We present an in-depth analysis of the electronic and vibrational band structure of uniaxially strained graphene by ab-initio calculations. Depending on the direction and amount of strain, the Fermi crossing moves away from the $K$-point. However, graphene remains semimetallic under small strains. The deformation of the Dirac cone near the $K$-point gives rise to a broadening of the 2D Raman mode. In spite of specific changes in the electronic and vibrational band structure the strain-induced frequency shifts of the Raman active E2g and 2D modes are independent of the direction of strain. Thus, the amount of strain can be directly determined from a single Raman measurement.
We revisit the problem of bound states in graphene under the influence of point electric monopole and dipole impurity potentials extended to the case in which the membrane of this material is uniformly and uniaxially strained, which leads to a redefinition of the charge and dipole moment, respectively. By considering an anisotropic Fermi velocity, we analytically solve the resulting Dirac equation for each potential. We observe that the effect of the anisotropy is to promote or inhibit the critical behavior known to occur for each kind of impurity, depending on the direction along which strain…
We have performed first-principles studies on adsorption patterns of hydrogen adatoms on uniaxially strained graphene. Our simulation reveals that the adsorption energy of adatoms are sensitive to the strain. Hydrogen adatoms on zigzag strained graphene tend to form a chain-like adsorption patterns perpendicular to the strain direction, but those under armchair strain cannot form any long-range chain pattern. We explain our results in terms of a tight-binding model and the electronic structure of strained graphene. These anisotropic adsorption behaviors under uniaxial strain suggest methods fo…
Intrinsic and Rashba spin-orbit interactions in strained graphene is studied within the tight-binding (TB) approach. Dependence of Slater-Koster (SK) parameters of graphene on strain are extracted by fitting the \emph{ab initio} band structure to the TB results. A generalized low-energy effective Hamiltonian in the presence of spin-orbit couplings is proposed for strained graphene subjected to an external perpendicular electric field. Dependence of the modified Rashba strength and other parameters of effective Hamiltonian on the strain and electric field are calculated. In order to analyze the…
The main goal of our study was investigation of the influence of the deformations (sufficiently large for the establishing the non-zero gap) on electrotransport properties of impure graphene. To achieve this purpose, we implemented the simulation package that allows to perform numerical calculation of the conductivity and mobility of graphene samples subjected to two types of the uniaxial strain: along zigzag and armchair edges. All numerical calculations are performed within the Kubo-Greenwood methodology along with a tight-binding model. Transport properties are studied in case of a presence…
We revisit the uniaxially strained graphene immersed in a uniform homogeneous magnetic field orthogonal to the layer in order to describe the time evolution of coherent states build from a semi-classical model. We consider the symmetric gauge vector potential to render the magnetic field, and we encode the tensile and compression deformations on an anisotropy parameter $ζ$. After solving the Dirac-like equation with an anisotropic Fermi velocity, we define a set of matrix ladder operators and construct electron coherent states as eigenstates of a matrix annihilation operator with complex eigen…
Electronic screening renormalizes the linear bands of graphene and in the vicinity of the Dirac point, creates a diamond shaped structure in the quasiparticle spectral density. This is a result of electron-plasmon scattering processes which produce a finite momentum feature referred to as the `plasmaron ring'. In this work we explore the effects of uniaxial strain on these spectral features with the aim of understanding how strain modifies correlations. We derive and calculate the spectral density to the G$_0$W-RPA level which allows us to identify the dispersive behaviour of the diamond geome…
We investigate the effect of strain and isotopic disorder on thermal transport in suspended graphene by equilibrium molecular dynamics simulations. We show that the thermal conductivity of unstrained graphene, calculated from the fluctuations of the heat current at equilibrium is finite and converges with size at finite temperature. In contrast, the thermal conductivity of strained graphene diverges logarithmically with the size of the models, when strain exceeds a relatively large threshold value of 2%. An analysis of phonon populations and lifetimes explains the divergence of the thermal con…
The Continuum Model for Uniaxially Strained Bilayer Graphene Moiré Systems
Hong Kong University of Science and Technology（香港科技大学）；Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；Southern University of Science and Technology（南方科技大学）
The effect of strain on the Landau levels (LLs) spectra in graphene is studied, using an effective Dirac-like Hamiltonian which includes the distortion in the Dirac cones, anisotropy and spatial-dependence of the Fermi velocity induced by the lattice change through a renormalized linear momentum. We propose a geometrical approach to obtain the electron's wave-function and the LLs in graphene from the Sturm-Liouville theory, using the minimal substitution method. The coefficients of the renormalized linear momentum are fitted to the energy bands, which are obtained from a Density Functional The…
Asymmetric Veselago lenses (AVLs) can be created from ballistic $p$-$n$ and $n$-$p$-$n$ homojunctions of uniaxially strained graphene. This atypical converging electron flow emerges by applying uniaxial tension out of the device's symmetry axes. A part of electron flow needs to be positively refracted for focusing in an asymmetric spot, whose location is tunable with the strain. In AVLs, Klein tunneling is angularly shifted regards to the normal incidence. This perfect transmission occurs at the straight line that connects the point source and focus, which is unaffected by variation of the Fer…
In this work, we present a computational study on the possibility of strain engineering in monolayer Black Phosphorus (black P) and Blue Phosphorus (blue P) based MOSFETs. The material properties like band structure, carrier effective masses, carrier densities at band extrema are evaluated using Generalized Gradient Approximation (GGA) in Density Functional Theory (DFT).Thereafter self-consistent Non-Equilibrium Greens Function (NEGF) simulations are carried out to study the device performance metrics (such as output characteristics, ON currents, transconductance etc.) of such strained black P…
An explanation is proposed for the recently observed in optical spectra of monolayer graphene giant increase in the Drude peak width under applied uniaxial strain. We argue that the underlying mechanism of this increase can be based on resonant scattering of carriers from inevitably present impurities such as adsorbed atoms that can be described by the Fano-Anderson model. We demonstrate that the often neglected scalar deformation potential plays the essential role in this process. The conditions necessary for the maximum effect of the giant Drude peak broadening are determined. It is stressed…
The interplay of strain engineering and photon-assisted tunneling of electrons in graphene is considered for giving rise to atypical transport phenomena. The combination of uniaxial strain and a time-periodic potential barrier helps to control the particle transmission for a wide range of tunable parameters. With the use of the tight-biding approach, the elasticity theory, and the Floquet scattering, we found an angular shift of the maximum transmission in the sidebands for uniaxial strains breaking the mirror symmetry with respect to the normal incidence, which is called anomalous Floquet tun…
Recent experimental advances in the reconstruction of the Wigner function (WF) for electronic systems have led us to consider the possibility of employing this theoretical tool in the analysis of electron dynamics of uniaxially strained graphene. In this paper, we study the effect of strain on the WF of electrons in graphene under the interaction of a uniform magnetic field. This mechanical deformation modifies drastically the shape of the Wigner function of Landau and coherent states. The WF has a different behavior straining the material along the zigzag direction in comparison with the armc…
The optical conductivity of graphene strained uniaxially is studied within the Kubo-Greenwood formalism. Focusing on inter-band absorption, we analyze and quantify the breakdown of universal transparency in the visible region of the spectrum, and analytically characterize the transparency as a function of strain and polarization. Measuring transmittance as a function of incident polarization directly reflects the magnitude and direction of strain. Moreover, direction-dependent selection rules permit identification of the lattice orientation by monitoring the van-Hove transitions. These photoel…
Twist bilayer graphenes with magical angle have nearly flat band, which become strongly correlated electron systems. Herein, we propose another system based on strained bilayer graphene that have flat band at the intrinsic Fermi level. The top and bottom layers are uniaxially stretched along different directions. When the strength and directions of the strain satisfy certain condition, the periodical lattices of the two layers are commensurate to each other. The regions with AA, AB and BA stacking arrange in a triangular lattice. With magical strain, the bands around the intrinsic Fermi level …
The spin and valley polarizations and plasmonics in Van der Waals heterostructures of strained graphene monolayer on 2D transition metal dichalcogenide (GrTMD) substrate are reported in this communication. The substrate induced interactions (SII) involve sub-lattice-resolved, and enhanced intrinsic spin-orbit couplings, the extrinsic Rashba spin-orbit coupling (RSOC), and the orbital gap related to the transfer of the electronic charge from graphene to the substrate. Furthermore, magnetic impurity atoms are deposited to the graphene surface and the corresponding exchange field is included in t…
We study the 2D Raman band of in-plane uniaxially strained graphene within a non-orthogonal tight-binding model. At non-zero strain, the obtained 2D band splits into two subbands at strain angles $0^{\circ}$ and $30^{\circ}$ or into three subbands at intermediate angles. The evolution of the 2D subbands is calculated systematically in the range of the accessible strains from -1% to 3% and for the commonly used laser photon energy from 1.5 eV to 3.0 eV. The strain rate and dispersion rate of the 2D subbands are derived and tabulated. In particular, these two quantities show large variations up …
Based on the BTK theory, we investigate the tunneling conductance in a uniaxially strained graphene-based normal metal (NG)/ barrier (I)/superconductor (SG) junctions. In the present model, we assume that depositing the conventional superconductor on the top of the uniaxially strained graphene, normal graphene may turn to superconducting graphene with the Cooper pairs formed by the asymmetric Weyl-Dirac electrons, the massless fermions with direction-dependent velocity. The highly asymmetrical velocity, vy/vx>>1, may be created by strain in the zigzag direction near the transition point betwee…
It has been recently established that optoelectronic and non-linear transport experiments can give direct access to the dipole moment of the Berry curvature in non-magnetic and non-centrosymmetric materials. Thus far, non-vanishing Berry curvature dipoles have been shown to exist in materials with substantial spin-orbit coupling where low-energy Dirac quasiparticles form tilted cones. Here, we prove that this topological effect does emerge in two-dimensional Dirac materials even in the complete absence of spin-orbit coupling. In these systems, it is the warping of the Fermi surface that trigge…
We study the role of long-range electron-electron interactions in a system of two-dimensional anisotropic Dirac fermions, which naturally appear in uniaxially strained graphene, graphene in external potentials, some strongly anisotropic topological insulators, and engineered anisotropic graphene structures. We find that while for small interactions and anisotropy the system restores the conventional isotropic Dirac liquid behavior, strong enough anisotropy can lead to the formation of a quasi-one dimensional electronic phase with dominant charge order (anisotropic excitonic insulator).
We present the theory describing the various surface electronic states arisen from the mixing of conduction and valence bands in a strained mercury telluride (HgTe) bulk material. We demonstrate that the strain-induced band gap in the Brillouin zone center of HgTe results in the surface states of two different kinds. Surface states of the first kind exist in the small region of electron wave vectors near the center of the Brillouin zone and have the Dirac linear electron dispersion characteristic for topological states. The surface states of the second kind exist only far from the center of th…
Recent advances in strain engineering at the nanoscale have shown the feasibility to modulate the properties of graphene. Although the electron-phonon (e-ph) coupling and Kohn anomalies in graphene define the phonon branches contributing to the resonance Raman scattering, and is relevant to the electronic and thermal transport as a scattering source, the evolution of the e-ph coupling as a function of strain has been less studied. In this work, the Kohn anomalies and the e-ph coupling in uniaxially strained graphene along armchair (AC) and zigzag (ZZ) directions were studied by means of densit…
We explore the tunability of the phonon polarization in suspended uniaxially strained graphene by magneto-phonon resonances. The uniaxial strain lifts the degeneracy of the LO and TO phonons, yielding two cross-linearly polarized phonon modes and a splitting of the Raman G peak. We utilize the strong electron-phonon coupling in graphene and the off-resonant coupling to a magneto-phonon resonance to induce a gate-tunable circular phonon dichroism. This, together with the strain-induced splitting of the G peak, allows us to controllably tune the two linearly polarized G mode phonons into circula…
We evaluate the optical reflectivity for a uniaxially strained graphene single layer between a SiO2 substrate and air. A tight binding model for the band dispersion of graphene is employed. As a function of the strain modulus and direction, graphene may traverse one of several electronic topological transitions, characterized by a change of topology of its Fermi line. This results in features in the conductivity within the optical range, which might be observable experimentally.
We study theoretically effects of an anisotropic elastic strain on the exciton energy spectrum fine structure and optical selection rules in atom-thin crystals based on transition-metal dichalcogenides. The presence of strain breaks the chiral selection rules at the $\bm K$-points of the Brillouin zone and makes optical transitions linearly polarized. The orientation of the induced linear polarization is related to the main axes of the strain tensor. Elastic strain provides an additive contribution to the exciton fine structure splitting in agreement with experimental evidence obtained from un…
Topological origin of flat-bands as pseudo-Landau levels in uniaxial strained graphene nanoribbons and induced magnetic ordering due to electron-electron interactions
We evaluate the van der Waals (vdW) interaction energy at zero temperature between two undoped strained graphene layers separated by a finite distance. We consider the following three models for the anisotropic case: (a) where one of the two layers is uniaxially strained, (b) the two layers are strained in the same direction, and (c) one of the layers is strained in the perpendicular direction with respect to the other. We find that for all three models and given value of the electron-electron interaction coupling, the vdW interaction energy increases with increasing anisotropy. The effect is …
Strain qualitatively changes the low-energy band structure of bilayer graphene, leading to the appearance of a pair of low-energy Dirac cones near each corner of the Brillouin zone, and a Lifshitz transition, (a saddle point in the dispersion relation) at an energy proportional to the strain [M. Mucha-Kruczynski, I.L. Aleiner, and V.I. Fal'ko, Phys. Rev. B 84, 041404 (2011)]. Here, we show that in the vicinity of the Lifshitz transition the conductance of a ballistic n-p and n-p-n junction exhibits an anomaly: a non-monotonic temperature and chemical potential dependence, with the size dependi…
We study uniaxially strained graphene under the influence of non-uniform magnetic fields perpendicular to the material sample with a coordinate independent strain tensor. For that purpose, we solve the Dirac equation with anisotropic Fermi velocity and explore the conditions upon which such an equation possesses a supersymmetric structure in the quantum mechanical sense through examples. Working in a Laudau-like gauge, wave functions and energy eigenvalues are found analytically in terms of the magnetic field intensity, the anisotropy scales and other relevant parameters that shape the magneti…
In topological semimetals, nodes appear at symmetry points in the Brillouin zone as a result of band inversion, and yield quasi-relativistic massless fermions at low energies. Cd3As2 is a three-dimensional topological semimetal that hosts two Dirac cones responsible for a variety of quantum phenomena. In this work, we demonstrate the strain tuning of the Dirac nodes of Cd3As2 through a combination of magnetooptical infrared spectroscopy and high-resolution X-ray diffraction studies performed on epitaxial films. In these thin films, we observe a giant enhancement of the node separation in momen…
Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory（斯坦福材料能源科学研究所，SLAC国家加速器实验室）；Stanford PULSE Institute, SLAC National Accelerator Laboratory（斯坦福PULSE研究所，SLAC国家加速器实验室）；Department of Chemistry, Massachusetts Institute of Technology（麻省理工学院化学系）；Elettra-Sincrotrone（埃莱特拉同步辐射中心）；Paul Scherrer Institut（保罗谢尔研究所）
We propose a general framework for constructing a large set of nodal-point semimetals by tuning the number of linearly ($d_L$) and (at most) quadratically ($d_Q$) dispersing directions. By virtue of such a unifying scheme, we identify a new perturbative route to access various strongly interacting non-Dirac semimetals with $d_Q>0$. As a demonstrative example, we relate a two dimensional anisotropic semimetal with $d_L=d_Q=1$, describing the topological transition between a Dirac semimetal and a normal insulator, and its three dimensional counterparts with $d_L=1$, $d_Q=2$. We address the quant…
Extended transfer matrix method for electron transmission in anisotropic 2D materials: Interplay of strain and (a)periodicity of potentials
Instituto Politécnico Nacional, UPIIH（墨西哥国立理工学院，UPIIH）；Instituto de Física, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理研究所）；Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo（米却肯圣尼古拉斯德伊达尔戈大学物理与数学研究所）；Centro de Ciencias Exactas, Universidad del Bío-Bío（比奥-比奥大学精确科学中心）
The chapter generalizes results on influence of uniaxial strain and adsorption on the electron states and charge transport or localization in graphene with different configurations of imperfections (point defects): resonant (neutral) adsorbed atoms either oxygen- or hydrogen-containing molecules or functional groups, vacancies or substitutional atoms, charged impurity atoms or molecules, and distortions. To observe electronic properties of graphene-admolecules system, we applied electron paramagnetic resonance technique in a broad temperature range for graphene oxides as a good basis for under…
Machine-learned multi-orbital tight-binding (MMTB) Hamiltonian models have been developed to describe the electronic characteristics of intermetallic compounds $\rm Mg_2Si, Mg_2Ge, Mg_2Sn$, and $\rm Mg_2Pb$ subject to strain. The MMTB models incorporate spin-orbital mediated interactions and they are calibrated to the electronic band structures calculated via density functional theory (DFT) by a massively parallelized multi-dimensional Monte-Carlo search algorithm. The results show that a machine-learned five-band tight-binding model reproduces the key aspects of the valence band structures in…
Strain engineering has emerged as a powerful tool to modify the optical and electronic properties of two-dimensional crystals. Here we perform a systematic study of strained semiconducting transition metal dichalcogenides. The effect of strain is considered within a full Slater-Koster tight-binding model, which provides us with the band structure in the whole Brillouin zone. From this, we derive an effective low-energy model valid around the K point of the BZ, which includes terms up to second order in momentum and strain. For a generic profile of strain, we show that the solutions for this mo…
The electronic implications of strain in graphene can be captured at low energies by means of pseudovector potentials which can give rise to pseudomagnetic fields. These strain-induced vector potentials arise from the local perturbation to the electronic hopping amplitudes in a tight-binding framework. Here we complete the standard description of the strain-induced vector potential, which accounts only for the hopping perturbation, with the explicit inclusion of the lattice deformations or, equivalently, the deformation of the Brillouin zone. These corrections are linear in strain and are diff…
We compute the effects of generic short-range interactions on gapless electrons residing at the quantum critical point separating a two-dimensional Dirac semimetal (DSM) and a symmetry-preserving band insulator (BI). The electronic dispersion at this critical point is anisotropic ($E_{\mathbf k}=\pm \sqrt{v^2 k^2_x + b^2 k^{2n}_y}$ with $n=2$), which results in unconventional scaling of physical observables. Due to the vanishing density of states ($\varrho(E) \sim |E|^{1/n}$), this anisotropic semimetal (ASM) is stable against weak short-range interactions. However, for stronger interactions t…
