Phonon Distribution Research Articles

A comprehensive study on the Hall mobility of an ohmic ensemble of two-dimensional electrons confined in a quantum well of a heterostructure at low lattice temperatures

In the present study, the characteristic dependence of the Hall mobility upon the temperature of a degenerate ensemble of two-dimensional electrons in a well of heterostructure were calculated in broader detail, for the ohmic field region, at low temperatures. Apart from the electronic interactions with the remote ionized impurities and the surface roughness, the study also duly considered some factors that are often ignored for mathematical simplicity. These include the inelasticity of the electron–phonon collisions and the true phonon distribution. The results thus obtained for heterostructures such as AlGaAs/GaAs, AlGaN/GaN, and AlInSb/InSb show that the consideration of the above details significantly changes the overall characteristics, and makes them agree quite well with the experimental data.

Full quantum theory of nonequilibrium phonon condensation and phase transition

Fr\"olich condensation is a room-temperature nonequilibrium phenomenon which is expected to occur in many physical and biological systems. Though predicted theoretically a half century ago, the nature of such condensation remains elusive. In this Letter, we derive a full quantum theory of Fr\"ohlich condensation from the Wu-Austin Hamiltonian and present for the first time an analytical proof that a second-order phase transition induced by nonequilibrium and nonlinearity emerges in the large-$D$ limit with and without decorrelation approximation. This critical behavior cannot be witnessed if external sources are treated classically. We show that the phase transition is accompanied by large fluctuations in the statistical distribution of condensate phonons and that the Mandel-Q factor which characterizes fluctuations becomes negative in the limit of excessive external energy input. In contrast with the cold atom equilibrium BEC, the Fr\"ohlich condensate is a result of the nonequilibrium driving where the pump plays a role of setting the number of particles, and the medium plays a role of setting the temperature. Hence, BEC can either arise by reducing the medium temperature at fixed pump (equilibrium case), or by increasing the pump at fixed medium temperature (nonequilibrium case).

Focusing on Some Physical Properties of Li2TlIn: an Ab Initio Study

Structural, electronic, elastic and dynamic properties of Li2TlIn were studied for the ground state (i. e. P = 0 kbar) and under pressure value of 4.53 kbar, using Density Functional Theory (DFT). The electronic band and density of states (DOS) calculations reveal that Li2TlIn crystal is in a metallic structure. Focusing on the elastic properties has shown that this compound is a ductile and mechanically stable material for both ground state and under pressure of 4.53 kbar. In addition, the phonon dispersion curve and the phonon DOS were obtained by density functional perturbation theory. Li2TlIn has negative frequency values both in the phonon distribution curve and phonon DOS graphs which indicate that Li2TlIn compound is dynamically unstable in the ground state. However, our results show that, when a pressure of 4.53 kbar is applied, the Li2TlIn crystal becomes dynamically stable.

The influence of initial phonon states on the generation of coherent optical phonons

The generation of coherent phonons is theoretically studied using a thermal equilibrium phonon distribution as the initial condition. The time evolution of the coherent phonon amplitude and phonon population is calculated for 4.5-THz phonons with initial phonon distributions at 10 and 300 K. It is determined that the coherent-phonon amplitudes of state-selected phonons are dependent on the initial phonon distribution. The coherent-phonon amplitudes, when considering all phonon states instead of selecting certain phonon levels, are almost the same for both initial distributions. The variance of the coherent-phonon amplitudes is found to oscillate with twice the phonon frequency, and its oscillation amplitude depends on the initial phonon distribution.

A novel optical temperature sensor based on Boltzmann function in BiZn2PO6 phosphor

In this paper, a new scheme of optical temperature measurement based on Boltzmann function is reported for the first time. The BiZn2PO6 and BiZn2PO6:Eu3+ phosphors with strong host emission intensity were investigated from the perspective of crystal structure, electronic band structure, phonon distribution, and fluorescence properties. By exploring the relationship between host emission intensity and temperature, or between fluorescence lifetime and temperature, a novel optical temperature sensor based on Boltzmann function was designed. With this scheme, the performance of the optical temperature sensors can be visualized in the fitting results of Boltzmann function. The absolute sensitivity of the optical temperature sensor designed based on this function reaches a maximum value Sa=14dT at T0, while relative sensitivity is 12dT. For example, in BiZn2PO6 phosphor, the absolute and relative sensitivities reached 0.88% and 1.78% at 260 K. Therefore, the new optical temperature sensor based on Boltzmann function provides the theoretical basis and practical experience for the development of high-sensitivity non-contact optical temperature sensor.

Non-equilibrium phonon distribution caused by an electrical current

In an attempt to explain flash sintering experiments, it had been proposed that the electron–phonon coupling leads to a proliferation of short wave-length lattice vibrations in an electric field. In this paper we investigate this by solving two coupled Boltzmann equations, describing a free electron gas in an electric field scattering from a crystal lattice coupled to a heat bath. The electric field imposes cylindrical symmetry and drives the electrons and the phonons into a non-equilibrium steady state. We find that the phonon distribution shows a strong excess population at the Brillouin zone edge in the direction of the electric field. We argue analytically, that this can be traced back to the shifted Fermi sphere for the electrons. Furthermore, not only energy but also momentum is exchanged in the electron–phonon system, which defies any attempt at describing the system by a two-temperature model.

Hydrodynamic heat transport in dielectric crystals in the collective limit and the drifting/driftless velocity conundrum

We apply a recently developed method for solving the linearized phonon Boltzmann equation to study the hydrodynamic thermal transport in dielectrics in the collective limit, i.e., when normal collisions dominate resistive ones. The method recovers Guyer and Krumhansl results for a single Debye branch and extends them to general dispersion relations and branches. Specifically, we obtain explicit microscopic expressions for the phonon distribution and for the transport coefficients in this limit. We find that the phonon distribution differs from the commonly used displaced distribution in two terms: one accounting for viscous flow and another one which allows us to solve a long-standing issue on drifting and driftless second-sound velocities. Thus, the new method allows us to generalize previous results and fill some gaps on fundamental aspects of the collective limit through a simple mathematical formalism. We compare the hydrodynamic framework with previous models and discuss its limitations.

Hot and cold phonons in electrically biased graphene

Based on first-principles calculations and semiclassical transport theory, we study the nonequilibrium phonon distribution in graphene in the presence of electrical current. In addition to the hot-phonon effect, we observe a cooling of phonon modes at the same time. Interestingly, the presence of electric current along the direction connecting $K$ and ${K}^{\ensuremath{'}}$ valleys induces an opposite dipolelike temperature distribution in the two valleys and at the $\mathrm{\ensuremath{\Gamma}}$ point. This leads to a ``high-order'' valley polarization of phonon distribution between $K$ and ${K}^{\ensuremath{'}}$. Based on the nonequilibrium phonon distribution, we furthermore study their effect on the lattice parameters and find a negative current-induced expansion coefficient. Similar to graphene's negative thermal expansion, this is rooted in the dominant contribution of out-of-plane acoustic phonons, which do not couple directly to electrons, but gain energy from in-plane phonons through anharmonic scattering.

Molecular dynamics study on the contribution of anisotropic phonon transmission to thermal conductivity of silicon

The analysis of the contribution of anisotropic phonon transmission to thermal conductivity is helpful to focus on high-energy phonons in heat transport. We calculated a series of anharmonic phonon properties and heat transport properties of Si by Fourier projection method from atomic trajectories. Under this theoretical scheme, we have obtained very consistent results with the experimental data through very low computational cost, especially the anharmonic phonon properties at high temperature. We carefully analyze the contribution of different phonons to thermal conductivity and the anisotropic feature of phonon. It is found that the longitudinal acoustic (LA) phonons have the special thermal broadening near the point L at the boundary of the Brillouin zone. The optical phonons cannot be safely ignored in the study of heat transport, especially the longitudinal optical phonon that shows a large contribution to thermal conductivity at room temperature. The thermal conductivity contribution of different phonons varies with temperature. The anisotropic features of the contribution of different phonons to thermal conductivity are mainly reflected in the short-wavelength phonons. Our work explains the reason why other research works have different opinions on whether LA phonon is the main contributor of thermal conductivity. These investigations also provide insights for further understanding phonon heat transport and distribution of high-energy phonons.

(Invited) High Temperature Light Emission Spectra of Metallic Carbon Nanotubes Under Different Heating Methods

Semiconducting single-walled carbon nanotubes (SWCNTs) show exceptional optical properties such as excitonic thermal radiation under thermal equilibrium [1,2] as well as exciton luminescence under nonequilibrium conditions, which potentially provides various promising applications including photonic and thermo-optic devices. With regard to the counterpart, metallic SWCNTs, high-temperature light emission induced by Joule heating has been reported [3,4], but the effects of nonequilibrium induced by the current injection on the light emission remain to be clarified. Here, we report comparison of high-temperature light emission from an identical individual metallic SWCNT under laser- and Joule-heating conditions. The spectral shapes were qualitatively different depending on the heating methods. We will discuss these high-temperature light emission phenomena quantitatively in terms of the electron and phonon distribution. [1] T. Nishihara, A. Takakura, Y. Miyauchi, and K. Itami, Nat. Commun. 9, 3144 (2018). [2] S. Konabe, T. Nishihara, and Y. Miyauchi, Opt. Lett. 46, 3021 (2021). [3] D. Mann et al., Nat. Nanotechnol. 2, 33 (2007), [4] Z. Liu et al., ACS Nano 5, 4634 (2011).

A fast-converging scheme for the phonon Boltzmann equation with dual relaxation times

The phonon Boltzmann transport equation with dual relaxation times is often used to describe the heat conduction in semiconductor materials when the classical Fourier's law is no longer valid. For practical engineering designs, accurate and efficient numerical methods are highly demanded to solve the equation. At a large Knudsen number (i.e., the ratio of the phonon mean free path to a characteristic system length), steady-state solutions can be obtained via the conventional iterative scheme (CIS) within a few iterations. However, when the Knudsen number becomes small, i.e., when the phonon transport occurs in the diffusive or hydrodynamic regime, thousands of iterations are required to obtain converged results. In this work, a general synthetic iterative scheme (GSIS) is proposed to tackle the inefficiency of CIS. The key ingredient of the GSIS is that a set of macroscopic synthetic equations, which is exactly derived from the Boltzmann transport equation, is simultaneously solved with the kinetic equation to obtain the temperature and heat flux. During the iteration, the macroscopic quantities are used to evaluate the equilibria in the scattering terms of the kinetic equation, thus guiding the evolution of the phonon distribution function, while the distribution function, in turn, provides closures to the synthetic equations. The Fourier stability analysis is conducted to reveal the superiority of the GSIS over the CIS in terms of fast convergence in periodic systems. It is shown that the convergence rate of the GSIS can always be maintained under 0.2 so that only two iterations are required to reduce the iterative error by one order of magnitude. Numerical results in wall-bounded systems are presented to demonstrate further the efficiency of GSIS, where the CPU time is reduced by up to three orders of magnitude, especially in both the diffusive and hydrodynamic regimes where the Knudsen number is small.

Determination of the Heating Rate and Temperature of an Ion Chain in a Linear Paul Trap by the Dephasing of Rabi Oscillations

The optimization of the parameters of laser cooling and the investigation of the heating rate in ion traps require the measurement of the temperature of ion chains for which the Lamb–Dicke regime is satisfied. A novel method based on the investigation of the dynamics of Rabi oscillations at a narrow electron transition in an individual ion of the chain has been suggested for such measurement. An analytical expression for the population of the upper state as a function of the excitation time is derived taking into account the thermal distribution of phonons over the vibrational modes of a chain with an arbitrary number of ions. The method is tested experimentally for the chain of five ^{{171}}{text{Y}}{{{text{b}}}^{ + }} ions using the quadrupole transition at 435 nm, as well as for a single ion. The heating rate measured for the axial vibrational mode in the implemented trap is 8 × 103 phonons/s.

Off-diagonal electron-phonon coupling effects on two-level system dynamics

Electromagnetically coupled two-level systems play a central role in several condensed matter components being considered for quantum information processing applications. If the states couple to phonon excitations, their electromagnetic response is altered via phonon-assisted transitions and lifetime broadening. The former has been treated extensively for a number of specific two-level systems (e.g., excitons in artificial quantum dots, localized states associated with impurities or defects, etc.), but the latter has received less attention. Here we study a microscopic model of the dipole transition of a two-level system under the influence of both diagonal and nondiagonal interactions with a bath of phonons. Our results capture both the influence of the frequency distribution of phonons on the relative spectral weight of the zero-phonon transition and the phonon sidebands, and the broadening of the zero-phonon line due to nondiagonal electron-phonon coupling. We use a formalism that includes non-Markovian effects related to the feedback mechanism between the two-level system and the phonon bath. For simplified forms of the phonon spectral functions we provide analytical expressions up to second order in the coupling strength that demonstrate the importance of including both forms of electron-phonon coupling in studies of these systems. Our formalism can be generalized to higher orders of coupling and for realistic phonon spectral functions.

Quantum Non-Gaussianity of Multiphonon States of a Single Atom

Quantum non-Gaussian mechanical states are already required in a range of applications. The discrete building blocks of such states are the energy eigenstates-Fock states. Despite progress in their preparation, the remaining imperfections can still invisibly cause loss of the aspects critical for their applications. We derive and apply the most challenging hierarchy of quantum non-Gaussian criteria on the characterization of single trapped-ion oscillator mechanical Fock states with up to 10 phonons. We analyze the depth of these quantum non-Gaussian features under intrinsic mechanical heating and predict their requirement for reaching quantum advantage in the sensing of a mechanical force.

Stochastic Galerkin methods for the Boltzmann-Poisson system

We study uncertainty quantification for a Boltzmann-Poisson system that models electron transport in semiconductors and the physical collision mechanisms over the charges, using the stochastic Galerkin method in order to handle the randomness associated with the problem. In this study we choose first as a source of uncertainty the phonon energy, taking it as a random variable, as its value influences the energy jump appearing in the collision integral for electron-phonon scattering. Then we choose the lattice temperature as a random variable, since it defines the value of the collision operator terms in the case of electron-phonon scattering by being a parameter of the phonon distribution. Finally, we present our numerical simulations for the latter case. We calculate then with our stochastic Discontinuous Galerkin methods the uncertainty in kinetic moments such as density, mean energy, current, etc. associated to a possible physical temperature variation (assumed to follow a uniform distribution) in the lattice environment, as this uncertainty in the temperature is propagated into the electron PDF. Our mathematical and computational results let us predict then in a real world problem setting the impact that possible variations in the lab conditions (such as temperature) or limitations in the mathematical model (such as assumption of a constant phonon energy) will have over the uncertainty in the behavior of electronic devices.

Direct View of Phonon Dynamics in Atomically Thin MoS2.

Transition-metal dichalcogenide monolayers and heterostructures are highly tunable material systems that provide excellent models for physical phenomena at the two-dimensional (2D) limit. While most studies to date have focused on electrons and electron-hole pairs, phonons also play essential roles. Here, we apply ultrafast electron diffraction and diffuse scattering to directly quantify, with time and momentum resolution, electron-phonon coupling (EPC) in monolayer molybdenum disulfide and phonon transport from the monolayer to a silicon nitride substrate. Optically generated hot carriers result in a profoundly anisotropic distribution of phonons in the monolayer within ∼5 ps. A quantitative comparison with ab initio ultrafast dynamics simulations reveals the essential role of dielectric screening in weakening EPC. Thermal transport from the monolayer to the substrate occurs with the phonon system far from equilibrium. While screening in 2D is known to strongly affect equilibrium properties, our findings extend this understanding to the dynamic regime.

Study of phonon transport across Si/Ge interfaces using Full-Band phonon Monte Carlo simulation

A Full Band Monte Carlo simulator has been developed to consider phonon transmission across interfaces disposed perpendicularly to the heat flux. This solver of the Boltzmann transport equation does not require any assumption on the shape the phonon distribution and can naturally consider all phonon transport regimes from the diffusive to the fully ballistic regime. This simulator is used to study single and double Si/Ge heterostructures from the micrometer scale down to the nanometer scale, i.e. in all phonon transport regime from fully diffusive to ballistic. A methodology to determine the thermal conductivity at thermal interfaces is presented. It is also shown that the different transport regimes are correlated to different spectral contributions of the phonon modes to the heat flux along the devices. This local indicator of the transport regime gives new insights into the out-of-equilibrium phonon transport near the interfaces.

Transport and relaxation of current-generated nonequilibrium phonons from nonlocal electronic measurements

We study phonons generated by current in a Pt nanowire, by measuring resistance of another nanowire separated from the first one by an insulating spacer. For thin spacers, the resistance varies almost linearly with current at cryogenic temperatures, while an additional quadratic contribution emerges for thicker spacers. These observations suggest a non-thermal distribution of current-generated phonons that relax via strongly nonlinear dynamical processes rather than few-phonon scattering. Our results provide insight into the nonequilibrium phonon dynamics at nanoscale, which may facilitate efficient heat management in electronic nanodevices.

Real-time evolution of static electron-phonon models in time-dependent electric fields.

We present an exact Monte Carlo method to simulate the nonequilibrium dynamics of electron-phonon models in the adiabatic limit of zero phonon frequency. The classical nature of the phonons allows us to sample the equilibrium phonon distribution and efficiently evolve the electronic subsystem in a time-dependent electromagnetic field for each phonon configuration. We demonstrate that our approach is particularly useful for charge-density-wave systems experiencing pulsed electric fields, as they appear in pump-probe experiments. For the half-filled Holstein model in one and two dimensions, we calculate the out-of-equilibrium response of the current and the energy after a pulse is applied as well as the photoemission spectrum before and after the pump. Finite-size effects are under control for chains of 162 sites (in one dimension) or 16×16 square lattices (in two dimensions).

Potential distribution of polar optical phonons and their electron–phonon coupling properties of a wurtizite GaN-based trianglar quantum dot

Polar optical phonon modes of a wurtzite nitride trianglar quantum dot (QD) are deduced and analyzed by using the dielectric continuum model. Based on a method of nonseparable variables, the Laplace equation of electristatic potential of the structure is solved, and the exact and analytical phonon states of exact confined (EC) modes are derived. It is found that the frequency of EC modes in the nitride trianglar QD systems can take both the longitudinal optical phonons in [Formula: see text]-direction [Formula: see text] and the longitudinal optical phonons in [Formula: see text]-plane [Formula: see text], which is obviously different from the cases of EC modes in wurtzite GaN quantum wells and quantum wires due to their different confined dimensions. The polarization eigenvectors and their orthogonality relations for the EC phonon modes are derived, which could form a set of orthogonal and completed basis vectors. By using the orthogonality relations of polarization eigenvector and field quantization method, the free phonon field of EC modes and the corresponding Fröhlich electron–phonon interaction Hamiltonian are obtained. Numerical calculations on a wurtztie GaN trianglar QD are performed. The spatial distributions of phonon potentials of EC phonons both in [Formula: see text]-plane and in [Formula: see text]-direction as well as the electron–phonon coupling strength are plotted and discussed. It is observed that the potential of these EC phonon modes is strictly confined within the trianglar QD ranges. The dependence of symmetries and electron–phonon coupling strength on the quantum numbers [Formula: see text] and [Formula: see text] in [Formula: see text]-plane, and the quantum number [Formula: see text] in [Formula: see text]-direction are analyzed in detail. The relationship of the total number of peaks and troughs with these quantum numbers are also discussed and induced.