Electron-optical Phonon Interaction Research Articles

HfSe2: Unraveling the microscopic reason for experimental low mobility.

Monolayer HfSe2, in the family of transition metal dichalcogenides (TMDCs), is a potential thermoelectric candidate due to its low thermal conductivity. While its mobility remains low as in other 2D TMDCs is inconceivable for electronic and thermoelectric applications. Earlier theoretical attempts have failed to give justification for the orders of low experimental mobility obtained for monolayer HfSe2. We calculate the carrier mobility in the framework of the density functional perturbation theory in conjunction with the Boltzmann transport equation and correctly ascertain the experimental value. We also calculate the carrier mobility with the previously employed method, the deformation potential (DP) model, to figure out the reason for its failure. We found that it is the strong electron-optical phonon interaction that is causing the low mobility. As the DP model does not account for the optical phonons, it overestimates the relaxation time by an order of two and also underestimates the temperature dependence of mobility. A strong polar type interaction is evidenced as a manifestation of a discontinuity in the first derivative of the optical-phonons at the K and Γ points as well as a dispersive optical phonon at the K point. We also included the spin-orbit coupling which leads to an energy splitting of ∼330meV and significantly affects mobility and scattering rates.

Magneto-transport properties of monolayer borophene in perpendicular magnetic field: influence of electron-phonon interaction

The magneto-transport properties of a borophene monolayer in a perpendicular magnetic field B are studied via calculating the conductivity tensor and resistance under electron-optical phonon interaction by using the linear response theory. Numerical results are obtained and discussed for some specific parameters. The magnetic field-dependent longitudinal conductivity shows the magneto-phonon resonance effect that describes the transition of electrons between Landau levels by absorbing/emitting an optical phonon. The Hall conductivity increases first and then decreases with the magnetic field strength. Also, the longitudinal resistance increases significantly with increasing temperature, which shows the metal behaviour of the material. Practically, the observed magneto-phonon resonance can be applied to experimentally determine some material parameters, such as the distance between Landau levels and the optical phonon energy.

The effect of hydrostatic pressure on binding energy and polaron effect of bound polaron in wurtzite AlyGa1−yN/AlxGa1−xN parabolic quantum well

The effect of hydrostatic pressure on binding energy and polaron effect of the bound polaron in a wurtzite Al[Formula: see text]Ga[Formula: see text]N/Al[Formula: see text]Ga[Formula: see text]N parabolic quantum well (QW) is studied using the Lee–Low–Pines intermediate coupling variational method in the paper. The numerical relationship of binding energy and polaron effect of the bound polaron are given as a functions of pressure [Formula: see text], composition [Formula: see text] and well width [Formula: see text]. In the theoretical calculations, the anisotropy of the electron effective band mass, the optical phonon frequency, the dielectric constant and other parameters in the system varying with the pressure [Formula: see text] and the coordinate [Formula: see text] are included. The electron–optical phonon interaction and the impurity center–optical phonon interaction are considered. The results show that hydrostatic pressure has a very obvious effect on binding energy and polaron effect of the bound polaron in the wurtzite Al[Formula: see text]Ga[Formula: see text]N/Al[Formula: see text]Ga[Formula: see text]N parabolic QW. For QWs with determined structural parameters, the contributions of the three branch of phonons, i.e., the confined (CF) phonon, half-space (HS) phonon and the interface (IF) phonon, to binding energy of the polaron increase with the increase of the pressure [Formula: see text], the CF phonons contribute the most. Under the condition of a certain well width and hydrostatic pressure, with the increase of the composition [Formula: see text], the ground state binding energy of the bound polaron in the wurtzite Al[Formula: see text]Ga[Formula: see text]N/Al[Formula: see text]Ga[Formula: see text]N parabolic QW increases, and the contribution of the IF phonon and HS phonons to the binding energy decreases, while the contribution of the CF phonons and the total contribution of all phonons increase significantly. In the wurtzite Al[Formula: see text]Ga[Formula: see text]N/Al[Formula: see text]Ga[Formula: see text]N parabolic QW, the ground state binding energy of the bound polaron decreases with the increase of the well width. The decrease rate is greater in the narrow well, and smaller in the wide well. The contribution of different branches of phonons to binding energy varies with the change of the well width. With the increase of the well width, the contribution of CF phonons to binding energy increases, the contribution of HS phonons to binding energy decreases, and the IF phonon contribution and the total phonon contribution first increase to the maximum value and then gradually decrease slightly. The changing trend of binding energy of bound polaron in the wurtzite Al[Formula: see text]Ga[Formula: see text]N/Al[Formula: see text]Ga[Formula: see text]N parabolic QW, of the contribution of different branch phonons to binding energy with the pressure [Formula: see text], composition [Formula: see text] and well width [Formula: see text] is similar to that of the GaN/Al[Formula: see text]Ga[Formula: see text]N square QW, but the change in the parabolic QW is more obvious.

Electron-phonon coupling in n -type Ge two-dimensional systems

Electron-optical phonon interaction is the dominant energy-loss mechanism in low-dimensional Ge/SiGe heterostructures and represents a key parameter for the design and realization of electronic and optoelectronic devices based on this material system compatible with the mainstream Si complementary metal-oxide semiconductor technology. Here we investigate the intersubband relaxation dynamics of $n$-type Ge/SiGe multiquantum wells with different symmetry and design by means of single-color pump-probe spectroscopy. By comparing the experimental differential transmittance data as a function of the pump-probe delay with numerical calculations based on an energy-balance rate-equation model, we could quantify an effective value for the optical phonon deformation potential describing the electron-phonon coupling in two-dimensional Ge-based systems. We found nonradiative relaxation times longer than 20 ps even in samples having intersubband energy separations larger than the optical phonon energy, evidencing the presence of a less effective electron-phonon coupling with respect to that estimated in bulk Ge.

Study of the Quantum Magneto-Thermoelectric Effect in the Two-Dimensional Compositional Superlattice GaAs/AlGaAs under the influence of an Electromagnetic Wave by Using the Quantum Kinetic Equation

The quantum magneto-thermoelectric effect in a two-dimensional compositional superlattice under the influence of an electromagnetic wave (EMW) in two cases is investigated. Two cases of the electron scattering mechanism are considered: the electron-acoustic phonon scattering and electron-optical phonon scattering. Analytical expressions for the quantum Ettingshausen coefficient (EC), the thermopower tensor, the thermoelectric tensor and the kinetic tensor are obtained by using a quantum kinetic equation. These expressions are numerically solved for the two-dimensional compositional superlattice GaAs/AlGaAs and the results are discussed. The results show that in the case of electron-acoustic phonon scattering, the Shubnikov-de Haas oscillations appear when we examine the dependences of the quantum EC, the thermopower tensor and the thermoelectric tensor on the magnetic field. In the case of electron-optical phonon scattering, resonance peaks that satisfy the condition of the inter-subband magneto-phonon resonance appear. In the two cases, the superlattice period (a parameter specific to the material) strongly affects the quantum magneto-thermoelectric effect. When the superlattice period is small, quantum EC oscillations (in the case of electron-acoustic phonon interaction) and quantum EC resonance peaks (in the case of electron-optical phonon interaction) appear. However, when the superlattice period is large, these oscillations and resonance peaks are not observed. Especially, the influence of electromagnetic waves on the quantum magneto-thermoelectric effect is also clarified. The quantum theory of the magneto-thermoelectric effect has been studied from low temperature to high temperature. This overcomes the limitations of the Boltzmann kinetic equation which was studied at high temperature. The results are new and can serve as a basis for further development of the theory of quantum magneto-thermoelectric effects in low-dimensional semiconductor systems.

Influence of Pressure on Polaron Energy in a Wurtzite GaN/Al<sub>x</sub>Ga<sub>1-x</sub>N Quantum Well

The influence of hydrostatic pressure on the polaron energy level in wurtzite GaN/AlxGa1-xN quantum well is studied by a Lee-Low-Pines variational method, and the numerical results of the ground state energy, transition energy and contributions of different phonons to polaron energy (polaron effects) are given as functions of pressure p and composition x. The results show that the ground state energy and transition energy in the wurtzite GaN/AlxGa1-xN quantum well decrease with the increase of the hydrostatic pressure p, and increase with the increase of the composition x. The contributions of different phonons to polaron energy with pressure p and composition x are obviously different. With the increase of hydrostatic pressure, the contribution of half-space phonon, confined phonon and the total contribution of phonons of all branches increases obviously, while the contribution of interface phonon slowly increases. During the increase of the composition, the contribution of interface phonon decreases and the contribution of half-space phonon increases slowly, while the contribution of confined phonon and the total contribution of phonons increases significantly. In general, the electron-optical phonon interaction play an important role in electronic states of GaN/AlxGa1-xN quantum wells and can not be neglected.

Investigation of cyclotron-phonon resonance in monolayer molybdenum disulfide

Transition-metal dichalcogenide monolayers recently have attracted much attention motivated by their exotic physical properties. In this paper, we theoretically investigate the optical absorption in the monolayer MoS2 which is subjected to a uniform static magnetic field and an electromagnetic wave. The magneto-optical absorption power (MOAP) is calculated using the projection operator technique in the linear response scheme, taking account of the electron–optical phonon interaction at high temperature. Both phonon emission and phonon absorption processes are included. The cyclotron–phonon resonance (CPR) is observed in the photon energy dependence of the MOAP. Numerical analyses show that the photon energy satisfying CPR condition depends linearly on the strength of magnetic field, which is similar to that in conventional low-dimensional semiconductors but different from that in graphene. The increase of the full width at half maximum (FWHM) of CPR peaks with increasing magnetic field shows a similar behaviour to that in graphene. In addition, FWHM increases slightly with temperature, which is different from that in graphene where the FWHM is temperature independent. Our investigation provides basic information about the magneto-optical properties of the monolayer MoS2 that are useful for further experiments and applications.

Electronic Structure of FeSe Monolayer Superconductors: Shallow Bands and Correlations

Electronic spectra of typical single FeSe layer superconductors obtained from ARPES data reveal several puzzles: what is the origin of shallow and the so called "replica" bands near M-point and why the hole-like Fermi surfaces near $\Gamma$-point are absent. Our extensive LDA+DMFT calculations show that correlation effects on Fe-3d states can almost quantitatively reproduce rather complicated band structure, which is observed in ARPES, in close vicinity of the Fermi level for FeSe/STO and K$_x$Fe$_{2-y}$Se$_{2}$. Rather unusual shallow electron-like bands around the M(X)-point in the Brillouin zone are well reproduced. However, in FeSe/STO correlation effects are apparently insufficient to eliminate the hole-like Fermi surfaces around the $\Gamma$-point, which are not observed in most ARPES experiments. Detailed analysis of the theoretical and experimental quasiparticle bands with respect to their origin and orbital composition is performed. It is shown that for FeSe/STO system the LDA calculated Fe-3d$_{xy}$ band, renormalized by electronic correlations within DMFT gives the quasiparticle band almost exactly in the energy region of the experimentally observed "replica" quasiparticle band at the M-point. For the case of K$_x$Fe$_{2-y}$Se$_{2}$ most bands observed in ARPES can also be understood as correlation renormalized Fe-3d LDA calculated bands, with overall semi-quantitative agreement with our LDA+DMFT calculations. Thus the shallow bands near the M-point are common feature for FeSe-based systems, not just FeSe/STO. We also present some simple estimates of "forward scattering" electron-optical phonon interaction at FeSe/STO interface, showing that it is apparently irrelevant for the formation of "replica" band in this system and significant increase of superconducting $T_c$.

Impurity-Bound Polaronic States in ZnSe Quantum Dots Under Electric Field: Image Charge Effect

A Landau–Pekar variational approach is used to study the ground and first excited states of an impurity-bound polaron in a ZnSe quantum dot under an external electric field, by taking into account the image charge effect (ICE). The binding energy (BE) of the donor impurity is calculated considering the interaction of an electron with both the bulk-type longitudinal optical phonons and the interface optical phonons. Both electric field and parabolic confinement effects on the BE and its polaronic shift for 1s and 2s hydrogen-like states with and without ICE are investigated in detail. We have shown that the ICE strongly reduces the donor BEs in both ignoring and considering electron–optical phonon interaction.

Magneto-optical absorption and cyclotron–phonon resonance in graphene monolayer

The optical absorption power by Dirac fermions in a graphene monolayer subjected to a perpendicular magnetic field is calculated using a projection operator technique. The electron–optical phonon interaction with optical deformation potential is taken into account. By varying the photon frequency (energy), we observe in the absorption power a series of cyclotron–phonon resonance (CPR) peaks (i.e., the phonon-assisted cyclotron resonance). It is seen that the resonant photon energy is linearly proportional to the square root of the magnetic field. Also, the half width at half maximum (HWHM) of CPR peaks depends on the magnetic field by the law HWHM = 7.42B but does not depend on the temperature. In particular, the magnetic field and temperature dependences of the position and HWHM of CPR peaks are in good agreement with those obtained recently by the perturbation theory and an experiment in graphene.

Free polaron energy levels in AlyGa1−yN/AlxGa1−xN triangle quantum well structures

In this work, a variational method is used to examine the problems relevant to the free polaron energy spectrum in a wurtzite Al[Formula: see text]Ga[Formula: see text]N/Al[Formula: see text]Ga[Formula: see text]N triangle quantum well structure. The numerical calculations for the ground state energy, transition energy and polaron energy shifts as the functions of well-width [Formula: see text] and composition [Formula: see text] are carried out by considering the anisotropies of the parameters, such as the optical phonon frequency, dielectric constant and electron effective mass, as well as their observed changes with coordinate [Formula: see text] in this system. The research results show that the polaron energy shift caused by the electron–optical phonon interaction is large, and leads to an obvious energy decrease in the Al[Formula: see text]Ga[Formula: see text]N/Al[Formula: see text]Ga[Formula: see text]N triangular quantum well structure. The contribution of the confined phonon is found to increase with the increasing of the well-width and composition [Formula: see text], while that of the half space phonon is observed to decrease with the increasing of the well-width and composition [Formula: see text]. The total contribution of the phonon increases with the increasing composition [Formula: see text], while a minimum is found to occur to the total contribution of the phonon during the decreasing process with the well-width. As the [Formula: see text] increases, the free polaron energies and transition energies decrease. Meanwhile, with the increasing of the composition [Formula: see text], the energy and transition energy are found to be increased. In the Al[Formula: see text]Ga[Formula: see text]N/Al[Formula: see text]Ga[Formula: see text]N triangular quantum well structure, the trends of the free polaron energy, transition energy and polaron energy shifts with the well-width and composition [Formula: see text] are found to be similar to those in the GaN/Al[Formula: see text]Ga[Formula: see text]N square quantum well structure. However, the corresponding values in the triangular quantum well structure are obviously greater than those in the square quantum well structure.

Electrical transport properties of nickel chromium alloy films

The effect of the electron–phonon interactions on the electrical transport properties of NiCr alloy films is studied. The resistivity of the NiCr films is measured between 2 and 300 K, and reveals an overall metallic conduction behavior. The resistivity–temperature curves of NiCr films are successfully interpreted using the traditional electron–phonon coupling theory. The results reveal that the electrons coupling with the acoustic-mode phonons dominate the electrical properties of NiCr films over the entire temperature range investigated, and weak corrections by the electron–optical–phonon interactions are present in the high temperature regime. The dominance of the electron–phonon interactions on the transport behavior of NiCr films is further confirmed by the magnetotransport analysis. The electron–phonon interaction constant of NiCr films is also discussed.

The Ettingshausen coefficient in quantum wells under influence of laser radiation in the case of electron-optical phonon interaction

The Ettingshausen coefficient in quantum wells under influence of laser radiation in the case of electron-optical phonon interaction

The influence of built-in electric field on binding energy of bound polaron and polaron effects in wurtzite ZnO/MgxZn1−xO quantum well

The influence of the built-in electric field on the binding energy of a bound polaron and the polaron effect in a wurtzite ZnO/MgxZn1−xO quantum well are studied using the improved Lee-Low-Pines intermediate coupling method. The ground-state binding energy, the contributions from different branches of optical phonons to the energy and the binding energy are presented as the functions of well width, impurity position and composition. In the numerical calculations, the anisotropic properties of the frequencies of the different branches of optical phonons, electron effective mass, dielectric constant, the electron-optical phonon interaction and the impurity center-optical phonon interaction are considered. The results show that the built-in electric field has obvious influence on the energy, the binding energy and the polaron effect, and it affects the contributions of different phonon modes to the energy and the binding energy with different degrees. The built-in electric field significantly increases the total phonon contribution to the energy, but it reduces the total phonon contribution to the binding energy. The binding energy of the bound polaron with the built-in electric field is less than that without the built-in electric field, and it declines rapidly with increasing well width. Because of the built-in electric field effects, the contributions from different branches of phonons to the energy and the binding energy and the functions of binding energy with well width and impurity center position are different from the cases without the built-in electric field. The built-in electric field in the wurtzite ZnO/MgxZn1−xO quantum wells has a great impact on the binding energy and polaron effect, and the polaron effect in the wurtzite ZnO/MgxZn1−xO quantum wells is significantly greater than that in the zinc blende GaAs/AlxGa1−xAs QWs, hence, it is necessary to discuss the built-in electric field and polaron effect when considering the problem of electronic state in such systems.

Influence of spin–orbit interactions on the polaron properties in wurtzite semiconductor quantum well

We have study the simultaneous effect of Rashba and Dresselhaus spin–orbit interactions on the polaron properties in wurtzite semiconductor quantum wells. The linear and cubic contributions of the bulk Dresselhaus spin–orbit coupling and the effects of phonon confinement on electron–optical-phonon interaction Hamiltonians are taken into account. We have found analytical solutions for the polaron energies as well as polaron effective mass within the range of validity of perturbation theory. It is shown that the polaron energy and effective mass correction are both significantly enhanced by the spin–orbit coupling. Wave number dependent phonon contribution on the electron energy has minima and varies differently of the spin-up and spin-down states. Polaron self-energy due to interface optical phonon modes has larger values than of the confined optical phonon modes ones. The polaron effective mass exhibits anisotropy and the contribution of the Dresselhaus spin–orbit coupling term on the polaron effective mass is dominated by Rashba one.

Electron–phonon interaction in quasi-1D ternary mixed crystals of polar semiconductors

The electron–optical-phonon interaction between an electron and two branches of LO-phonon modes in a quasi-one-dimensional ternary mixed crystal (TMC) of polar semiconductors is studied. The new electron–phonon interaction Hamiltonian including the unit-cell volume variation in TMCs is obtained by using the modified random element isodisplacement model and Born–Huang method. The energies of polaron are numerically calculated for several systems of III–V compounds. A group of III-nitride mixed crystals is also taken into numerical calculation in our theory. It is verified theoretically that the obvious nonlinearity of the polaronic energy and effective mass with the composition is essential and the unit-cell volume effects cannot be neglected except the very weak e–p coupling.

Effects of electron–optical phonon interactions on the polaron energy in a wurtzite ZnO/MgxZn1−xO quantum well**Project supported by the National Natural Science Foundation of China (Grant Nos. 11264027 and 11364030), the Project of Prairie Excellent Specialist of Inner Mongolia, China, and the “Thousand, Hundred and Ten” Talent Training Project Foundation of Inner Mongolia Normal University, China (Grant No. RCPY-2-2012-K-039).

We investigated the properties of polarons in a wurtzite ZnO/MgxZn1−xO quantum well by adopting a modified Lee–Low–Pines variational method, giving the ground state energy, transition energy, and phonon contributions from various optical-phonon modes to the ground state energy as functions of the well width and Mg composition. In our calculations, we considered the effects of confined optical phonon modes, interface-optical phonon modes, and half-space phonon modes, as well as the anisotropy of the electron effective band mass, phonon frequency, and dielectric constant. Our numerical results indicate that the electron–optical phonon interactions importantly affect the polaronic energies in the ZnO/MgxZn1−xO quantum well. The electron–optical phonon interactions decrease the polaron energies. For quantum wells with narrower wells, the interface optical phonon and half-space phonon modes contribute more to the polaronic energies than the confined phonon modes. However, for wider quantum wells, the total contribution to the polaronic energy mainly comes from the confined modes. The contributions of the various phonon modes to the transition energy change differently with increasing well width. The contribution of the half-space phonons decreases slowly as the QW width increases, whereas the contributions of the confined and interface phonons reach a maximum at d ≈ 5.0 nm and then decrease slowly. However, the total contribution of phonon modes to the transition energy is negative and increases gradually with the QW width of d. As the composition x increases, the total contribution of phonons to the ground state energies increases slowly, but the total contributions of phonons to the transition energies decrease gradually. We analyze the physical reasons for these behaviors in detail.

The effects of optical phonon on the binding energy of bound polaron in a wurtzite ZnO/MgxZn1−xO quantum well

An improved Lee-Low-Pines intermediate coupling method is used to study the energies and binding energies of bound polarons in a wurtzite ZnO/MgxZn1−xO quantum well. The contributions from different branches of long-wave optical phonons, i.e., confined optical phonons, interface optical phonons, and half-space optical phonons are considered. In addition to electron-phonon interaction, the impurity-phonon interaction, and the anisotropy of material parameters, such as phonon frequency, electron effective mass, and dielectric constant, are also included in our computation. Ground-state energies, binding energies and detailed phonon contributions from various phonons as functions of well width, impurity position and composition are presented. Our result suggests that total phonon contribution to ground state and binding energies in the studied wurtzite ZnO/Mg0.3Zn0.7O quantum wells varies between 28–23 meV and 62–45 meV, respectively, which are much larger than the corresponding values (about 3.2–1.8 meV and 1.6–0.3 meV) in GaAs/Al0.3Ga0.7As quantum wells. For a narrower quantum well, the phonon contribution mainly comes from interface and half-space phonons, for a wider quantum well, most of phonon contribution originates from confined phonons. The contribution from all the phonon modes to binding energies increases slowly either when impurity moves far away from the well center in the z direction or with the increase in magnesium composition (x). It is found that different phonons have different influences on the binding energies of bound polarons. Furthermore, the phonon contributions to binding energies as functions of well width, impurity position, and composition are very different from one another. In general, the electron-optical phonon interaction and the impurity center-optical phonon interaction play an important role in electronic states of ZnO-based quantum wells and cannot be neglected.

Polaronic Effects in Wurtzite In<sub><i>x</i></sub>Ga<sub>1-<i>x</i></sub>N/GaN Parabolic Quantum Well

The energy levels of polaron in a wurtzite InxGa1-xN/GaN parabolic quantum well are investigated by adopting a modified Lee-Low-Pines variational method. The ground state energy, the transition energy and the contributions of different branches of optical phonon modes to the ground state energy as functions of the well width are given. The effects of the anisotropy of optical phonon modes and the spatial dependence effective mass, dielectric constant, phonon frequency on energy levels are considered in calculation. In order to compare, the corresponding results in zinc-blende parabolic quantum well are given. The results indicate that the contributions of the electron-optical phonon interaction to ground state energy of polaron in InxGa1-xN/GaN is very large, and make the energy of polaron reduces. For a narrower quantum well，the contributions of half-space optical phonon modes is large , while for a wider one, the contributions of the confined optical phonon modes are larger. The ground state energy and the transition energy of polaron in wurtzite InxGa1-xN/GaN are smaller than that of zinc-blende InxGa1-xN/GaN, and the contributions of the electron-optical phonon interaction to ground state energy of polaron in wurtzite InxGa1-xN/GaN are greater than that of zinc-blende InxGa1-xN/GaN. The contributions of the electron-optical phonon interaction to ground state energy of polaron in wurtzite InxGa1-xN/GaN (about from 22 to 32 meV) are greater than that of GaAs/AlxGa1-xAs parabolic quantum well (about from 1.8 to 3.2 meV). Therefore, the electron-optical phonon interaction should be considered for studying electron state in InxGa1-xN/GaN parabolic quantum well.

Possible formation of chiral polarons in graphene

A theoretical investigation of the possible existence of chiral polaron formation in graphene is reported. We present an analytical method to calculate the ground-state of the electron–phonon system within the framework of the Lee–Low–Pines theory. On the basis of our model, the influence of electron–optical phonon interaction on the graphene electronic spectrum is investigated. We considered only the doubly degenerate optical phonon modes of E2g symmetry near the zone center Γ. It is analytically shown that the energy dispersions of both valence and conduction bands of the pristine graphene differ significantly from those obtained through the standard electron self-energy calculations arising from the electron–optical phonon interactions. In this paper, we also show for the first time that the degenerate band structure of the graphene promotes the chiral polaron formation. Furthermore, due to the k-dependent nature of the polaronic self-energy, in analogy with quantum chromodynamics, we also propose a running electron–phonon coupling constant as a function of energy.