Influence of the Interaction Between Phonons and Coulomb Potential on the Properties of a Bound Polaron in a Quantum Dot

The properties of a bound polaron in a parabolic quantum dot with weak electron-LO-phonon coupling under a Coulomb field are studied. The ground state energy of the bound polaron is derived by using a linear combination operator and the perturbation method. The influence of the interaction between phonons with different wave vectors in the recoil process on the ground state energy of the bound polaron is discussed. Numerical calculations are performed,and the results show that the ground state energy increases significantly as the effective confinement length of the quantum dot decreases,considering of the interaction between phonons. When l0〉1.0, the influence of the interaction between phonons on the ground state energy cannot be ignored.

Effects of electron–optical phonon interactions on the polaron energy in a wurtzite ZnO/Mg_xZn_(1-x)O quantum well

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.

Properties of ground state and anomalous quantum fluctuations in one-dimensional polaron-soliton systems-the effects of electron-two-phonon interaction and non-adiabatic quantum correlations

Based on the Holstein model Hamiltonian of one-dimensional molecular crystals, by making use of the expansion approach of the correlated squeezed-coherent states of phonon instead of the two-phonon coherent state expansion scheme, the properties of the ground state and the anomalous quantum fluctuations are investigated in a strongly coupled electron-phonon system with special consideration of the electron-two-phonon interaction. The effective renormalization （ai） of the displacement of the squeezed phonons with the effect of the squeezed-coherent states of phonon and both the electron-displaced pbonon and the polaron-squeezed phonon correlations have been combined to obtain the anomalous quantum fluctuations for the corrections of the coherent state. Due to these non-adiabatic correlations, the effective displacement parameter ai is larger than the ordinary parameter ai （0） In comparison with the electron-one-phonon interaction （g） corrected as oig, we have found the electron-two-phonon interaction （gl） corrected as ai2gi is enhanced significantly. For this reason, the ground state energy （E（2）） contributed by the electron-two-phonon interaction is more negative than the single-phonon case （E01）） and the soliton solution is more stable. At the same time, the effects of the electron-two-phonon interaction greatly increase the polaron energy and the quantum fluctuations. Furthermore, in a deeper level, we have considered the effect of the polaron-squeezed phonon correlation （f-correlation）. Since this correlation parameter f 〉 1, this effect will strengthen the electron-one and two-phonon interactions by fai9 and f2ai2g1, respectively. The final results show that the ground state energy and the polaron energy will appear more negative further and the quantum fluctuations will gain further improvement.

The effect of interface hopping on inelastic scattering of oppositely charged polarons in polymers

The inelastic scattering of oppositely charge polarons in polymer heterojunctions is believed to be of fundamental importance for the light-emitting and transport properties of conjugated polymers. Based on the tight-binding SSH model, and by using a nonadiabatic molecular dynamic method, we investigate the effects of interface hopping on inelastic scattering of oppositely charged polarons in a polymer heterojunction. It is found that the scattering processes of the charge and lattice defect depend sensitively on the hopping integrals at the polymer/polymer interface when the interface potential barrier and applied electric field strength are constant. In particular, at an intermediate electric field, when the interface hopping integral of the polymer/polymer heterojunction material is increased beyond a critical value, two polarons can combine to become a lattice deformation in one of the two polymer chains, with the electron and the hole bound together, i.e., a self-trapped polaron-exciton. The yield of excitons then increases to a peak value. These results show that interface hopping is of fundamental importance and facilitates the formation of polaron-excitons.

On the possibility of self-trapping transition of acoustic polarons in two dimensions

A 2D electron-longitudinal-acoustic-phonon interaction Hamiltonian is derived and used to calculate the groundstate energy of the acoustic polarons in two dimensions. The numerical results for the ground-state energy of the acoustic polarons in two and three dimensions are obtained. The 3D results agree with those obtained by using the Feynman path-integral approach. It is found that the critical coupling constant of the transition from the quasifree state to the self-trapped state in the 2D case is much smaller than in the 3D case for a given cutoff wave-vector. The theory has been used to judge the possibility of the self-trapping for several real materials. The results indicate that the self-trappings of the electrons in AlN and the holes in AlN and GaN are expected to be observed in 2D systems.

Electron–acoustic phonon interaction and mobility in stressed rectangular silicon nanowires

We investigate the effects of pre-stress and surface tension on the electron–acoustic phonon scattering rate and the mobility of rectangular silicon nanowires. With the elastic theory and the interaction Hamiltonian for the deformation potential, which considers both the surface energy and the acoustoelastic effects, the phonon dispersion relation for a stressed nanowire under spatial confinement is derived. The subsequent analysis indicates that both surface tension and pre-stress can dramatically change the electron–acoustic phonon interaction. Under a negative（positive） surface tension and a tensile（compressive） pre-stress, the electron mobility is reduced（enhanced） due to the decrease（increase） of the phonon energy as well as the deformation-potential scattering rate. This study suggests an alternative approach based on the strain engineering to tune the speed and the drive current of low-dimensional electronic devices.

PERSISTENT CURRENT IN A ONE-DIMENSIONAL MESOSCOPIC RING WITH ELECTRON-PHONON INTERACTION IN THE LATTICE MODEL

A new non-perturbative method is used to discuss the persistent current in a one-dimensional mesoscopic ring threaded by a flux φ with electron-phonon interaction in the lattice model. The current is periodic in φ with a flux quantum φ 0 and the electron-phonon interaction suppresses the persistent current. By considering the contributions of many-phonon correlations, we could obtain more accurate results.

Tight-binding electron–phonon coupling and band renormalization in graphene

The kink structure in the quasiparticle spectrum of electrons in graphene observed at 200 me V below the Fermi level by angle-resolved photoemission spectroscopy（ARPES） was claimed to be caused by a tight-binding electron–phonon（e–ph） coupling in the previous theoretical studies. However, we numerically find that the e–ph coupling effect in this approach is too weak to account for the ARPES data. The former agreement between this approach and the ARPES data is due to an enlargement of the coupling constant by almost four times.

Oscillatory electron phonon coupling in Pb/Si（111）deduced by temperature-dependent quantum well states

Photoemission study of atomically flat Pb films with a thickness from 15 to 24 monolayers （ML） have been performed within a temperature range 75-270K. Well-defined quantum well states （QWSs） are observed, which exhibit interesting temperature-dependent behaviours. The peak position of the QWSs shifts towards higher binding energy with increasing substrate temperature, whereas the peak width broadens linearly due to enhanced electron-phonon coupling strength （λ）. An oscillatory A with a period of 2ML is deduced. Preliminary analysis shows that the oscillation can be explained in terms of the interface induced phase variations, and is thus a manifestation of the quantum size effects.

Phonon dichroism in proximitized graphene

We systematically investigate the phonon dichroism in proximitized graphene with broken time-reversal symmetry.We find that in the absence of any type of spin–orbit coupling,phonon dichroism vanishes.Linear and circular phonon dichroism occur in the presence of uniform(staggered)intrinsic spin–orbit coupling and ferromagnetic(antiferromagnetic)exchange coupling.All these situations can be distinguished by their specific behaviors of phonon absorption at the transition point.Our finding provides new possibilities to use phonon dichroism to identify the form of spin–orbit coupling and exchange coupling in proximitized graphene on various magnetic substrates.

Interaction between photons and electrons

By using a path-integral theory, the photoemission spectra of the electron-phonon (e-ph) coupled systems are calculated exactly. The spectral properties of the e-ph coupled systems based on the 1D and 2D Holstein models are systematically studied under various conditions. The electronic band structure is found to be greatly modified by the multiple scattering effect of electron with phonons, so as to produce a spectral evolution from broad Gaussian at band bottom to two-headed Lorentzian near the Fermi energy. This evolution reflects a transition of electronic states from localized incoherent one to the extended coherent one near the Fermi energy. The results qualitatively agree with recent experiments of high resolution ARPES on the Be (0001) surface and Bi2Sr2CaCu2O8.

Phonon-dependent transport through a serially coupled double quantum dot system

Using Keldysh nonequilibrium Green function formalism and mapping a many-body electron-phonon interaction onto a one body problem, the electron transport through a serially coupled double quantum dot system is analyzed. The influence of the electron-phonon interaction, temperature, detuning, and interdot tunneling on the transmission coefficient and current is studied. Our results show that the electron-phonon interaction results in the appearance of the side peaks in the transmission coefficient, whose height is strongly dependent on the phonon temperature. We have also found that the inequality of the electron-phonon interaction strength in two dots gives rise to an asymmetry in the current-voltage characteristic. In addition, the temperature difference between the phonon and electron subsystems results in the reduction of the saturated current and the destruction of the step-like behavior of the current. It is also observed that the detuning can improve the magnitude of the current by compensating the mismatch of the quantum dots energy levels induced by the electron-phonon interaction.

Electrically-driven ultrafast out-of-equilibrium light emission from hot electrons in suspended graphene/hBN heterostructures

Nanoscale light sources with high speed of electrical modulation and low energy consumption are key components for nanophotonics and optoelectronics.The record-high carrier mobility and ultrafast carrier dynamics of graphene make it promising as an atomically thin light emitter which can be further integrated into arbitrary platforms by van der Waals forces.However,due to the zero bandgap,graphene is difficult to emit light through the interband recombination of carriers like conventional semiconductors.Here,we demonstrate ultrafast thermal light emitters based on suspended graphene/hexagonal boron nitride(Gr/hBN)heterostructures.Electrons in biased graphene are significantly heated up to 2800 K at modest electric fields,emitting bright photons from the near-infrared to the visible spectral range.By eliminating the heat dissipation channel of the substrate,the radiation efficiency of the suspended Gr/hBN device is about two orders of magnitude greater than that of graphene devices supported on SiO2or hBN.Wefurther demonstrate that hot electrons and low-energy acoustic phonons in graphene are weakly coupled to each other and are not in full thermal equilibrium.Direct cooling ofhigh-temperature hot electrons to low-temperature acoustic phonons is enabled by the significant near-field heat transfer at the highly localized Gr/hBN interface,resulting in ultrafast thermal emission with up to 1 GHz bandwidth under electrical excitation.It is found thatsuspending the Gr/hBN heterostructures on the SiO2trenches significantly modifies the light emission due to the formation of the optical cavity and showed a~440%enhancement inintensity at the peak wavelength of 940 nm compared to the black-body thermal radiation.The demonstration of electrically driven ultrafast light emission from suspended Gr/hBNheterostructures sheds the light on applications of graphene heterostructures in photonicintegrated circuits,such as broadband light sources and ultrafast thermo-optic phase modulators.

Bound polaron in a strained wurtzite GaN/Al_xGa_(1-x)N cylindrical quantum dot

Within the effective-mass approximation,a variational method is adopted to investigate the polaron effect in a strained GaN/Al_xGa_（1-x）N cylindrical quantum dot.The electron couples with both branches of longitudinal optical-like（LO-like）and transverse optical-like（TO-like）phonons and the built-in electric field are taken into account.The numerical results show that the binding energy of the bound polaron is reduced obviously by the polaron effect on the impurity states.Furthermore,the contribution of LO-like phonons to the binding energy is dominant,and the anisotropic angle and Al content influence on the binding energy are small.

Reconstruction of electron-phonon interaction function from temperature dependence of electrical resistivity for metals

The determination of the electron phonon interaction function (EPIF) from the temperature dependence of the electrical resistivity (TDER) for metals within a selected moderate temperature range is numerically demonstrated based on the general theory of the amplitude phase retrieval problem and an iterative algorithm. From the model calculation, the convergent solution can be obtained; however,the profile of the recovered EPIF depends on the initial frequency distribution used in the algorithm since this inversion problem is inherently ill posed. In order to get reasonable result,it is necessary to introduce additional information about the feature of the EPIF for guiding the choice of the initial distribution. The algorithm can also furnish a robust reconstruction of EPIF from TDER contaminated with random noise. It means that this algorithm is relatively stable and insensitive to external perturbation; therefore in a sense, the presented algorithm overcomes the ill posedness of the inversion problem.

Anisotropic polarization due to electron-phonon interactions in graphene

Polarization plays an important role in the Raman spectroscopy. We study, in graphene, anisotropic polarization due to electron-phonon coupling （EPC）. The numerical results show that the anisotropy is obvious even when the wave vector is in the range of the Raman experiment. The analytical expression is deduced from the structure factor, which indicates the crucial origin of the anisotropy. We also find that, as the phonon energy increases the polarization is clearly weakened due to the screen effect of EPC, but the anisotropy totally remains.

Waveguide mechanism and design of thermal contact resistance at metal rheologic interface

The main factors and their varied disciplines affecting the heat transfer at the metal rheologic interface were studied from the waveguide mechanism of heat transfer of electrons and phonons, guiding the design of thermal contact resistance through studying the microscale mechanism of heat transfer at the interface. The results show that electron has stronger quantum tunneling effect when the thickness of oxide film is smaller than de Broglie wavelength of electron and the heat conduction of oxide film produces microscale effect. The thickness and nature of oxide film dominate the heat transfer at the metal rheologic interface. The main means to design the interface contact conductance are to control the formation of oxide film as well as the process of machining of roller surface and lubrication of interface.

Density Dependence of Electron Spin Relaxation Time in GaA

The electron density dependence of the electron spin relaxation time in a system of electrons interacting with phonons through phonon-modulated spin-orbit coupling was calculated using the formula for electron spin resonance derived by the projection-reduction method. The electron spin relaxation time in GaAs increased with increasing electron density, and the electron density was found to affect the electron spin relaxation differently according to temperature. The electron spin in GaAs was relaxed mainly by optical phonon scattering at high electron densities and piezoelectric phonon scattering at relatively low electron densities.

Properties of nonadiabatic quantum fluctuations of the strongly coupled electron-phonon systems

A new variational-ansatz of states of electrons and phonons was proposed on the basis of the Holstein model in strongly coupled electron-phonon systems for studying the influence of nonadiabatic phonon fluctuation,arising from the motion and density fluctuation of electrons,on the properties of ground state,uncertainty relation,stability of polarons,charge density wave (CDW) and phonon staggered ordering. The new ansatz represents the correlation among the displacement and squeezing states of phonons and polaron’s state of electrons as well as the squeezing-antisqueezing effect. The correlation and squeezing-antisqueezing ef-fect result in the decrease of ground state energy,enhancement of stability of the systems,increase of binding energy of the polarons,weakening of the growing speed of polaron narrowing of the electron band,increase of the charge density wave order and suppression of the increased tendency of anomalous quantum fluctuation of the phonons in such a case,when compared with the uncorrelated case in the systems. The results obtained show that the ground state determined by the new state ansatz is most stable,thus the new ansatz describing the properties of the coupled electron phonon systems is very relevant and available,especially in strongly coupled and largely squeezed cases.