arXiv subjects

J. L. Cheng

Publications and source records attributed to J. L. Cheng.

At least 19 recordsLinked to original sources

arXiv2022

Theory of Optical Activity in Doped Systems with Application to Twisted Bilayer Graphene

We theoretically study the optical activity in a doped system and derive the optical activity tensor from a light wavevector-dependent linear optical conductivity. Although the light-matter interaction is introduced through the velocity gauge from a minimal coupling Hamiltonian, we find that the well-known ``false divergences'' problem can be avoided in practice if the electronic states are described by a finite band effective Hamiltonian, such as a few-band tight-binding model. The expression we obtain for the optical activity tensor is in good numerical agreement with a recent theory derived for an undoped topologically trivial gapped system. We apply our theory to the optical activity of a gated twisted bilayer graphene, with a detailed discussion of the dependence of the results on twist angle, chemical potential, gate voltage, and location of rotation center forming the twisted bilayer graphene.

cond-mat.mes-hall↗

arXiv2020

Third order optical nonlinearity of three dimensional massless Dirac fermions

We present analytic expressions for the electronic contributions to the linear conductivity $σ^{(1)}_{3d}(ω)$ and the third order optical conductivity $σ^{(3)}_{3d}(ω_1,ω_2,ω_3)$ of three dimensional massless Dirac fermions, the quasi-particles relevant for the low energy excitation of topological Dirac semimetals and Weyl semimetals. Although there is no gap for massless Dirac fermions, a finite chemical potential $μ$ can lead to an effective gap parameter, which plays an important role in the qualitative features of interband optical transitions. For gapless linear dispersion in three dimension, the imaginary part of the linear conductivity diverges as a logarithmic function of the cutoff energy, while the real part is linear with photon frequency $ω$ as $\hbarω>2|μ|$. The third order conductivity exhibits features very similar to those of two dimensional Dirac fermions, i.e., graphene, but with the amplitude for a single Dirac cone generally two orders of magnitude smaller in three dimension than in two dimension. There are many resonances associated with the chemical potential induced gap parameters, and divergences associated with the intraband transitions. The details of the third order conductivity are discussed for third harmonic generation, the Kerr effect and two-photon carrier injection, parametric frequency conversion, and two-color coherent current injection. Although the expressions we derive are limited to the clean limit at zero temperature, the generalization to include phenomenological relaxation processes at finite temperature is straightforward and is presented.

cond-mat.mtrl-sci↗

arXiv2019

Third harmonic generation of undoped graphene in Hartree-Fock approximation

We theoretically investigate the effects of Coulomb interaction, at the level of unscreened Hartree-Fock approximation, on third harmonic generation of undoped graphene in an equation of motion framework. The unperturbed electronic states are described by a widely used two-band tight binding model, and the Coulomb interaction is described by the Ohno potential. The ground state is renormalized by taking into account the Hartree-Fock term, and the optical conductivities are obtained by numerically solving the equations of motion. The absolute values of conductivity for third harmonic generation depend on the photon frequency $Ω$ as $Ω^{-n}$ for $\hbarΩ<1$, and then show a peak as $3\hbarΩ$ approaches the renormalized energy of the $M$ point. Taking into account the Coulomb interaction, $n$ is found to be $5.5$, which is significantly greater than the value of $4$ found with the neglect of the Coulomb interaction. Therefore the Coulomb interaction enhances third harmonic generation at low photon energies -- for our parameters $\hbarΩ<0.8$~eV -- and then reduces it until the photon energy reaches about $2.1$~eV. The effect of the background dielectric constant is also considered.

cond-mat.mes-hall↗

arXiv2018

Intraband divergences in third order optical response of 2D systems

The existence of large nonlinear optical coefficients is one of the preconditions for using nonlinear optical materials in nonlinear optical devices. For a crystal, such large coefficients can be achieved by matching photon energies with resonant energies between different bands, and so the details of the crystal band structure play an important role. Here we demonstrate that large third-order nonlinearities can also be generally obtained by a different strategy: As any of the incident frequencies or the sum of any two or three frequencies approaches zero, the doped or excited populations of electronic states lead to divergent contributions in the induced current density. We refer to these as intraband divergences, by analogy with the behavior of Drude conductivity in linear response. Physically, such resonant processes can be associated with a combination of inraband and interband optical transitions. Current-induced second order nonlinearity, coherent current injection, and jerk currents are all related to such divergences, and we find similar divergences in degenerate four wave mixing and cross-phase modulation under certain conditions. These divergences are limited by intraband relaxation parameters, and lead to a large optical response from a high quality sample; we find they are very robust with respect to variations in the details of the band structure. To clearly track all of these effects, we analyze gapped graphene, describing the electrons as massive Dirac fermions; under the relaxation time approximation, we derive analytic expressions for the third order conductivities, and identify the divergences that arise in describing the associated nonlinear phenomena.

cond-mat.mtrl-sci↗

arXiv2018

Nonlinear optics of graphene and other 2D materials in layered structures

We present a theoretical framework for nonlinear optics of graphene and other 2D materials in layered structures. We derive a key equation to find the effective electric field and the sheet current density in the 2D material for given incident light beams. Our approach takes into account the effect of the surrounding environment and characterizes its contribution as a structure factor. We apply our approach to two experimental setups, and discuss the structure factors for several nonlinear optical processes including second harmonic generation, third harmonic generation, and parametric frequency conversion. Our systematic study gives a strict extraction method for the nonlinear coefficients, and provides new insights in how layered structures influence the nonlinear signal observed from 2D materials.

physics.optics↗

arXiv2018

Nonlinear magneto-optic effects in doped graphene and gapped graphene: a perturbative treatment

The nonlinear magneto-optic responses are investigated for gapped graphene and doped graphene in a perpendicular magnetic field. The electronic states are described by Landau levels, and the electron dynamics in an optical field is obtained by solving the density matrix in the equation of motion. In the linear dispersion approximation around the Dirac points, both linear conductivity and third order nonlinear conductivities are numerically evaluated for infrared frequencies. The nonlinear phenomena, including third harmonic generation, Kerr effects and two photon absorption, and four wave mixing, are studied. All optical conductivities show strong dependence on the magnetic field. At weak magnetic fields, our results for doped graphene agree with those in the literature. We also present the spectra of the conductivities of gapped graphene. At strong magnetic fields, the third order conductivities show peaks with varying the magnetic field and the photon energy. These peaks are induced by the resonant transitions between different Landau levels. The resonant channels, the positions, and the divergences of peaks are analyzed. The conductivities can be greatly modified, up to orders of magnitude. The dependence of the conductivities on the gap parameter and the chemical potential is studied.

cond-mat.mtrl-sci↗

arXiv2018

Nonperturbative model for optical response under intense periodic fields with application to graphene in a strong perpendicular magnetic field

Graphene exhibits extremely strong optical nonlinearity when a strong perpendicular magnetic field is applied, the response current shows strong field dependence even for moderate light intensity, and the perturbation theory fails. We nonperturbatively calculate full optical conductivities induced by a periodic field in an equation-of-motion framework based on the Floquet theorem, with the scattering described phenomenologically. The nonlinear response at high fields is understood in terms of the dressed electronic states, or Floquet states, which is further characterized by the optical conductivity for a weak probe light field. This approach is illustrated for a magnetic field at $5$ T and a driving field with photon energy $0.05$ eV. Our results show that the perturbation theory works only for weak fields $<3$ kV/cm, confirming the extremely strong light matter interaction for Landau levels of graphene. This approach can be easily extended to the calculation of optical conductivities in other systems.

cond-mat.mes-hall↗

arXiv2017

Coherent control of current injection in zigzag graphene nanoribbons

We present Fermi's golden rule calculations of the optical carrier injection and the coherent control of current injection in graphene nanoribbons with zigzag geometry, using an envelope function approach. This system possesses strongly localized states (flat bands) with a large joint density of states at low photon energies; for ribbons with widths above a few tens of nanometers, this system also posses large number of (non-flat) states with maxima and minima close to the Fermi level. Consequently, even with small dopings the occupation of these localized states can be significantly altered. In this work, we calculate the relevant quantities for coherent control at different chemical potentials, showing the sensitivity of this system to the occupation of the edge states. We consider coherent control scenarios arising from the interference of one-photon absorption at $2\hbarω$ with two-photon absorption at $\hbarω$, and those arising from the interference of one-photon absorption at $\hbarω$ with stimulated electronic Raman scattering (virtual absorption at $2\hbarω$ followed by emission at $\hbarω$). Although at large photon energies these processes follow an energy-dependence similar to that of 2D graphene, the zigzag nanoribbons exhibit a richer structure at low photon energies, arising from divergences of the joint density of states and from resonant absorption processes, which can be strongly modified by doping. As a figure of merit for the injected carrier currents, we calculate the resulting swarm velocities. Finally, we provide estimates for the limits of validity of our model.

cond-mat.mtrl-sci↗

arXiv2017

Second order optical nonlinearity of graphene due to electric quadrupole and magnetic dipole effects

We present a practical scheme to separate the contributions of the electric quadrupole-like and the magnetic dipole-like effects to the forbidden second order optical nonlinear response of graphene, and give analytic expressions for the second order op- tical conductivities, calculated from the independent particle approximation, with relaxation described in a phenomenological way. We predict strong second order nonlinear effects, including second harmonic generation, photon drag, and difference fre- quency generation. We discuss in detail the controllability of these effects by tuning the chemical potential, taking advantage of the dominant role played by interband optical transitions in the response.

cond-mat.mtrl-sci↗

arXiv2015

Third order nonlinearity of graphene: effects of phenomenological relaxation and finite temperature

We investigate the effect of phenomenological relaxation parameters on the third order optical nonlinearity of doped graphene by perturbatively solving the semiconductor Bloch equation around the Dirac points. An analytic expression for the nonlinear conductivity at zero temperature is obtained under the linear dispersion approximation. With this analytic formula as starting point, we construct the conductivity at finite temperature and study the optical response to a laser pulse of finite duration. We illustrate the dependence of several nonlinear optical effects, such as third harmonic generation, Kerr effects and two photon absorption, parametric frequency conversion, and two color coherent current injection, on the relaxation parameters, temperature, and pulse duration. In the special case where one of the electric fields is taken as a dc field, we investigate the dc-current and dc-field induced second order nonlinearities, including dc-current induced second harmonic generation and difference frequency generation.

cond-mat.mtrl-sci↗

arXiv2015

Numerical study of the optical nonlinearity of doped and gapped graphene: From weak to strong field excitation

Numerically solving the semiconductor Bloch equations within a phenomenological relaxation time approximation, we extract both the linear and nonlinear optical conductivities of doped graphene and gapped graphene under excitation by a laser pulse. We discuss in detail the dependence of second harmonic generation, third harmonic generation, and the Kerr effects on the doping level, the gap, and the electric field amplitude. The numerical results for weak electric fields agree with those calculated from available analytic perturbation formulas. For strong electric fields when saturation effects are important, all the effective third order nonlinear response coefficients show a strong field dependence.

cond-mat.mtrl-sci↗

arXiv2013

Spin-dependent inter- and intra-valley electron-phonon scattering in germanium

We investigate the spin-dependent electron-phonon scatterings of the $L$ and $Γ$ valleys and the band structure near the conduction band minima in germanium. We first construct a $16\times16$ ${\bm k}\cdot{\bm p}$ Hamiltonian in the vicinity of the $L$ point in germanium, which ensures the correctness of the band structure of the lowest three conduction bands and highest two valence bands. This Hamiltonian facilitates the analysis of the spin-related properties of the conduction electrons. We then demonstrate the phonon-induced electron scatterings of the $L$ and $Γ$ valleys, i.e., the intra-$Γ$/ $L$ valley, inter--$Γ$-$L$ valley and inter--$L$-$L$ valley scatterings in germanium. The selection rules and complete scattering matrices for these scatterings are calculated, where the scattering matrices for the intra-$Γ$ valley scattering, inter--$Γ$-$L$ valley scattering and the optical-phonon and the separated transverse-acoustic- and longitudinal-acoustic-phonon contributions to the intra-$Γ$ valley scattering have not been reported in the literature. The coefficients in these scattering matrices are obtained via the pseudo-potential calculation, which also verifies our selection rules and wave-vector dependence. We further discuss the Elliott-Yafet mechanisms in these electron-phonon scatterings with the ${\bm k}$$\cdot$${\bm p}$ eigenstates at the $L$ and $Γ$ valleys. Our investigation of these electron-phonon scatterings are essential for the study of the optical orientation of spin and hot-electron relaxation in germanium.

cond-mat.mtrl-sci↗

arXiv2013

Disorder-induced significant enhancement in magnetization of ball-milled Fe2CrGa alloy

A new disordered atom configuration in Fe2CrGa alloy has been created by ball-milling method. This leads to a significant enhancement of the magnetic moment up to 3.2~3.9 μB and an increase of Curie temperature by about 200 K, compared with the arc-melt samples. Combination of first-principles calculations and experimental results reveals that Fe2CrGa alloy should crystallize in Hg2CuTi based structure with different atomic disorders for the samples prepared by different methods. It is addressed that magnetic interactions play a crucial role for the system to adopt such an atomic configuration which disobeys the empirical rule.

cond-mat.mtrl-sci↗

arXiv2011

Two-photon Indirect Optical Injection and Two-color Coherent Control in Bulk Silicon

Using an empirical pseudopotential description of electron states and an adiabatic bond charge model for phonon states in bulk silicon, we theoretically investigate two-photon indirect optical injection of carriers and spins and two-color coherent control of the motion of the injected carriers and spins. For two-photon indirect carrier and spin injection, we identify the selection rules of band edge transitions, the injection in each conduction band valley, and the injection from each phonon branch at 4 K and 300 K. At 4 K, the TA phonon-assisted transitions dominate the injection at low photon energies, and the TO phonon-assisted at high photon energies. At 300 K, the former dominates at all photon energies of interest. The carrier injection shows anisotropy and linear-circular dichroism with respect to light propagation direction. For light propagating along the $<001>$ direction, the carrier injection exhibits valley anisotropy, and the injection into the $Z$ conduction band valley is larger than that into the $X/Y$ valleys. For $σ^-$ light propagating along the $<001>$ ($<111>$) direction, the degree of spin polarization gives a maximum value about 20% (6%) at 4 K and -10% (20%) at 300 K, and at both temperature shows abundant structure near the injection edges due to contributions from different phonon branches. Forthe two-color coherent current injection with an incident optical field composed of a fundamental frequency and its second harmonic, the response tensors of the electron (hole) charge and spin currents are calculated at 4 K and 300 K. We show the current control for three different polarization scenarios. The spectral dependence of the maximum swarm velocity shows that the direction of charge current reverses under increase in photon energy.

cond-mat.mtrl-sci↗

arXiv2011

Full Band Structure Calculation of Two-photon Indirect Absorption in Bulk Silicon

Degenerate two-photon indirect absorption in silicon is an important limiting effect on the use of silicon structures for all-optical information processing at telecommunication wavelengths. We perform a full band structure calculation to investigate two-photon indirect absorption in bulk silicon, using a pseudopotential description of the energy bands and an adiabatic bond charge model to describe phonon dispersion and polarization. Our results agree well with some recent experimental results. The transverse acoustic/optical phonon-assisted processes dominate.

cond-mat.mtrl-sci↗

arXiv2011

Theory of optical spin orientation in silicon

We theoretically investigate the indirect optical injection of carriers and spins in bulk silicon, using an empirical pseudopotential description of electron states and an adiabatic bond charge model for phonon states. We identify the selection rules, the contribution to the carrier and spin injection in each conduction band valley from each phonon branch and each valence band, and the temperature dependence of these processes. The transition from the heavy hole band to the lowest conduction band dominates the injection due to the large joint density of states. For incident light propagating along the $[00\bar{1}]$ direction, the injection rates and the degree of spin polarization of injected electrons show strong valley anisotropy. The maximum degree of spin polarization is at the injection edge with values 25% at low temperature and 15% at high temperature.

cond-mat.mtrl-sci↗

arXiv2009

Theory of the spin relaxation of conduction electrons in silicon

A realistic pseudopotential model is introduced to investigate the phonon-induced spin relaxation of conduction electrons in bulk silicon. We find a surprisingly subtle interference of the Elliott and Yafet processes affecting the spin relaxation over a wide temperature range, suppressing the significance of the intravalley spin-flip scattering, previously considered dominant, above roughly 120 K. The calculated spin relaxation times $T_1$ agree with the spin resonance and spin injection data, following a $T^{-3}$ temperature dependence. The valley anisotropy of $T_1$ and the spin relaxation rates for hot electrons are predicted.

cond-mat.mtrl-sci↗

arXiv2009

Spin relaxation in $n$-type ZnO quantum wells

We perform an investigation on the spin relaxation for $n$-type ZnO (0001) quantum wells by numerically solving the kinetic spin Bloch equations with all the relevant scattering explicitly included. We show the temperature and electron density dependence of the spin relaxation time under various conditions such as impurity density, well width, and external electric field. We find a peak in the temperature dependence of the spin relaxation time at low impurity density. This peak can survive even at 100 K, much higher than the prediction and measurement value in GaAs. There also exhibits a peak in the electron density dependence at low temperature. These two peaks originate from the nonmonotonic temperature and electron density dependence of the Coulomb scattering. The spin relaxation time can reach the order of nanosecond at low temperature and high impurity density.

cond-mat.mes-hall↗