Presence Of Phonons Research Articles

Mixed Quantum-Classical Dynamics under Arbitrary Unitary Basis Transformations.

A common approach to minimizing the cost of quantum computations is by unitarily transforming a quantum system into a basis that can be optimally truncated. Here, we derive classical equations of motion subjected to similar unitary transformations and propose their integration into mixed quantum-classical dynamics, allowing this class of methods to be applied within arbitrary bases for both the quantum and classical coordinates. To this end, canonical positions and momenta of the classical degrees of freedom are combined into a set of complex-valued coordinates amenable to unitary transformations. We demonstrate the potential of the resulting approach by means of surface hopping calculations of an electronic carrier scattering onto a single impurity in the presence of phonons. Appropriate basis transformations, capturing both the localization of the impurity and the delocalization of higher-energy excitations, are shown to faithfully capture the dynamics within a fraction of the classical and quantum basis sets.

Light absorption by free charge carriers in the presence of phonons in an anisotropic quantum wire

The absorption of light by free charge carriers has been theoretically studied considering the processes related to scattering from phonons in an anisotropic parabolic quantum wire. The case in which the electromagnetic wave is polarized along the axis of the wire and the case of non-degenerate electron gas statistics have been considered. In this work, it was determined that the dependence of the location of the peaks of the intraband optical absorption coefficient on the characteristic frequency of the confinement potential in quantum wires with asymmetric parabolic potential was .

Phonon-induced breakdown of Thouless pumping in the Rice-Mele-Holstein model

Adiabatic and periodic variation of the lattice parameters can make it possible to transport charge through a system even without net external electric or magnetic fields, known as Thouless charge pumping. The amount of charge pumped in a cycle is quantized and entirely determined by the system's topology, which is robust against perturbations such as disorder and interactions. However, coupling to the environment may play a vital role in topological transport in many-body systems. We study the topological Thouless pumping, where the charge carriers interact with local optical phonons. The semi-classical multi-trajectory Ehrenfest method is employed to treat the phonon trajectories classically and charge carriers quantum mechanically. We find a breakdown of the quantized charge transport in the presence of phonons. It happens for any finite electron-phonon coupling strength at the resonance condition when the pumping frequency matches the phonon frequency, and it takes finite phonon coupling strength away from the resonance. Moreover, there exist parameter regimes with non-quantized negative and positive charge transport. The modified effective pumping path due to electron-phonon coupling accurately explains the underlying physics. In the large coupling regime where the pumping disappears, the phonons are found to eliminate the staggering of the onsite potentials, which is necessary for the pumping protocol. Finally, we present a stability diagram of quantized pumping as a function of time period of pumping and phonon coupling strength.

Zero-point lattice expansion and band gap renormalization: Grüneisen approach versus free energy minimization

The zero-point lattice expansion (ZPLE) is a small variation of the lattice parameters induced by the presence of phonons in a material compared to the static lattice picture. It contributes significantly to the zero-point renormalization (ZPR) of the band gap energy, but its consequences have not been investigated as thoroughly as those stemming from electron-phonon interactions. In the usual first-principles approach, one evaluates the ZPLE by minimizing the $T=0$ K Helmholtz free energy. In this work, we show that the formalism based on the Gr\"uneisen parameters, which commonly neglects zero-point effects, can be efficiently used to compute the ZPLE for both isotropic and anisotropic materials at a much lower computational cost. We systematically test this formalism on 22 cubic and wurtzite materials, and we obtain excellent agreement with free energy minimization results for both the ZPLE and the resulting band gap ZPR. We use our results to validate an empirical expression estimating the ZPLE-induced ZPR, and we unveil its sensitivity to the temperature range involved in estimating the ZPLE from experimental data. Our findings finally reveal that the ZPLE contribution to the band gap ZPR can reach from 20% to more than 80% of the electron-phonon interaction contribution for heavier or more ionic materials, including materials containing light atoms. Considering both contributions on an equal footing is thus essential should one attempt to compare theoretical ZPR results with experimental data.

Dynamics of photosynthetic light harvesting systems interacting with N-photon Fock states.

We develop a method to simulate the excitonic dynamics of realistic photosynthetic light harvesting systems, including non-Markovian coupling to phonon degrees of freedom, under excitation by N-photon Fock state pulses. This method combines the input-output and the hierarchical equations of motion formalisms into a double hierarchy of density matrix equations. We show analytically that under weak field excitation relevant to natural photosynthesis conditions, an N-photon Fock state input and a corresponding coherent state input give rise to equal density matrices in the excited manifold. However, an N-photon Fock state input induces no off-diagonal coherence between the ground and excited subspaces, in contrast with the coherences created by a coherent state input. We derive expressions for the probability to absorb a single Fock state photon with or without the influence of phonons. For short pulses (or, equivalently, wide bandwidth pulses), we show that the absorption probability has a universal behavior that depends only upon a system-dependent effective energy spread parameter Δ and an exciton-light coupling constant Γ. This holds for a broad range of chromophore systems and for a variety of pulse shapes. We also analyze the absorption probability in the opposite long pulse (narrow bandwidth) regime. We then derive an expression for the long time emission rate in the presence of phonons and use it to study the difference between collective vs independent emission. Finally, we present a numerical simulation for the LHCII monomer (14-mer) system under single photon excitation that illustrates the use of the double hierarchy equations.

Synthesis, Neutron Diffraction, and DFT Studies of NaLa(WO4)2: Yb3+/Er3+; NIR Induced Green Fluorescent Bifunctional Probes for In Vitro Cell Imaging and Solid State Lighting

AbstractWe report the synthesis, systematic crystal structure, and upconversion (UC) emission in bulk and nanomaterials of NaLa(WO4)2: Yb3+/Er3+. The disordered NaLa(WO4)2 matrix has been considered as the UC host and host lattice dynamics were investigated using DFT, and neutron diffraction studies. The presence of phonons at the cut‐off frequency of ∼912 cm−1 is revealed by DFT analysis which is further confirmed by room temperature Raman studies. The optimized concentration of NaLa0.865Er0.035Yb0.1(WO4)2 is referred to as UCB and UCN with respect to particle size derived from a facile solvothermal method. Interestingly, high‐resolution microscopy studies uncovered the existence of high‐density edge dislocations in UCN nanomaterials leading to enhanced phonon scattering. Both UCB and UCN materials have shown pump power‐dependent intense UC green emission upon 980 nm laser irradiation. In addition, we have also demonstrated an excellent non‐toxicity of UCB and UCN towards Escherichia coli, Staphylococcus aureus, Candida albicans, and mammalian HeLa cell lines followed by the potential use of nanomaterials for in vitro cell imaging. Thus, the combined neutron diffraction, DFT, microscopy, and spectroscopic analysis collectively resulted in the right structure‐property relationship in these biocompatible UC green fluorescent bifunctional NaLa(WO4)2 materials.

Breathing modes of repulsive polarons in Bose–Bose mixtures

We consider impurity atoms embedded in a two-component Bose–Einstein condensate in a quasi-one dimensional regime. We study the effects of repulsive coupling between the impurities and Bose species on the equilibrium of the system for both miscible and immiscible mixtures by numerically solving the underlying coupled Gross–Pitaevskii equations. Our results reveal that the presence of impurities may lead to a miscible–immiscible phase transition due to the interaction of the impurities and the two condensates. Within the realm of the Bogoliubov–de Gennes equations we calculate the quantum fluctuations due to the different types of interactions. The breathing modes and the time evolution of harmonically trapped impurities in both homogeneous and inhomogeneous binary condensates are deeply discussed in the miscible case using variational and numerical means. We show in particular that the self-trapping, the miscibility and the inhomogeneity of the trapped Bose mixture may strongly modify the low-lying excitations and the dynamical properties of impurities. The presence of phonons in the homogeneous Bose mixture gives rise to the damping of breathing oscillations of impurities width.

Influence of a magnetic field on Rashba spin–orbit interaction in an anisotropic quantum dot

The influence of a magnetic field on the Rashba spin–orbit interaction in an anisotropic quantum dot is theoretically studied, and the expression of the ground state energy of a magnetopolaron is obtained with the Pekar variational method. The ground state energy of the magnetopolaron splits into two branches due to the Rashba effect, and the splitting appears saturated phenomenon with increasing the transverse and longitudinal effective confinement lengths. Because the contribution of the magnetic field cyclotron resonance frequency to the Rashba spin–orbit splitting is a positive value, the energy spacing becomes larger as the magnetic field cyclotron resonance frequency increases. Due to the spin–orbit coupling interaction, the energy splits at zero magnetic field. The total energy is reduced due to the presence of phonons. Therefore, the polaron state is more stable than the bare electron state, and the polaron energy splitting is more stable.

Influence of magnetic field on the properties of polaron in an asymmetric quantum dot

Influence of the magnetic field on the properties of the polaron in an asymmetric quantum dot is studied by using the Pekar variation method. The expression of the magnetopolaron ground-state energy is obtained by theoretical derivation. The relationship between the ground-state energy of the magnetopolaron with the transverse confinement strength, the longitudinal confinement strength and the magnetic field cyclotron resonance frequency are further discussed by us. Due to the crystal structure inversion asymmetry and the time inversion asymmetry, the polaron energy causes Rashba spin–orbit splitting and Zeeman splitting. Under the strong and weak magnetic fields, we discuss the dominant position of Rashba effect and Zeeman effect, respectively. Due to the presence of phonons, the polaron is more stable than the bare electron state, and the energy splitting is more stable.

Electron transport properties of silicene: Intrinsic and dirty cases with screening effects

The electronic transport characteristics of silicene sheets are studied by an Ensemble Monte Carlo (EMC) technique in the presence of phonon (acoustic, non-polar optic, surface polar optic), surface roughness and ionized impurity scattering mechanisms. Both intrinsic and silicene on an Al2O3 substrate are considered. Screening is also considered for both ionized impurity and surface polar optic phonon scattering of electrons. The velocity-applied field characteristics are obtained for both cases. A negative differential resistance (NDR) behaviour is observed for intrinsic case only. The mobility of carriers are calculated as a function of temperature for both cases and the results are compatible with existing experimental results and theoretical predictions. The effects of screening and flexural phonons on mobility are also studied.

Determination of the contribution of a phonon and a magnetic field to the chemical properties of the hydrogen molecule using the density functional theory approach

The chemical properties of the hydrogen molecule under a magnetic field in a transverse configuration and in the presence of phonons are investigated using the Density Functional Theory. The hydrogen molecule is considered as a two-electron system confined in a Coulomb type parabolic external potential. It is shown that the electron density and the chemical hardness are not influenced by the presence of the phonon but strongly depend on the magnetic field. The latter preserves the intrinsic chemical properties of the molecule but weakens the electron-electron interaction. On the other hand, the chemical potential and the energy of the system are found to strongly depend on the phonon dynamics. It is also seen that phonon dynamics lead to an increase in the internal energy even at a constant critical value of the magnetic field.

Band-Edge Quasiparticles from Electron-Phonon Coupling and Resistivity Saturation.

We address the problem of resistivity saturation observed in materials such as the A-15 compounds. To do so, we calculate the resistivity for the Hubbard-Holstein model in infinite spatial dimensions to second order in on-site repulsion U≤D and to first order in (dimensionless) electron-phonon coupling strength λ≤0.5, where D is the half bandwidth. We identify a unique mechanism to obtain two parallel quantum conducting channels: low-energy and band-edge high-energy quasi-particles. We identify the source of the hitherto unremarked high-energy quasiparticles as a positive slope in the frequency dependence of the real part of the electron self-energy. In the presence of phonons, the self-energy grows linearly with the temperature at high T, causing the resistivity to saturate. As U is increased, the saturation temperature is pushed to higher values, offering a mechanism by which electron correlations destroy saturation.

Nonequilibrium thermoelectric transport through vibrating molecular quantum dots

We employ the functional renormalization group to study the effects of phonon-assisted tunneling on the nonequilibrium steady-state transport through a single level molecular quantum dot coupled to electronic leads. Within the framework of the spinless Anderson-Holstein model, we focus on small to intermediate electron-phonon couplings, and we explore the evolution from the adiabatic to the antiadiabatic limit and also from the low-temperature non-perturbative regime to the high temperature perturbative one. We identify the phononic signatures in the bias-voltage dependence of the electrical current and the differential conductance. Considering a temperature gradient between the electronic leads, we further investigate the interplay between the transport of charge and heat. Within the linear response regime, we compare the temperature dependence of various thermoelectric coefficients to our earlier results obtained within the numerical renormalization group [Phys.~Rev.~B {\bf 96}, 195156 (2017)]. Beyond the linear response regime, in the context of thermoelectric generators, we discuss the influence of molecular vibrations on the output power and the efficiency. We find that the molecular energy dissipation, which is inevitable in the presence of phonons, is significantly suppressed in the antiadiabatic limit resulting in the enhancement of the thermoelectric efficiency.

Comparison of different concurrences characterizing photon pairs generated in the biexciton cascade in quantum dots coupled to microcavities

We compare three different notions of concurrence to measure the polarization entanglement of two-photon states generated by the biexciton cascade in a quantum dot embedded in a microcavity. We focus on the often-discussed situation of a dot with finite biexciton binding energy in a cavity tuned to the two-photon resonance. Apart from the time-dependent concurrence, which can be assigned to the two-photon density matrix at any point in time, we study single- and double-time integrated concurrences commonly used in the literature that are based on different quantum state reconstruction schemes. We argue that the single-time integrated concurrence can be thought of as the concurrence of photons simultaneously emitted from the cavity without resolving the common emission time, while the more widely studied double-time integrated concurrence refers to photons that are neither filtered with respect to the emission time of the first photon nor with respect to the delay time between the two emitted photons. Analytic and numerical calculations reveal that the single-time integrated concurrence indeed agrees well with the typical value of the time-dependent concurrence at long times, even in the presence of phonons. Thus, the more easily measurable single-time integrated concurrence gives access to the physical information represented by the time-dependent concurrence. However, the double-time integrated concurrence shows a different behavior with respect to changes in the exciton fine structure splitting and even displays a completely different trend when the ratio between the cavity loss rate and the fine structure splitting is varied while keeping their product constant. This implies the non-equivalence of the physical information contained in the time-dependent and single-time integrated concurrence on the one hand and the double-time integrated concurrence on the other hand.

LiTaO3 phonon dispersion and ferroelectric transition calculated from first principles

Abstractauthoren The phonon dispersions of the ferro- and paraelectric phase of LiTaO3 are calculated within density-functional perturbation theory. The longitudinal optical phonon modes are theoretically derived and compared with available experimental data. Our results confirm the recent phonon assignment proposed by Margueron et al. [J. Appl. Phys. 111, 104105 (2012)] on the basis of spectroscopical studies. A comparison with the phonon band structure of the related material LiNbO3 shows minor differences that can be traced to the atomic-mass difference between Ta and Nb. The presence of phonons with imaginary frequencies for the paraelectric phase suggests that it does not correspond to a minimum energy structure, and is compatible with an order-disorder type phase transition.

Fate of the excitonic insulator in the presence of phonons

The influence of phonons on the formation of the excitonic insulator has hardly been analyzed so far. Recent experiments on $\rm Ta_2NiSe_5$, 1$T$-$\rm TiSe_2$, and $\rm TmSe_{0.45}Te_{0.55}$, being candidates for realizing the excitonic-insulator state, suggest, however, that the underlying lattice plays a significant role. Employing the Kadanoff-Baym approach we address this issue theoretically. We show that owing to the electron-phonon coupling a static lattice distortion may arise at the excitonic instability. Most importantly such a distortion will destroy the acoustic phase mode being present if the electron-hole pairing and condensation is exclusively driven by the Coulomb interaction. The absence of off-diagonal long-range order, when lattice degrees of freedom are involved, challenges that excitons in these materials form a superfluid condensate of Bose particles or Cooper pairs composed of electrons and holes.

Cavity-coupled double-quantum dot at finite bias: Analogy with lasers and beyond

We present a theoretical and experimental study of photonic and electronic transport properties of a voltage biased InAs semiconductor double quantum dot (DQD) that is dipole-coupled to a superconducting transmission line resonator. We obtain the Master equation for the reduced density matrix of the coupled system of cavity photons and DQD electrons accounting systematically for both the presence of phonons and the effect of leads at finite voltage bias. We subsequently derive analytical expressions for transmission, phase response, photon number and the non-equilibrium steady state electron current. We show that the coupled system under finite bias realizes an unconventional version of a single-atom laser and analyze the spectrum and the statistics of the photon flux leaving the cavity. In the transmission mode, the system behaves as a saturable single-atom amplifier for the incoming photon flux. Finally, we show that the back action of the photon emission on the steady-state current can be substantial. Our analytical results are compared to exact Master equation results establishing regimes of validity of various analytical models. We compare our findings to available experimental measurements.

Current-conserving and gauge-invariant quantum ac transport theory in the presence of phonon

Using the nonequilibrium Green’s function (NEGF) approach, we develop a microscopic ac transport theory in the presence of electron-phonon interaction. Taking into account the self-consistent Coulomb interaction, the displacement current is included. This ensures that our theory satisfies the current-conserving and gauge-invariant conditions. Importantly, the inclusion of self-consistent Coulomb interaction naturally connects the NEGF formalism to the density functional theory (DFT). This allows us to calculate the self-consistent Hamiltonian using DFT within the NEGF framework, which paves the way for first principles ac transport calculation of nanoelectronic devices in the presence of electron-phonon interaction. It is known that the inelastic electron tunneling spectroscopy (IETS) is a powerful tool in studying the inelastic dc quantum transport in molecular devices. The basic idea of IETS is to obtain the information of vibrational spectrum of molecular devices by measuring the second derivative of the dc current with respect to the bias voltage. In the ac transport, we find that the phonon spectrum and electron-phonon coupling strength can be obtained from the second derivative of the admittance with respect to the frequency which is the working principle of the inelastic electron admittance spectroscopy (IEAS). Hence we propose to use IEAS to probe the effect of the phonon in ac transport. As an example, dynamic conductance of a quantum dot is discussed in detail and the concept of IEAS is demonstrated.

Impact of Dimensional Scaling and Size Effects on Spin Transport in Copper and Aluminum Interconnects

In this paper, compact models of spin-relaxation lengths (SRLs) in copper and aluminum interconnects by incorporating contributions to spin relaxation from phonon-induced and defect-induced scatterings are developed. The proposed models have been exhaustively calibrated with experimental data from mesoscopic lateral spin valves. The compact models are used to predict the SRL in ultrascaled copper and aluminum interconnects with cross-sectional dimensions of only few hundreds of nm2. Even though the SRL in bulk copper can be as large as 400 nm, it is predicted that SRL can become sub-100 nm for a 7.5-nm-wide channel in the presence of nominal size effects. It is found that the SRL in aluminum is more than that in copper for the same size effects and interconnect cross-sectional dimensions. The degradation in SRL in aluminum with size effects is slower than that in copper. Using the compact models for SRL in conjunction with spin-diffusion theory, spin injection and transport efficiency (SITE) for metallic interconnects in a conventional spin-valve configuration is quantified in the presence of phonon and defect scatterings.

Thermal phase transition for some spin-boson models

In this work we study two different spin-boson models. Such models are generalizations of the Dicke model, it means they describe systems of N identical two-level atoms coupled to a single-mode quantized bosonic field, assuming the rotating wave approximation. In the first model, we consider the wavelength of the bosonic field to be of the order of the linear dimension of the material composed of the atoms, therefore we consider the spatial sinusoidal form of the bosonic field. The second model is the Thompson model, where we consider the presence of phonons in the material composed of the atoms. We study finite temperature properties of the models using the path integral approach and functional methods. In the thermodynamic limit, N→∞, the systems exhibit phase transitions from normal to superradiant phase at some critical values of temperature and coupling constant. We find the asymptotic behavior of the partition functions and the collective spectrums of the systems in the normal and the superradiant phases. We observe that the collective spectrums have zero energy values in the superradiant phases, corresponding to the Goldstone mode associated to the continuous symmetry breaking of the models. Our analysis and results are valid in the limit of zero temperature β→∞, where the models exhibit quantum phase transitions.