@article{iafrate_sokolov_2024, title={Bloch-electron dynamics under the influence of a quantized radiation field}, volume={109}, ISSN={["2469-9934"]}, DOI={10.1103/PhysRevA.109.012223}, abstractNote={A theory is described for a Bloch electron accelerating in a homogeneous external electric field of arbitrary time dependence while interacting with a quantized radiation field. The external electric field is described in the vector potential gauge. The quantum radiation field is described by the free space quantized electromagnetic field in the Coulomb gauge. The instantaneous eigenstates for the Bloch Hamiltonian are introduced as basis states to analyze the Bloch dynamics to all orders in the external electric field; as well, the eigenstates of the free quantum electromagnetic field are utilized as a component of the full basis set to develop a direct time-dependent solution of the Schr\"odinger equation. As an alternative consideration, the Glauber displacement operator is utilized to transform the original problem to a canonical form. For both the initial and transformed scenarios considered, the first-order solution to the Schr\"odinger equation is obtained and used to calculate the Bloch electric current in a form useful for studying the spectral content of solids. It is found that the Glauber transformed Hamiltonian and subsequent quantum dynamics is quite effective in providing solid-state band information in general and as noted in the first-order calculated Bloch-electron current.}, number={1}, journal={PHYSICAL REVIEW A}, author={Iafrate, G. J. and Sokolov, V. N.}, year={2024}, month={Jan} }
 @article{iafrate_sokolov_2022, title={Quantum transport for electron quasiparticles interacting with a disordered binary alloy: A Wigner approach}, volume={105}, ISSN={["2469-9969"]}, DOI={10.1103/PhysRevB.105.224308}, abstractNote={Quantum transport is developed in the Wigner function representation for a Bloch electron quasiparticle interacting with a disordered binary alloy in the presence of a homogeneous electric field of arbitrary time dependence and amplitude. The electron quasiparticle is described by a single-band effective Hamiltonian, and the homogeneous electric field is treated in the vector potential gauge. The methodology for the quantum transport analysis proceeds by first transforming the Liouville equation to one in which the interaction Hamiltonian (the binary alloy Hamiltonian) appears quadratically. The basis states employed in evaluating the requisite matrix elements are the instantaneous eigenstates of the electron quasiparticle Hamiltonian in the presence of the electric field. The Wigner quantum transport equations are derived, and the binary alloy collision term is suitably ensemble averaged over the disordered binary alloy matrix elements. In addition, the general drift and diffusion terms are exactly obtained, resulting in the complete Wigner-Boltzmann equation for the binary alloy system. In approximating the collision term for the two separate cases of parabolic energy dispersion and the long-wavelength limit, it is found that the reduced Wigner-Boltzmann equation includes the manifestation of the intracollisional field effect and other quantum generalities. As a contrast to the actual random alloy treatment, attention is given to the canonical problem of quantum transport for a virtual crystal (VC). As an alternative to the random binary alloy scattering problem, the VC Hamiltonian adopted for this treatment is derived by ensemble averaging the random binary alloy Hamiltonian. The resulting Wigner transport equation for the VC case is descriptive of Bloch dynamics in a graded semiconductor alloy.}, number={22}, journal={PHYSICAL REVIEW B}, author={Iafrate, G. J. and Sokolov, V. N.}, year={2022}, month={Jun} }
 @article{iafrate_sokolov_2021, title={Bloch-electron dynamics in homogeneous electric fields: Application to multiphoton absorption in semiconductors and insulators}, volume={104}, ISSN={["2469-9934"]}, DOI={10.1103/PhysRevA.104.063113}, abstractNote={The theory of Bloch-electron dynamics for carriers in a homogeneous electric field of arbitrary time dependence is developed in consideration of the properties of multiphoton absorption (MPA) in semiconductors and insulators. The general approach is to utilize the accelerated Bloch-state representation (ABR) as a basis thereby treating the electric field exactly; also, the electric field is described in the vector potential gauge. In developing the ABR, the instantaneous eigenstates for the central Hamiltonian are obtained as the accelerated Bloch states and utilized to find the time-dependent solution to the Schr\"odinger equation. In introducing the Wigner-Weisskopf approximation (WWA), the transition probability amplitude between the states of the system is obtained and used in the application to MPA in semiconductors and insulators. The probability amplitude for MPA is derived for a plane-polarized radiation field. The periodicity of the time-dependent electric field serves as a principle time constant in developing the probability amplitude per period. Utilizing the WWA, the general MPA transition probability is derived for transitions between an arbitrary set of valence and conduction bands for a time-varying electric field in the $x$ direction. Within the WWA, the MPA transition probability, equivalent to the well-known Keldysh transition amplitude, is derived and expressed in terms of infinite-variable generalized Bessel functions and modified Bessel functions. The exact MPA result is analyzed in the small ($\ensuremath{\lesssim}{10}^{6}$ V/cm) and large ($\ensuremath{\gtrsim}{10}^{8}$ V/cm) electric field amplitude limits.}, number={6}, journal={PHYSICAL REVIEW A}, author={Iafrate, G. J. and Sokolov, V. N.}, year={2021}, month={Dec} }
 @article{iafrate_sokolov_2020, title={The Bloch Electron Response to Electric Fields: Application to Graphene}, volume={257}, ISSN={["1521-3951"]}, DOI={10.1002/pssb.201900660}, abstractNote={The theory of Bloch electron dynamics for carriers in homogeneous electric fields of arbitrary time dependence is developed in consideration of the electronic transport properties in graphene. The general approach is to use the accelerated Bloch state representation (ABR) as a basis so that the dependence upon the electric field, including Zener tunneling, is treated exactly; also, the electric field is described in the vector potential gauge. Within the ABR, the instantaneous eigenstates for the central Hamiltonian are described and utilized to develop both the time‐dependent wave functions and the single‐particle density matrix pictures with explicit application to intrinsic graphene. The Bloch electron analysis for graphene in a constant electric field reveals the explicit manifestation of electron–hole pair creation, Bloch oscillations, and Wannier–Stark localization. The average velocity and acceleration are established as an explicit function of the electric field, and their behavior is characterized on short and long time scales. Further, it is shown that the average acceleration in a nonvanishing electric field gives rise to an electric field induced dynamical effective mass tensor in the direction of the field.}, number={6}, journal={PHYSICA STATUS SOLIDI B-BASIC SOLID STATE PHYSICS}, author={Iafrate, Gerald and Sokolov, Valeriy}, year={2020}, month={Jun} }
 @article{iafrate_sokolov_krieger_2017, title={Quantum transport and the Wigner distribution function for Bloch electrons in spatially homogeneous electric and magnetic fields}, volume={96}, ISSN={["2469-9969"]}, DOI={10.1103/physrevb.96.144303}, abstractNote={The theory of Bloch electron dynamics for carriers in homogeneous electric and magnetic fields of arbitrary time dependence is developed in the framework of the Liouville equation. The Wigner distribution function (WDF) is determined from the single particle density matrix in the ballistic regime, i.e., collision effects are excluded. The single particle transport equation is established with the electric field described in the vector potential gauge, and the magnetic field is treated in the symmetric gauge. 
The general approach is to employ the accelerated Bloch state representation (ABR) as a basis so that the dependence upon the electric field, including multiband Zener tunneling, is treated exactly. In the formulation of the WDF, we transform to a new set of variables so that the final WDF is gauge invariant and is expressed explicitly in terms of the position, kinetic momentum, and time. 
The methodology for developing the WDF is illustrated by deriving the exact WDF equation for free electrons in homogeneous electric and magnetic fields. The methodology is then extended to the case of electrons described by an effective Hamiltonian corresponding to an arbitrary energy band function. In treating the problem of Bloch electrons in a periodic potential, the methodology for deriving the WDF reveals a multiband character due to the inherent nature of the Bloch states. In examining the single-band WDF, it is found that the collisionless WDF equation matches the equivalent Boltzmann transport equation to first order in the magnetic field. These results are necessarily extended to second order in the magnetic field by employing a unitary transformation that diagonalizes the Hamiltonian using the ABR to second order. The work includes a discussion of the multiband WDF transport analysis and the identification of the combined Zener-magnetic field induced tunneling.}, number={14}, journal={PHYSICAL REVIEW B}, author={Iafrate, G. J. and Sokolov, V. N. and Krieger, J. B.}, year={2017}, month={Oct} }
 @article{sokolov_iafrate_2014, title={Spontaneous emission of Bloch oscillation radiation under the competing influences of microcavity enhancement and inhomogeneous interface degradation}, volume={115}, number={5}, journal={Journal of Applied Physics}, author={Sokolov, V. N. and Iafrate, G. J.}, year={2014} }
 @article{iafrate_krieger_2013, title={Extension of the KLI approximation toward the exact optimized effective potential}, volume={138}, number={9}, journal={Journal of Chemical Physics}, author={Iafrate, G. J. and Krieger, J. B.}, year={2013} }
 @article{sokolov_iafrate_krieger_2009, title={Bloch electron spontaneous emission from a single energy band in a classical ac field}, volume={80}, ISSN={["1098-0121"]}, DOI={10.1103/PhysRevB.80.165328}, abstractNote={A theory for the spontaneous emission of radiation for a Bloch electron in a single superlattice (SL) energy band under the influence of an external, spatially homogeneous, classical ac electric field is presented. The classical external ac electric field is described in the vector-potential gauge. The quantum radiation field is described by the free-space quantized electromagnetic field in the Coulomb gauge. Utilizing the instantaneous eigenstates of the Bloch Hamiltonian as the basis states, the Bloch electron dynamics is described to all orders in the classical ac electric field. It is shown that the spontaneous emission occurs with frequencies equal to integral multiples of the classical ac electric field frequency; this is due to the imposition of temporal periodic motion of the Bloch electrons in the SL miniband from the external periodic ac field. From appropriately derived selection rules for photon frequency and wave-vector transitions, the total spontaneous-emission probability (TSEP) is derived to first-order perturbation theory in the quantized radiation field. A general expression is obtained for the TSEP in terms of arbitrary SL miniband parameters; further, the TSEP is analyzed in detail based on the band model for the nearest-neighbor tight-binding approximation, and results show multiharmonic behavior and ac electric field tuning properties. In the nearest-neighbor tight-binding approximation, specific results for single Bloch electron manifest distinct plateaulike step structure in the analysis of normalized TSEP as a function of the ratio ${\ensuremath{\omega}}_{0}/\ensuremath{\omega}$, where ${\ensuremath{\omega}}_{0}$ is the characteristic frequency, proportional to the ac electric field amplitude, and $\ensuremath{\omega}$ is the ac electric field frequency; the plateau centers of gravity are found to be defined by the Stark delocalization condition established in ac-field transport. Further, the influence of a microcavity waveguide is established and shows enhancement as well as harmonic tuning of the TSEP due to coupling to the microcavity modal environment. Finally, the one-electron TSEP is extended, within the independent electron approximation, so as to include fractional band filling along with a constant-temperature-dependent and electron-density-dependent analysis; from this analysis, TSEP numerical estimates are projected at terahertz external field frequencies for a half-filled GaAs/AlGaAs SL miniband at zero temperature.}, number={16}, journal={PHYSICAL REVIEW B}, author={Sokolov, V. N. and Iafrate, G. J. and Krieger, J. B.}, year={2009}, month={Oct} }
 @article{kiselev_iafrate_2008, title={Phonon dynamics and phonon assisted losses in Euler-Bernoulli nanobeams}, volume={77}, ISSN={["2469-9969"]}, DOI={10.1103/physrevb.77.205436}, abstractNote={Nonequilibrium phonon processes and related degradation effects are treated for a Euler-Bernoulli flexural beam undergoing scaling from a micro to nanospatial regime. For the scaling lengths under consideration, the lowest resonator mode is in the frequency range of 1\char21{}10 GHz. In this range, it is found that the beam thermal environment routinely exceeds the limits of validity for the local temperature approximation; this is due to sharp inhomogeneities in strain pattern across the thin beam cross sections induced by flexural motion as opposed to the often assumed temporal dynamics of high frequency operation. In a Euler-Bernoulli-Boltzmann framework, an analysis of the internal phonon flow in the flexural beam is conducted, and dissipative losses are evaluated. The complexity of the microscopic phonon dynamics is delineated and strategically graphed in terms of the parameters characterizing the flexural beam and the phonon system therein. In limiting cases, two major intrinsic dissipative mechanisms are operative, one due to the diffusive spatial redistribution of phonons resulting in heat transfer and thermoelastic loss, and the other due to thermalization of the local phonon population distorted by strain resulting in the manifestation of the Akhiezer effect. In the frequency domain of interest, these two loss mechanisms lose their distinctive character with decreased spatial scaling and transition to a unified dissipative process governed by the ballistic phonon transfer across the beam.}, number={20}, journal={PHYSICAL REVIEW B}, author={Kiselev, A. A. and Iafrate, G. J.}, year={2008}, month={May} }
 @article{semenov_kim_iafrate_2007, title={Electron spin relaxation in semiconducting carbon nanotubes: The role of hyperfine interaction}, volume={75}, ISSN={1098-0121 1550-235X}, url={http://dx.doi.org/10.1103/PhysRevB.75.045429}, DOI={10.1103/physrevb.75.045429}, abstractNote={A theory of electron spin relaxation in semiconducting carbon nanotubes is developed based on the hyperfine interaction with disordered nuclei spins $I=1∕2$ of $^{13}\mathrm{C}$ isotopes. It is shown that strong radial confinement of electrons enhances the electron-nuclear overlap and subsequently electron spin relaxation (via the hyperfine interaction) in the carbon nanotubes. The analysis also reveals an unusual temperature dependence of longitudinal (spin-flip) and transversal (dephasing) relaxation times: the relaxation becomes weaker with the increasing temperature as a consequence of the particularities in the electron density of states inherent in one-dimensional structures. Numerical estimations indicate relatively high efficiency of this relaxation mechanism compared to the similar processes in bulk diamond. However, the anticipated spin relaxation time of the order of $1\phantom{\rule{0.3em}{0ex}}\mathrm{s}$ in carbon nanotubes is still much longer than those found in conventional semiconductor structures. Moreover, it is found that the curvature effect and subsequent rehybridization of $s$ and $p$ orbitals in ultrathin nanotubes may significantly impact the electron spin relaxation leading to its further suppression at certain dimensions.}, number={4}, journal={Physical Review B}, publisher={American Physical Society (APS)}, author={Semenov, Y. G. and Kim, K. W. and Iafrate, G. J.}, year={2007}, month={Jan} }
 @article{sokolov_iafrate_krieger_2007, title={Microcavity enhancement of spontaneous emission for Bloch oscillations}, volume={75}, ISSN={["1098-0121"]}, DOI={10.1103/physrevb.75.045330}, abstractNote={A theory for the spontaneous emission of a Bloch electron traversing a single energy miniband of a superlattice while accelerating under the influence of a constant external electric field and radiating into a microcavity is presented. In the analysis, the quantum electromagnetic radiation field is described by the dominant microcavity ${\mathrm{TE}}_{10}$ rectangular waveguide mode in the Coulomb gauge, and the instantaneous eigenstates of the Bloch Hamiltonian are utilized as the basis states in describing the Bloch electron dynamics to all orders in the constant external electric field. The results show that the spontaneous emission amplitude, when analyzed over many integral multiple values of the Bloch period, gives rise to selection rules for photon emission in both frequency and wave number with preferred transitions at the Wannier-Stark ladder levels. From these selection rules, the total spontaneous emission probability is derived to first-order perturbation theory in the quantized radiation field. It is shown that the power radiated into the dominant ${\mathrm{TE}}_{10}$ waveguide mode can be enhanced by an order of magnitude over the free-space value by tuning the Bloch frequency to align with the waveguide spectral density peak. A general expression for the total spontaneous emission probability is obtained in terms of arbitrary superlattice single band parameters, showing multiharmonic behavior and cavity tuning properties. For $\mathrm{GaAs}$-based superlattices, described in the nearest-neighbor tight-binding approximation, the power radiated into the waveguide from spontaneous emission due to Bloch oscillations in the terahertz frequency range is estimated to be several microwatts.}, number={4}, journal={PHYSICAL REVIEW B}, author={Sokolov, V. N. and Iafrate, G. J. and Krieger, J. B.}, year={2007}, month={Jan} }
 @article{sokolov_zhou_iafrate_krieger_2006, title={Spontaneous emission of Bloch oscillation radiation from a single energy band}, volume={73}, ISSN={["2469-9969"]}, DOI={10.1103/physrevb.73.205304}, abstractNote={Abstract : In this study, we explored the possibility of enhanced spontaneous emission of radiation beyond the free space value by analyzing a superlattice structure placed in a microcavity whose resonant modes were tuned to the Bloch frequency. In particular, we considered the spontaneous emission of Bloch radiation into the rectangular waveguide dominant mode. In the analysis, the quantum radiation field was described by the waveguide quantized electromagnetic field in the Coulomb gauge, and the instantaneous eigenstates of the Bloch Hamiltonian were used as basis states to analyze the Bloch dynamics to all orders in the constant external electric field. The results predict that the spontaneous emission occurs with frequencies equal to integral mutltiples of the Bloch frequency without any ad hoc assumptions made concerning the existence of Wannier-Stark ladder levels; such quantization effects arise from a natural consequence of the implicit quantum selection rules.}, number={20}, journal={PHYSICAL REVIEW B}, author={Sokolov, V. N. and Zhou, L. and Iafrate, G. J. and Krieger, J. B.}, year={2006}, month={May} }
 @article{krieger_kiselev_iafrate_2005, title={Quantum transport for a Bloch electron quasiparticle in an inhomogeneous electric field scattering from a random distribution of impurities: A Wigner approach}, volume={72}, ISSN={["2469-9969"]}, DOI={10.1103/physrevb.72.195201}, abstractNote={The quantum transport equation is derived in terms of the Wigner distribution function for a Bloch electron quasiparticle, that is, a Bloch electron in a single band, interacting with a random, inhomogeneous distribution of impurities, and subject to general homogeneous and inhomogeneous electric fields. The time dependent homogeneous electric field is described through the vector potential gauge. The derivation of the transport equation makes use of a unitary transformation of the Liouville equation based on the interaction picture to a form in which the scattering interaction appears quadratically, and utilizes accelerated Bloch states as basis states; the resulting generalized drift and diffusion terms are obtained exactly for an arbitrary band structure. In taking the limit of slowly varying inhomogeneous electric field and slowly varying scatterer density distribution, a quantum generalization of the Boltzmann-like Wigner transport equation is obtained which includes impurity-related intracollisional field effects in the collision term and a drift term comprising the total force due to both the homogeneous and inhomogeneous fields.}, number={19}, journal={PHYSICAL REVIEW B}, author={Krieger, JB and Kiselev, AA and Iafrate, GJ}, year={2005}, month={Nov} }
 @article{kim_iafrate_2004, title={Entanglement in the interaction between two quantum oscillator systems}, volume={17}, ISSN={["0894-9875"]}, DOI={10.1007/s10702-004-0902-9}, abstractNote={The fundamental quantum dynamics of two interacting oscillator systems are studied in two different scenarios. In one case, both oscillators are assumed to be linear, whereas in the second case, one oscillator is linear and the other is a non-linear, angular-momentum oscillator; the second case is, of course, more complex in terms of energy transfer and dynamics. These two scenarios have been the subject of much interest over the years, especially in developing an understanding of modern concepts in quantum optics and quantum electronics. In this work, however, these two scenarios are utilized to consider and discuss the salient features of quantum behaviors resulting from the interactive nature of the two oscillators, i.e., coherence, entanglement, spontaneous emission, etc., and to apply a measure of entanglement in analyzing the nature of the interacting systems. The Heisenberg equation for both coupled oscillator scenarios are developed in terms of the relevant reduced kinematics operator variables and parameterized commutator relations. For the second scenario, by setting the relevant commutator relations to one or zero, respectively, the Heisenberg equations are able to describe the full quantum or classical motion of the interaction system, thus allowing us to discern the differences between the fully quantum and fully classical dynamical picture. For the coupled linear and angular-momentum oscillator system in the fully quantum-mechanical description, we consider special examples of two, three, four-level angular momentum systems, demonstrating the explicit appearances of entanglement. We also show that this entanglement persists even as the coupled angular momentum oscillator is taken to the limit of a large number of levels, a limit which would go over to the classical picture for an uncoupled angular momentum oscillator.}, number={6}, journal={FOUNDATIONS OF PHYSICS LETTERS}, author={Kim, I and Iafrate, GJ}, year={2004}, month={Nov}, pages={507–534} }
 @article{belenky_dutta_b. gorfinkel_haddad_iafrate_kim_kisin_luryi_stroscio_sun_et al._1999, title={Tailoring of optical phonon modes in nanoscale semiconductor structures: role of interface-optical phonons in quantum-well lasers}, volume={263-264}, ISSN={0921-4526}, url={http://dx.doi.org/10.1016/S0921-4526(98)01410-0}, DOI={10.1016/S0921-4526(98)01410-0}, abstractNote={This paper discusses the concept of enhancing semiconductor laser performance through tailoring of scattering rates of confined polar-optical phonons. Studies of optically pumped intersubband scattering in coupled quantum-well lasers have demonstrated that interface-phonon-assisted transitions are important in such structures; furthermore, simple analytical expressions have been derived that indicate the importance of interface-phonon scattering in quantum-well lasers. These calculations reveal that the interface-phonon-assisted transitions are dominant for small quantum well dimensions of approximately 40 Å; such dimensions are typical of novel lasers including both the unipolar quantum cascade laser and the tunneling injection laser. Recent numerical calculations have confirmed these effects and have extended them to indicate how confined and interface phonons also affect critical laser properties such as optical gain. The application of confined phonon effects to intersubband lasers is one of the most important applications of confined-phonon physics to the present time.}, journal={Physica B: Condensed Matter}, publisher={Elsevier BV}, author={Belenky, Gregory and Dutta, Mitra and B. Gorfinkel, Vera and Haddad, George I. and Iafrate, G.J. and Kim, K.W. and Kisin, Mikhail and Luryi, Serge and Stroscio, Michael A. and Sun, J.P. and et al.}, year={1999}, month={Mar}, pages={462–465} }
 @misc{iafrate_he_dutta_stroscio_1998, title={Field controlled current modulators based on tunable barrier strengths}, volume={5705824}, publisher={Washington, DC: U.S. Patent and Trademark Office}, author={Iafrate, G. J. and He, J. and Dutta, M. and Stroscio, M. A.}, year={1998} }
 @article{yu_kim_stroscio_iafrate_sun_haddad_1997, title={Transfer matrix method for interface optical-phonon modes in multiple-interface heterostructure systems}, volume={82}, ISSN={0021-8979 1089-7550}, url={http://dx.doi.org/10.1063/1.365649}, DOI={10.1063/1.365649}, abstractNote={Interactions of carriers with interface optical phonons dominate over other carrier–phonon scatterings in narrow quantum-well structures. Herein, a transfer matrix method is used to establish a formalism for determining the dispersion relations, electrostatic potentials, and Fröhlich interaction Hamiltonians of the interface optical phonons for multiple-interface heterostructure systems within the framework of the macroscopic dielectric continuum model. This method facilitates systematic calculations for complex structures where the conventional method is very difficult to implement. Several specific cases are treated to illustrate the advantages of the general formalism.}, number={7}, journal={Journal of Applied Physics}, publisher={AIP Publishing}, author={Yu, SeGi and Kim, K. W. and Stroscio, Michael A. and Iafrate, G. J. and Sun, J.-P. and Haddad, G. I.}, year={1997}, month={Oct}, pages={3363–3367} }