layer graphene is observed over a wide range of temperatures. We also investigate the nonlinear response of extrinsic metallic acGNR with |E_F|<<200 meV. We find that the third-order conductance exhibits a strong Fermi level dependence at low temperatures. A third-order critical field strength of between 1 and 5 kV/m is computed for the Kerr conduct…
Zigzag nanoribbons of monolayer graphene-like two-dimensional materials host spontaneous edge magnetism at the zigzag terminations, whose configuration controls the band gap. In this article, the edge magnetism of zigzag nanoribbons of bilayer hexagonal crystals are studied. The specific models of bilayer graphene and bilayer silicene are both studied. As the gated voltage increases, the total energy level, magnetic structure and band structures of the ground state and the first quasi-stable excited state are tuned. For certain region of the gated voltage, the band gaps of spin up and down are…
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 study the interaction energy between two graphene nanoribbons by first principles calculations, including van der Waals interactions and spin polarization. For ultranarrow zigzag nanoribbons, the direct stacking is even more stable than Bernal, competing in energy for wider ribbons. This behavior is due to the magnetic interaction between edge states. We relate the reduction of the magnetization in zigzag nanoribbons with increasing ribbon width to the structural changes produced by the magnetic interaction, and show that when deposited on a substrate, zigzag bilayer ribbons remain magnetic…
We present an analytical description of pi electrons of a finite size bilayer graphene within a framework of the tight-binding model. The bilayered structures considered here are characterized by a rectangular geometry and have a finite size in one or both directions with armchair- and zigzag-shaped edges. We provide an exact analytical description of the spectrum of pi electrons in the zigzag and armchair bilayer graphene nanoribbons and nanotubes. We analyze the dispersion relations, the density of states, and the conductance quantization.
In this work the tight binding model calculations are carried out for AA-Bilayer Graphene nanoribbons as an example of bilayer systems. The effects of edges, NNN hopping, and impurities of a single layer are introduced numerically as a change in the elements of the relevant block diagonal matrix appearing in the direct diagonalization method. The direct interlayer hopping between the top and the bottom single layers is constructed in the generalized direct diagonalization method by the off-diagonal block matrices in which the strength of the interlayer hopping is included.
We investigate the transport properties of double-gated bilayer graphene nanoribbons at room temperature. The devices were fabricated using conventional CMOS-compatible processes. By analyzing the dependence of the resistance at the charge neutrality point as a function of the electric field applied perpendicular to the graphene surface, we show that a band gap in the density of states opens, reaching an effective value of ~sim50 meV. This demonstrates the potential of bilayer graphene as FET channel material in a conventional CMOS environment.
On the basis of tight-binding lattice model, the edge states of monolayer and bilayer graphene nanoribbons (GNRs) with different edge terminations are studied. The effects of edge-hopping modulation, spin-orbital coupling (SOC), and bias voltage on bilayer GNRs are discussed. We observe the following: (i) Some new extra edge states can be created by edge-hopping modulation for monolayer GNRs. (ii) Intralayer Rashba SOC plays a role in depressing the band energy gap $E_g$ opened by intrinsic SOC for both monolayer and bilayer GNRs. An almost linear dependent relation, i.e., $E_g\sim λ_R$, is fo…
The effects of Coulomb interactions on the electronic properties of bilayer graphene nanoribbons (BGNs) covered by a gate electrode are studied theoretically. The electron density distribution and the potential profile are calculated self-consistently within the Hartree approximation. A comparison to their single-particle counterparts reveals the effects of interactions and screening. Due to the finite width of the nanoribbon in combination with electronic repulsion, the gate-induced electrons tend to accumulate along the BGN edges where the potential assumes a sharp triangular shape. This has…
We investigate the electron transport and thermoelectric property of twisted bilayer graphene nanoribbon junction (TBGNRJ) in $0^o$, $21.8^o$, $38.2^o$ and $60^o$ rotation angles by first principles calculation with Landauer-Buttiker and Boltzmann theories. It is found that TBGNRJs exhibit negative differential resistance (NDR) in $21.8^o$ and $38.2^o$ rotation angles under $\pm$ 0.2 V bias voltage. More importantly, three peak ZT values of 2.0, 2.7 and 6.1 can be achieved in the $21.8^o$ rotation angle at 300K. The outstanding ZT values of TBGNRJs are interpreted as the combination of the red…
Coherent spin-dependent transport through a junction containing of Normal/Ferromagnetic/Normal bilayer graphene nanoribbon with zigzag edges is investigated by using Landauer formalism. In a more realistic set-up, the exchange field is induced by two ferromagnetic insulator strips deposited on the ribbon edges while a perpendicular electric field is applied by the top gated electrodes. Our results show that, for antiparallel configuration, a band gap is opened giving rise a semiconducting behavior, while for parallel configuration, the band structure has no band gap. As a result, a giant magne…
We study theoretically a multi-frequency response of electrons in confined graphene subject to dc-ac driven fields. We explore the possibility for using graphene nanoribbons (GNRs) to generate and amplify terahertz (THz) radiations in electric field domainless regime. We discover two main important schemes of generation; when the frequencies are commensurate, THz generation is due to wave mixing and when they are non-commensurate, a single strong field suppresses space charge instability and any weak signals can get amplified. The use of graphene as a best substitute for semiconductor nanoelec…
We investigate the thermoelectric performance of armchair graphene nanoribbon (AGNR), bilayer GNRs junction (BGNRJ) and BGNRJ with holes (BGNRJ-H) by the first principles calculation with non-equilibrium Green function. It is found that the BGNRJ-H exhibits high ZT values of 9.65 and 5.55 at 300K. The reason of these significantly larger ZT values than previously observed has been calculated due to reduced thermal conductivity and enhanced electrical conductivity. The low thermal conductance comes from the van der waals (vdW) interaction between two graphene layers. The increased electrical co…
The Seebeck coefficient in single and bilayer graphene sheets has been observed to be modest due to the gapless characteristic of these structures. In this work, we demonstrate that this coefficient is significantly high in quasi-1D structures of bilayer armchair graphene nanoribbons (BL-AGNRs) thanks to the open gaps induced by the quantum confinement effect. We show that the Seebeck coefficient of BL-AGNRs is also classified into three groups 3p, 3p + 1, 3p + 2 as the energy gap. And for the semiconducting BL-AGNR of width of 12 dimer lines, the Seebeck coefficient is found as high as 707 uV…
We study exchange interaction in zigzag bilayer phosphorene nanoribbons (ZBLPNRs) under a perpendicular electric field. We evaluate the spatial and electric field dependency of static spin susceptibility in real space in various configurations of magnetic impurities at zero temperature. The electronic properties of ZBLPNR in the presence of a gate voltage is also obtained. In comparison to the other two-dimensional (2D) materials such as graphene and silicene, ZBLPNR has two nearly degenerated quasiflat edge modes at the Fermi level, isolated from the bulk states. The band gap modulation of ZB…
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…
We study magneto-optical (MO) properties of a semi-Dirac nanoribbon in presence of a perpendicular magnetic field using Kernel Polynomial Method (KPM) based on the Keldysh formalism in the experimental (terahertz frequency) regime. For comparison, we have also included results for the Dirac systems as well, so that the interplay of the band structure deformation and MO conductivities can be studied. We have found that the MO conductivity shows features in the semi-Dirac system that are quite distinct from the Dirac case near the ultra-violet and the visible regimes. The real parts of the longi…
We study the effect of vertical electric-field (E-field) on the electronic properties of the multilayer armchair graphene nanoribbon (aGNR). Under E-field, the band structure of a bilayer aGNR undergoes interesting transformations such as change in the electron velocity, sign of the electron effective mass, band gap, the position of the band gap in the momentum space. Depending on the width of the aGNR and the applied E-field, the band gap of the aGNR may either be increased or decreased. When the applied E-field is above a critical value, the band gap of the bilayer aGNR is identical to that …
We show measurements on a bilayer graphene quantum dot with an integrated charge detector. The focus lies on enabling charge detection with a 30 nm wide bilayer graphene nanoribbon located approximately 35 nm next to a bilayer graphene quantum dot with an island diameter of about 100 nm. Local resonances in the nanoribbon can be successfully used to detect individual charging events in the dot even in regimes where the quantum dot Coulomb peaks cannot be measured by conventional techniques.
We theoretically show that an interlayer bias voltage in the AB-stacked bilayer graphene nanoribbons with armchair edges induces an electric polarization along the ribbon. Both tight-binding and ab initio calculations consistently indicate that when the bias voltage is weak, the polarization shows opposite signs depending on the ribbon width modulo three. This nontrivial dependence is explained using a two-band effective model. A strong limit of the bias voltage in the tight-binding model shows either one-third or zero polarization, which agrees with topological argument.
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 study analytically, based on the tight-binding model, the electronic band structure of armchair AA-stacked bilayer graphene nanoribbons (BLGNRs) in several regimes. We apply hard-wall boundary conditions to determine the discretion dominating on the Bloch wavefunctions in the confined direction. First we consider an ideal case, perfect nanoribbons without any edge deformation, and show that their electronic properties are strongly size-dependent. We find that the narrow armchair AA-stacked BLGNRs (similar to single-layer graphene nanoribbons) may be metallic or semiconducting depending on t…
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 di…
We study in this paper the edge polarizations and their consequences for a biased Bernal stacked bilayer graphene nanoribbon with zigzag termination. The magnetic states are classified according to the interlayer and intralayer couplings between the edge polarizations, and the magnetic phase diagram of doping versus bias voltage is given. Coplanar magnetic phase is found and the variation of its magnetic structure with the bias voltage is investigated. For all the magnetic states, we also discuss the possibility of the half-metallicity, and for a ribbon with perfect zigzag edges we predict sev…
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.
In this chapter, semi-analytical models for the calculation of the quantum capacitance of both monolayer and bilayer graphene and its nanoribbons, are presented. Since electron-hole puddles are experimental facts in all graphene samples, they have been incorporated in our calculations. The temperature dependence of the quantum capacitance around the charge neutrality point is also investigated and the obtained results are in agreement with many features recently observed in quantum capacitance measurements on both monolayer and bilayer graphene devices. Furtheremore, the impact of finite-size …
We show that gated bilayer graphene zigzag ribbons possess a fast and a slow edge, characterized by edge state velocities that differ due to non-negligible next-nearest-neighbor hopping elements. By applying bosonization and renormalization group methods, we find that the slow edge can acquire a sizable interaction-induced gap, which is tunable via an external gate voltage V_{g}. In contrast to the gate-induced gap in the bulk, the interaction-induced gap depends non-monotonously on the on-site potential V.
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…
Electronic properties of bilayer graphene are distinct from both the conventional two dimensional electron gas and monolayer graphene due to its particular chiral properties and excitation charge carrier dispersions. We study the effect of strain on the electronic structure, the edge-states and charge transport of bilayer graphene nanoribbon at zero-temperature. We demonstrate a valley polarized quantum Hall effect in biased bilayer graphene when the system is subjected to a perpendicular magnetic field. In this system a topological phase transition from a quantum valley Hall to a valley polar…
Graphene features topological edge bands that connect the pair of Dirac points through either sectors of the 1D Brillouin zone depending on edge configurations (zigzag or bearded). Because of their flat dispersion, spontaneous edge magnetisation can arise from Coulomb interaction in graphene nanoribbons, which has caught remarkable interest. We find an anomalous Bloch oscillation in such edge bands, in which the flat dispersion freezes electron motion along the field direction, while the topological connection of the bands through the bulk leads to electron oscillation in the transverse direct…
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 theoretically investigate the thermoelectric properties of zigzag bilayer phosphorene nanoribbons (ZBPNR). We first, draw an analogy between the extended Su-Schrieffer-Heeger (SSH) ladder and ZBPNR edge states and obtain their corresponding band structure and wave functions analytically. Then, by applying the energy filtering method, we show that the electric power and thermoelectric efficiency of the ZBPNRs can be improved remarkably in the presence of mid-gap edge states. We also argue how to engineer the edge modes to further optimize thermoelectric power and efficiency of the system by …
A theoretical study of the magnetoelectronic properties of zigzag and armchair bilayer graphene nanoribbons (BGNs) is presented. Using the recursive Green's function method, we study the band structure of BGNs in uniform perpendicular magnetic fields and discuss the zero-temperature conductance for the corresponding clean systems. The conductance quantized as 2(n+1)G_ for the zigzag edges and nG_0 for the armchair edges with G_{0}=2e^2/h being the conductance unit and $n$ an integer. Special attention is paid to the effects of edge disorder. As in the case of monolayer graphene nanoribbons (GN…
We investigated the emergence of spin spiral ground state induced by the electric field in the bilayer zigzag graphene nanoribbons for the ferromagnetic edge states. To do that, we employed the generalized Bloch theorem to create flat spiral alignments for all the magnetic moments of carbon atoms at the edges within a constraint scheme approach. While the small ribbon width can preserve the ferromagnetic ground state, the large one shows the spiral ground state starting from a certain value of the electric field. We also pointed out that the spiral ground state is caused by the reduction of sp…
Stacking two-dimensional layered materials such as graphene and transitional metal dichalcogenides with nonzero interlayer twist angles has recently become attractive because of the emergence of novel physical properties. Stacking of one-dimensional nanomaterials offers the lateral stacking offset as an additional parameter for modulating the resulting material properties. Here, we report that the edge states of twisted bilayer zigzag graphene nanoribbons (TBZGNRs) can be tuned with both the twist angle and the stacking offset. Strong edge state variations in the stacking region are first reve…
The edge physics of graphene based systems is well known to be highly sensitive to the atomic structure at the boundary, with localized zero mode edge states found only on the zigzag type termination of the lattice. Here we demonstrate that the graphene twist bilayer supports an additional class of edge states, that (i) are found for all edge geometries and thus are robust against edge roughness, (ii) occur at energies coinciding with twist induced van Hove singularities in the bulk and (iii) possess an electron density strongly modulated by the moiré lattice. Interestingly, these "moiré edge …
The magnetoelectronic properties of quasi-one-dimensional zigzag graphene nanoribbons are investigated by using the Peierls tight-binding model. Quasi-Landau levels (QLLs), dispersionless Landau subbands within a certain region of k-space, are resulted from the competition between magnetic and quantum confinement effects. In bilayer system, the interlayer interactions lead to two groups of QLLs, one occurring at the Fermi level and the other one occurring at higher energies. Transverse electric fields are able to distort energy spectrum, tilt two groups of QLLs and cause semiconductor-metal tr…
A topological insulator is a novel quantum state, characterized by symmetry-protected non-trivial edge/surface states. Our first-principle simulations show the significant effects of the chemical decoration on edge states of topological Bi(111) bilayer nanoribbon, which remove the trivial edge state and recover the Dirac linear dispersion of topological edge state. By comparing the edge states with and without chemical decoration, the Bi(111) bilayer nanoribbon offers a simple system for assessing conductance fluctuation of edge states. The chemical decoration can also modify the penetration d…
In the phenomenon of electromagnetically induced transparency1 (EIT) of a three-level atomic system, the linear susceptibility at the dipole-allowed transition is canceled through destructive interference of the direct transition and an indirect transition pathway involving a meta-stable level, enabled by optical pumping. EIT not only leads to light transmission at otherwise opaque atomic transition frequencies, but also results in the slowing of light group velocity and enhanced optical nonlinearity. In this letter, we report an analogous behavior, denoted as phonon-induced transparency (PIT)…
We investigate the performance of bends and splitters in graphene nanoribbon waveguides. Although the graphene waveguides are lossy themselves, we show that bends and splitters do not induce any additional loss provided that the nanoribbon width is sub-wavelength. We use transmission line theory to qualitatively interpret the behavior observed in our simulation. Our results pave a promising way to realize ultra-compact devices operating in the terahertz region.
We consider a periodic array of graphene nanoribbons under the action of a strong dc electric field $E_0$ and an external electromagnetic excitation with the frequency $ω$ and the lateral wave vector $q$. Solving the quasi-classical Boltzmann kinetic equation and calculating the surface dynamic conductivity $σ_{2D}(q,ω,E_0)$ and the absorption coefficient of such a system we show that the real part of the conductivity and the absorption coefficient may become negative under certain conditions. Physically this corresponds to the amplification of the electromagnetic waves at the expense of the e…
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）
