Nonequilibrium Phonons Research Articles

Enhanced quasiparticle lifetime in a superconductor by selective blocking of recombination phonons with a phononic crystal

When quasiparticles in a BCS superconductor recombine into Cooper pairs, phonons are emitted within a narrow band of energies above the pairing energy at 2$\Delta$. We show that a phonon bandgap restricting the escape of recombination phonons from a superconductor can increase the quasiparticle recombination lifetime by more than an order of magnitude. A phonon bandgap can be realized and matched to the recombination energy with a phononic crystal, a periodically-patterned dielectric membrane. We discuss in detail the non-equilibrium quasiparticle and phonon distributions that arise in a superconductor due to a phonon bandgap and a pair-breaking photon signal. Although intrinsically a non-equilibrium effect, the lifetime enhancement in the small-signal regime is remarkably similar to an estimate from an equilibrium formulation. The equilibrium estimate closely follows $\exp(\Omega_{bg}/k_BT_b)$, where $\Omega_{bg}$ is the phonon bandgap energy bandwidth above 2$\Delta$, and $T_b$ is the phonon bath temperature of the coupled electron-phonon system. We discuss the impact of a phononic bandgap on the performance of superconducting devices, and propose a superconducting microwave resonator circuit to measure the enhancement in the quasiparticle lifetime.

Theoretical model and simulation of carrier heating with effects of nonequilibrium hot phonons in semiconductor photovoltaic devices

AbstractA theoretical model and its rate equations of carrier number and energy densities are proposed and presented for calculating carrier heating in semiconductor photovoltaic devices. The rate equation for carrier number density is the Shockley‐Queisser theoretical model, while the rate equation for carrier energy density includes the carrier interband energy relaxation via radiative recombination and the intraband energy relaxation via the interactions between carriers and polar longitudinal optical phonons. The carrier intraband energy relaxation is calculated by incorporating the effects of nonequilibrium hot phonons and the Thomas‐Fermi static screening. This model and its rate equations are employed for numerical simulations of the magnitude of carrier heating and its effects on the current‐voltage relations of bulk GaAs solar cells under different concentration ratios and with different widths of the active region. The simulation results demonstrate that carrier temperature in general heats up to 400 to 900 K at short‐circuit operating condition. This carrier heating cools down to lattice temperature when the device approaches its open‐circuit point. Based on these numerical results, effects of carrier heating on the performance of conventional solar cells and also their implications for the design of hot‐carrier solar cells will be discussed.

Thermal Engineering in Low‐Dimensional Quantum Devices: A Tutorial Review of Nonequilibrium Green's Function Methods

AbstractThermal engineering of quantum devices has attracted much attention since the discovery of quantized thermal conductance of phonons. Although easily submerged in numerous excitations in macrosystems, quantum behaviors of phonons manifest in nanoscale low‐dimensional systems even at room temperature. Especially in nanotransport devices, phonons move quasiballistically when the transport length is smaller than their bulk mean free paths. It has been shown that the phonon nonequilibrium Green's function method (NEGF) is effective for the investigation of nanoscale quantum transport of phonons. Here, two aspects of thermal engineering of quantum devices are discussed using NEGF methods. One covers transport properties of pure phonons; the other concerns caloritronic effects, which manipulate other degrees of freedom, such as charge, spin, and valley, via the temperature gradient. For each part, the basic theoretical formalisms are outlined first, then a survey of related investigations on models or realistic materials is presented. Particular attention is given to phonon topologies and the generalized phonon NEGF method. Finally, conclusions are offered and the study is summarized with an outlook.

Mapping momentum-dependent electron-phonon coupling and nonequilibrium phonon dynamics with ultrafast electron diffuse scattering

Despite their fundamental role in determining material properties, detailed momentum-dependent information on the strength of electron-phonon and phonon-phonon coupling (EPC and PPC, respectively) across the entire Brillouin zone (BZ) has proved difficult to obtain. Here we demonstrate that ultrafast electron diffuse scattering (UEDS) directly provides such information. By exploiting symmetry-based selection rules and time-resolution, scattering from different phonon branches can be distinguished even without energy resolution. Using graphite as a model system, we show that UEDS patterns map the relative EPC and PPC strength through their profound sensitivity to photoinduced changes in phonon populations. We measure strong EPC to the $K$-point transverse optical phonon of $A_1'$ symmetry ($K-A_1'$) and along the entire longitudinal optical branch between $\Gamma-K$, not only to the $\Gamma-E_{2g}$ phonon as previously emphasized. We also determine that the subsequent phonon relaxation pathway involves three stages; decay via several identifiable channels to transverse acoustic (TA) and longitudinal acoustic (LA) phonons (1-2 ps), intraband thermalization of the non-equilibrium TA/LA phonon populations (30-40 ps) and interband relaxation of the LA/TA modes (115 ps). Combining UEDS with ultrafast angle-resolved photoelectron spectroscopy will yield a complete picture of the dynamics within and between electron and phonon subsystems, helping to unravel complex phases in which the intertwined nature of these systems have a strong influence on emergent properties.

Thermalization in simple metals: Role of electron-phonon and phonon-phonon scattering

We study the electron and phonon thermalization in simple metals excited by a laser pulse. The thermalization is investigated numerically by solving the Boltzmann transport equation taking into account all the relevant scattering mechanism: the electron-electron, electron-phonon (e-ph), phonon-electron (ph-e), and phonon-phonon (ph-ph) scatterings. In the initial stage of the relaxation, most of the excitation energy is transferred from the electrons to phonons through the e-ph scattering. This creates hot high-frequency phonons due to the ph-e scatterings, followed by an energy redistribution between phonon subsystems through the ph-ph scatterings. This yields an overshoot of the total longitudinal-acoustic phonon energy at a time, across which a crossover occurs from a nonequilibrium state, where the e-ph and ph-e scatterings frequently occur, to a state, where the ph-ph scattering occurs to reach a thermal equilibrium. This picture is quite different from the scenario of the well-known two-temperature model (2TM). The behavior of the relaxation dynamics is compared with those calculated by several models, including the 2TM, the four-temperature model, and nonequilibrium electron or phonon models. The relationship between the relaxation time and the initial distribution function is also discussed.

Structure of the Room-Temperature 2.5 eV α-Quartz Single-Crystal Pulsed Cathodoluminescence Band

We study the room-temperature (RT) pulsed cathodoluminescence (PCL) spectrum of a high-purity synthetic α-quartz single crystal. The spectrum consists of two wide bands with intensity maxima at 415 and 490 nm (2.99 and 2.53 eV). The band at 490 nm (2.5 eV) is polarized in the XY crystal plane (perpendicular to the third-order symmetry axis) and possesses a structure with three peaks at 480±2, 487±2, and 493±2 nm (2.58±0.01, 2.55±0.01, and 2.52±0.01 eV). The intensities of the peaks at 480±2 and 493±2 nm increased with increase in the irradiation dose up to 45 kGy. Peaks are equidistant at the energetic scale. The energy separation between the peaks Δ = 0.03 ± 0.01 eV is equal in order of magnitude to energies of Li x O y molecular vibrations and to the energy of the optical phonon in α-quartz. We propose an explanation of the experimental data obtained. According to this explanation, the structure observed may be attributed to the amplitude modulation of the quartz 2.5 eV emission band by the crystalline electric fields on frequencies of optical phonons. The nonequilibrium phonons may arise during the electron-beam irradiation.

Nonequilibrium dynamics of the phonon gas in ultrafast-excited antimony

The ultrafast relaxation dynamics of a nonequilibrium phonon gas towards thermal equilibrium involves many-body collisions that cannot be properly described by perturbative approaches. Here, we develop a nonperturbative method to elucidate the microscopic mechanisms underlying the decay of laser-excited coherent phonons in the presence of electron-hole pairs, which so far are not fully understood. Our theory relies on ab initio molecular dynamics simulations on laser-excited potential-energy surfaces. Those simulations are compared with runs in which the laser-excited coherent phonon is artificially deoccupied. We apply this method to antimony and show that the decay of the ${A}_{1g}$ phonon mode at low laser fluences can be accounted mainly to three-body down-conversion processes of an ${A}_{1g}$ phonon into acoustic phonons. For higher excitation strengths, however, we see a crossover to a four-phonon process, in which two ${A}_{1g}$ phonons decay into two optical phonons.

Equivalent circuit-level model of quantum cascade lasers with integrated hot-electron and hot-phonon effects

We report a study of the effects of hot-electron and hot-phonon dynamics on the output characteristics of quantum cascade lasers (QCLs) using an equivalent circuit-level model. The model is developed from the energy balance equation to adopt the electron temperature in the active region levels, the heat transfer equation to include the lattice temperature, the nonequilibrium phonon rate to account for the hot phonon dynamics and simplified two-level rate equations to incorporate the carrier and photon dynamics in the active region. This technique simplifies the description of the electron–phonon interaction in QCLs far from the equilibrium condition. Using the presented model, the steady and transient responses of the QCLs for a wide range of sink temperatures (80 to 320 K) are investigated and analysed. The model enables us to explain the operating characteristics found in QCLs. This predictive model is expected to be applicable to all QCL material systems operating in pulsed and cw regimes.

Electron–hole liquid in semiconductors and low-dimensional structures

The condensation of excitons into an electron–hole liquid (EHL) and the main EHL properties in bulk semiconductors and low-dimensional structures are considered. The EHL properties in bulk materials are discussed primarily in qualitative terms based on the experimental results obtained for germanium and silicon. Some of the experiments in which the main EHL thermodynamic parameters (density and binding energy) have been obtained are described and the basic factors that determine these parameters are considered. Topics covered include the effect of external perturbations (uniaxial strain and magnetic field) on EHL stability; phase diagrams for a nonequilibrium exciton-gas–EHL system; information on the size and concentration of electron–hole drops (EHDs) under various experimental conditions; the kinetics of exciton condensation and of recombination in the exciton-gas–EHD system; dynamic EHD properties and the motion of EHDs under the action of external forces; the properties of giant EHDs that form in potential wells produced by applying an inhomogeneous strain to the crystal; and effects associated with the drag of EHDs by nonequilibrium phonons (phonon wind), including the dynamics and formation of an anisotropic spatial structure of the EHD cloud. In discussing EHLs in low-dimensional structures, a number of studies are reviewed on the observation and experimental investigation of phenomena such as spatially indirect (dipolar) electron–hole and exciton (dielectric) liquids in GaAs/AlGaAs structures with double quantum wells (QWs), EHDs containing only a few electron–hole pairs (dropletons), EHLs in type-I silicon QWs, and spatially direct and dipolar EHLs in type-II silicon–germanium heterostructures.

Self-consistent electro-opto-thermal model of quantum cascade lasers with coupled electron and phonon interactions far from equilibrium

A self-consistent model of quantum cascade lasers (QCLs) is presented here for the study of the QCL’s behavior in the far from equilibrium conditions. The approach is developed by employing a number of physics-based models such as the carrier and photon rate equations, the energy balance equation, the heat transfer equation and a simplified rate equation for the creation and annihilation of nonequilibrium optical phonons. The temperature dependency of the relevant physical effects such as stimulated gain cross section, longitudinal optical (LO) phonons and hot-phonon generation rates are included in the model. Using the presented model, the static and transient device characteristics are calculated and analyzed for a wide range of heat sink temperatures. Besides the output characteristics, this model also provides a way to study the hot-phonon dynamics in the device, and to explore the electron temperature and thermal roll-over in the QCLs.

Charge-vibration interaction effects in normal-superconductor quantum dots

We study the quantum transport and the nonequilibrium vibrational states of a quantum dot embedded between a normal and a superconducting lead with the charge on the quantum dot linearly coupled to a harmonic oscillator of frequency $\omega$. To the leading order in the charge-vibration interaction, we calculate the current and the nonequilibrium phonon occupation by the Keldsyh Green's function technique. We analyze the inelastic, vibration-assisted tunneling processes in the regime $\omega <\Delta$, with the superconducting energy gap $\Delta$, and for sharp resonant transmission through the dot. When the energy $\varepsilon_0$ of the dot's level is close to the Fermi energy $\mu$, i.e. $|\varepsilon_0-\mu|\ll \Delta$, inelastic Andreev reflections dominate up to voltage $eV\gtrsim\Delta$. The inelastic quasiparticle tunneling becomes the leading process when the dot's level is close to the gap $|\varepsilon_0-\mu|\sim \Delta \pm \omega$. In both cases, the inelastic tunneling processes appear as sharp and prominent peaks - not broadened by temperature - in the $I$-$V$ characteristic and pave the way for inelastic spectroscopy of vibrational modes even at temperatures $T \gg \omega$. We also found that inelastic Andreev reflections as well as quasiparticle tunneling induce a strong nonequilibrium state of the oscillator. In different ranges on the dot's level, we found that the current produces: (i) ground-state cooling of the oscillator with phonon occupation $n\ll 1$, (ii) accumulation of energy in the oscillator with $n\gg 1$ and (iii) a mechanical instability which is a precursor of self-sustained oscillations. We show that ground-state cooling is achieved simultaneously for several modes of different frequencies. Finally, we discuss how the nonequilibrium vibrational state can be detected by the asymmetric behavior of the inelastic current peaks respect to the gate voltage.

Probing Anisotropic Thermal Conductivity of Transition Metal Dichalcogenides MX2 (M = Mo, W and X = S, Se) using Time-Domain Thermoreflectance.

Transition metal dichalcogenides (TMDs) are a group of layered 2D semiconductors that have shown many intriguing electrical and optical properties. However, the thermal transport properties in TMDs are not well understood due to the challenges in characterizing anisotropic thermal conductivity. Here, a variable-spot-size time-domain thermoreflectance approach is developed to simultaneously measure both the in-plane and the through-plane thermal conductivity of four kinds of layered TMDs (MoS2 , WS2 , MoSe2 , and WSe2 ) over a wide temperature range, 80-300 K. Interestingly, it is found that both the through-plane thermal conductivity and the Al/TMD interface conductance depend on the modulation frequency of the pump beam for all these four compounds. The frequency-dependent thermal properties are attributed to the nonequilibrium thermal resistance between the different groups of phonons in the substrate. A two-channel thermal model is used to analyze the nonequilibrium phonon transport and to derive the intrinsic thermal conductivity at the thermal equilibrium limit. The measurements of the thermal conductivities of bulk TMDs serve as an important benchmark for understanding the thermal conductivity of single- and few-layer TMDs.

Ultrafast atomic-scale visualization of acoustic phonons generated by optically excited quantum dots

Understanding the dynamics of atomic vibrations confined in quasi-zero dimensional systems is crucial from both a fundamental point-of-view and a technological perspective. Using ultrafast electron diffraction, we monitored the lattice dynamics of GaAs quantum dots—grown by Droplet Epitaxy on AlGaAs—with sub-picosecond and sub-picometer resolutions. An ultrafast laser pulse nearly resonantly excites a confined exciton, which efficiently couples to high-energy acoustic phonons through the deformation potential mechanism. The transient behavior of the measured diffraction pattern reveals the nonequilibrium phonon dynamics both within the dots and in the region surrounding them. The experimental results are interpreted within the theoretical framework of a non-Markovian decoherence, according to which the optical excitation creates a localized polaron within the dot and a travelling phonon wavepacket that leaves the dot at the speed of sound. These findings indicate that integration of a phononic emitter in opto-electronic devices based on quantum dots for controlled communication processes can be fundamentally feasible.

Directed motion of vortices and annihilation of vortex–antivortex pairs in finite-gap superconductors via hot-lattice routes

Using finite gap, time-dependent Ginzburg–Landau equations, generalized to include non-thermal phonons, we report numerical simulations of vortex nucleation, propagation, and annihilation in thin, finite strips of magnetic-impurity free, perfectly homogeneous superconductors. When a steady electric current passes through the strip with either surface defects or nonequilibrium phonon sources (e.g., local “hotspots”), periodic vortex generation and annihilation is observed even in the absence of external magnetic fields. Local pulses of electric field are produced upon annihilation. The injected phonon lines steer the vortices during their motion within the strip, potentially allowing control of the annihilation site.

Transient energy relaxation in scattering-assisted terahertz quantum cascade lasers

We adopt a self-consistent Maxwell–Bloch method to investigate the energy relaxation process from unsaturated to saturated in the scattering-assisted terahertz quantum cascade laser. In the lasing-establishment process, more nonequilibrium LO phonons are accumulated and more electrons are thermalized. At the same time, more efficient energy relaxation of the saturated situation can be found compared with the unsaturated situation. These phenomena stem from the improved electron transport efficiency across the active region, due to the lasing-induced lifetime reduction of electrons in the upper lasing subband. The simulation results are qualitatively identical with previous experimental results.

Optical Generation and Detection of Local Nonequilibrium Phonons in Suspended Graphene.

The measured frequencies and intensities of different first- and second-order Raman peaks of suspended graphene are used to show that optical phonons and different acoustic phonon polarizations are driven out of local equilibrium inside a submicron laser spot. The experimental results are correlated with a first-principles-based multiple temperature model to suggest a considerably lower equivalent local temperature of the flexural phonons than those of other phonon polarizations. The finding reveals weak coupling between the flexural modes with hot electrons and optical phonons. Since the ultrahigh intrinsic thermal conductivity of graphene has been largely attributed to contributions from the flexural phonons, the observed local nonequilibrium phenomena have important implications for understanding energy dissipation processes in graphene-based electronic and optoelectronic devices, as well as in Raman measurements of thermal transport in graphene and other two-dimensional materials.

Heating and evaporation of a two-dimensional electron–hole liquid by heat pulses

The dynamics of low-temperature (T = 5 K) photoluminescence spectra of Si/Si1-xGex/Si heterostructures (x = 0.045) under the influence of a stream of nonequilibrium phonons (heat pulses) propagating in the structure is investigated. The rapid evaporation of the electron–hole liquid in the quantum well of the structure is observed as the liquid is heated by nonequilibrium phonons. It is established that an increase in the exciton-gas density in the quantum well is caused by the evaporation of the electron–hole liquid and by an increase in the rate of exciton capture by the quantum well. It is shown that the interaction with nonequilibrium phonons results in the dissociation of bound-exciton complexes in the Si layers, which is accompanied by an increase in the exciton concentration and lifetime.

A Finite Difference Lattice Boltzmann Method to Simulate Multidimensional Subcontinuum Heat Conduction

In this paper, a lattice Boltzmann method (LBM)-based model is developed to simulate the subcontinuum behavior of multidimensional heat conduction in solids. Based on a previous study (Chen et al., 2014, “Sub-Continuum Thermal Modeling Using Diffusion in the Lattice Boltzmann Transport Equation,” Int. J. Heat Mass Transfer, 79, pp. 666–675), phonon energy transport is separated to a ballistic part and a diffusive part, with phonon equilibrium assumed at boundaries. Steady-state temperature/total energy density solutions from continuum scales to ballistic scales are considered. A refined LBM-based numerical approach is applied to a two-dimensional simplified transistor model proposed by (Sinha et al. 2006, “Non-Equilibrium Phonon Distributions in Sub-100 nm Silicon Transistors,” ASME J. Heat Transfer, 128(7), pp. 638–647), and the results are compared with the Fourier-based heat conduction model. The three-dimensional (3D) LBM model is also developed and verified at both the ballistic and continuous limits. The impact of film thickness on the cross-plane and in-plane thermal conductivities is analyzed, and a new model of the supplementary diffusion term is proposed. Predictions based on the finalized model are compared with the existing in-plane thermal conductivity measurements and cross-plane thermal conductivity molecular dynamics (MD) results.

Current noise enhancement: channel mixing and possible nonequilibrium phonon backaction in atomic-scale Au junctions

We report measurements of the bias dependence of the Fano factor in ensembles of atomic-scale Au junctions at 77 K. Previous measurements of shot noise at room temperature and low biases have found good agreement of the Fano factor with the expectations of the Landauer–Büttiker formalism, while enhanced Fano factors have been observed at biases of hundreds of mV (Chen et al 2014 Sci. Rep. 4 4221). We find even stronger enhancement of shot noise at 77 K with an ‘excess’ Fano factor up to ten times the low bias value. We discuss the observed ensemble Fano factor bias dependence in terms of candidate models. The results are most consistent with either a bias-dependent channel mixing picture or a model incorporating noise enhancement due to current-driven, nonequilibrium phonon populations, though a complete theoretical treatment of the latter in the ensemble average limit is needed.

Thermoelectric coefficients ofn-doped silicon from first principles via the solution of the Boltzmann transport equation

We present a first-principles computational approach to calculate thermoelectric transport coefficients via the exact solution of the linearized Boltzmann transport equation, also including the effect of nonequilibrium phonon populations induced by a temperature gradient. We use density functional theory and density functional perturbation theory for an accurate description of the electronic and vibrational properties of a system, including electron-phonon interactions; carriers' scattering rates are computed using standard perturbation theory. We exploit Wannier interpolation (both for electronic bands and electron-phonon matrix elements) for an efficient sampling of the Brillouin zone, and the solution of the Boltzmann equation is achieved via a fast and stable conjugate gradient scheme. We discuss the application of this approach to $n$-doped silicon. In particular, we discuss a number of thermoelectric properties such as the thermal and electrical conductivities of electrons, the Lorenz number and the Seebeck coefficient, including the phonon drag effect, in a range of temperatures and carrier concentrations. This approach gives results in good agreement with experimental data and provides a detailed characterization of the nature and the relative importance of the individual scattering mechanisms. Moreover, the access to the exact solution of the Boltzmann equation for a realistic system provides a direct way to assess the accuracy of different flavors of relaxation time approximation, as well as of models that are popular in the thermoelectric community to estimate transport coefficients.