Strong Electron-phonon Coupling Regime Research Articles

Competing charge-density wave instabilities in the kagome metal ScV6Sn6

Owing to its unique geometry, the kagome lattice hosts various many-body quantum states including frustrated magnetism, superconductivity, and charge-density waves (CDWs). In this work, using inelastic X-ray scattering, we discover a dynamic short-range sqrt{3}times sqrt{3}times 2 CDW that is dominant in the kagome metal ScV6Sn6 above TCDW ≈ 91 K, competing with the sqrt{3}times sqrt{3}times 3 CDW that orders below TCDW. The competing CDW instabilities lead to an unusual CDW formation process, with the most pronounced phonon softening and the static CDW occurring at different wavevectors. First-principles calculations indicate that the sqrt{3}times sqrt{3}times 2 CDW is energetically favored, while a wavevector-dependent electron-phonon coupling (EPC) promotes the sqrt{3}times sqrt{3}times 3 CDW as the ground state, and leads to enhanced electron scattering above TCDW. These findings underscore EPC-driven correlated many-body physics in ScV6Sn6 and motivate studies of emergent quantum phases in the strong EPC regime.

Time-Dependent Density Matrix Renormalization Group Method for Quantum Transport with Phonon Coupling in Molecular Junction.

Quantum transport in molecular junctions has attracted great attention. The charge motion in a molecular junction can cause geometric deformation, leading to strong electron phonon coupling, which was often overlooked. We have formulated a nearly exact method to assess the time-dependent current and occupation number in the molecular junction modeled by the electron-phonon coupled bridge state using the time-dependent density matrix renormalization group (TD-DMRG) method. The oscillation period and amplitude of the current are found to be dependent on the electron phonon coupling strength and energy level alignment with the electrodes. In an attempt to better understand these phenomena, we have devised a new approximation that explains the bistability phenomenon and the behavior of steady currents in the strong electron-phonon coupling regime. Comparisons have been made with the multilayer-multiconfiguration time-dependent Hartree (ML-MCTDH) method and the analytical result in the purely electronic limit. Furthermore, we explore the entropy of different orderings, extending to the electron phonon model problems. Regarding finite temperature, the thermal Bogoliubov transformation of both fermions and bosons is used and compared with imaginary time evolution results.

Atomic, electronic, and superconducting properties of Zr[formula omitted]Ir compound

We have investigated the structural, electronic, mechanical, phononic, and superconducting properties of the Zr2Ir compound with a body-centered tetragonal crystal structure using first-principles calculations. Our analysis reveals that the Zr2Ir compound shows mechanical and dynamically stable by using with and without spin–orbit coupling (SOC) effect. After calculating some properties such as elastic constants, Bulk modulus, Young’s modulus, Poisson ratio, Debye temperature, and sound velocity, we found that Zr2Ir is ductile. When the elastic constants C11 and C33 are compared, it is determined that the situation changes in the opposite direction under the effect of SOC, that is, more compressibility along the x-axis turns into the z-axis. Here, the electronic band structure and intensity of the states calculated for the compound show a metallic character. The superconducting critical temperature (Tc) and electron–phonon coupling constant (λ) were found to be 7.50 K and 0.93 without SOC and 7.62 K and 0.96 with SOC, respectively. We determined that although the Zr2Ir compound has a strong electron–phonon coupling regime, the inclusion of SOC slightly reduces its critical temperature and electron–phonon coupling constant.

Formation of strong-coupling (bi)polarons and related in-gap states in lightly-doped cuprate superconductors

The formation of large polarons and bipolarons and related in-gap states in lightly-doped cuprates is studied in the strong electron–phonon coupling regime. The ground-state energies, binding energies and binding radius of strong-coupling large (bi)polarons are calculated using the continuum model and adiabatic approximation taking into account both the short- and long-range electron–phonon interactions. The obtained results show that the binding energies of such large (bi)polarons in the cuprates are progressively increased with decrease in the high frequency dielectric constant [Formula: see text] and ratio [Formula: see text] (where [Formula: see text] is the static dielectric constant). As a result, large (bi)polarons become nearly small (bi)polarons. It is shown that hole carriers strongly interact with acoustic and optical phonons and their self-trapping leads to the formation of (bi)polaronic states in the charge-transfer (CT) gap of the cuprates. As the cuprate system is doped, the CT gap of the parent compound is filled in with low-energy (bi)polaronic states. The calculated energies of such (bi)polaronic states are in good agreement with the experimentally observed energies of new states appearing in the CT gap of the parent cuprates. The calculated values of the binding radius of large polarons are also well consistent with the existing experimental data.

Environment-Assisted and Environment-Hampered Efficiency at Maximum Power in a Molecular Photocell

The molecular photo cell, i.e., a single molecule donor-acceptor complex, beside being technologically important, is a paradigmatic example of a many-body system operating in strong non-equilibrium. The quantum transport and the photo-voltaic energy conversion efficiency of the photocell, attached to two external leads, are investigated within the open quantum system approach by solving the Lindblad master equation. The interplay of the vibrational degrees of freedom corresponding to the molecules (via the electron-phonon interaction) and the environment (via dephasing) shows its signature in the efficiency at maximum power. We find vibration assisted electron transport in the medium to strong electron-phonon coupling regime when the system does not suffer dephasing. Exposure to dephasing hampers such a vibration assisted electron transport in a specific range of dephasing rate.

A variational approach for dissipative quantum transport in a wide parameter space.

Recent development of theoretical method for dissipative quantum transport has achieved notable progresses in the weak or strong electron-phonon coupling regime. However, a generalized theory for dissipative quantum transport in a wide parameter space had not been established. In this work, a variational polaron theory for dissipative quantum transport in a wide range of electron-phonon coupling is developed. The optimal polaron transformation is determined by the optimization of the Feynman-Bogoliubov upper bound of free energy. The free energy minimization ends up with an optimal mean-field Hamiltonian and a minimal interaction Hamiltonian. Hence, second-order perturbation can be applied to the transformed system, resulting in an accurate and efficient method for the treatment of dissipative quantum transport with different electron-phonon coupling strength. Numerical benchmark calculation on a single site model coupled to one phonon mode is presented.

Phonon effects on the current noise spectra and the ac conductance of a single molecular junction

By using nonequilibrium Green’s functions and the equation of motion method, we formulate a self-consistent field theory for the electron transport through a single-molecule junction (SMJ) coupled with a vibrational mode. We show that the nonequilibrium dynamics of the phonons in a strong electron–phonon coupling regime can be taken into account appropriately in this self-consistent perturbation theory, and the self-energy of the phonons is connected with the current fluctuations in the molecular junction. We calculate the finite-frequency nonsymmetrized noise spectra and the ac conductance, which reveal a wealth of inelastic electron tunneling characteristics on the absorption and emission properties of this SMJ. In the presence of a finite bias voltage and the electron tunneling current, the vibration mode of the molecular junction is heated and driven to an unequilibrated state. The influences of unequilibrated phonons on the current and the noise spectra are investigated.

Quantum transport of double quantum dots coupled to an oscillator in arbitrary strong coupling regime

In this paper, we investigate the quantum transport of a double quantum dot coupled with a nanomechanical resonator at arbitrary strong electron-phonon coupling regimes. We employ the generalized quantum master equation to study full counting statistics of currents. We demonstrate the coherent phonon states method can be applied to decouple the electron-phonon interaction non-perturbatively. With the help of this non-perturbative treatment of electron-phonon couplings, we find that the phonon-assisted resonant tunneling emerges when the excess energy from the left quantum dot to the right one can excite integer number of phonons and multi-phonon excitations can enhance the transport in strong electron-phonon coupling regime. Moreover, we find that as the electron-phonon coupling increases, it first plays a constructive role to assist the transport, and then plays the role of scattering and strongly represses the transport.

Impact of spin-orbit coupling on the Holstein polaron

We utilize an exact variational numerical procedure to calculate the ground state properties of a polaron in the presence of a Rashba-like spin orbit interaction. Our results corroborate with previous work performed with the Momentum Average approximation and with weak coupling perturbation theory. We find that spin orbit coupling increases the effective mass in the regime with weak electron phonon coupling, and decreases the effective mass in the intermediate and strong electron phonon coupling regime. Analytical strong coupling perturbation theory results confirm our numerical results in the small polaron regime. A large amount of spin orbit coupling can lead to a significant lowering of the polaron effective mass.

Influence of La doping on elastic and thermodynamic properties of SrMoO 3

The elastic and thermodynamic properties for Sr 1− x La x MoO 3 ( x = 0.0, 0.05, 0.1, 0.15, and 0.2) with temperature have been investigated, probably for the first time, by using modified rigid ion model (MRIM). The computed results on the elastic constants ( C 11, C 12, and C 44) are the first report on them. Using these elastic constants we have computed other elastic properties such as B, β, G′, G, E, σ, B/ G ratio, Cauchy pressure ( C 12 − C 44) and Lame's parameters ( μ, λ). We have also reported the thermodynamic properties such as ϕ, f, θ D, θ D1, υ 0, υ 1, γ, and α. The values of Young's modulus, shear modulus and compressibility for SrMoO 3 are in good agreement with the available experimental data. The concentration ( x) dependence of θ D in Sr 1− x La x MoO 3 suggests that increased La doping drives the system effectively away from the strong electron–phonon coupling regime. Specific heat is reported in the wide temperature range and compared with the respective experimental data available in the literature. The thermal expansion coefficient of SrMoO 3 is in good agreement with the other theoretical data.

Hartree-Fock approximation of bipolaron state in quantum dots and wires

The bipolaronic ground state of two electrons in a spherical quantum dot or a quantum wire with parabolic boundaries is studied in the strong electron-phonon coupling regime. We introduce a variational wave function that can conveniently conform to represent alternative ground state configurations of the two electrons, namely, the bipolaronic bound state, the state of two individual polarons, and two nearby interacting polarons confined by the external potential. In the bipolaron state the electrons are found to be separated by a finite distance about a polaron size. We present the formation and stability criteria of bipolaronic phase in confined media. It is shown that the quantum dot confinement extends the domain of stability of the bipolaronic bound state of two electrons as compared to the bulk geometry, whereas the quantum wire geometry aggravates the formation of stable bipolarons.

Optical-phonon scattering and theory of magneto-polarons in a quantum well in a strong magnetic field

We report a theoretical study of the carrier relaxation in a quantum cascade laser (QCL) subjected to a strong magnetic field. Both the alloy (GaInAs) disorder effects and the Frohlich interaction are taken into account when the electron energy differences are tuned to the longitudinal optical (LO) phonon energy. In the weak electron-phonon coupling regime, a Fermi's golden rule computation of LO phonon scattering rates shows a very fast non-radiative relaxation channel for the alloy broadened Landau levels (LL's). In the strong electron-phonon coupling regime, we use a magneto-polaron formalism and compute the electron survival probabilities in the upper LL's with including increasing numbers of LO phonon modes for a large number of alloy disorder configurations. Our results predict a nonexponential decay of the upper level population once electrons are injected in this state.

Charge dynamics in quasi-one dimensional β-Sr1/6V2O5

Polarized infrared reflectivity was measured as a function of temperature on a quasi-one dimensional β-Sr0.17V2O5 single crystal. Along the conduction direction, the optical conductivity exhibits a weak electronic background in the far infrared and a large mid infrared band. Sum rule analysis shows that both far infrared and midinfrared bands arise from 3d vanadium electrons. As temperature is decreased, the mid infrared band slightly narrows and redshifts, but does not exhibit drastic change. In contrast, the spectral weight grows at low frequencies and peaks appear in the phonon energy range. In the transverse direction, β-Sr0.17V2O5 shows an insulator-like behaviour at all temperatures. The optical response is compared with the iso-electronic and iso-structural compound β-Na0.33V2O5. Although spectra are very similar in both compounds at room temperature, their temperature dependence differs. However, some general trends indicate that charge carriers are of the same nature in both compounds. The results suggest that electron- phonon coupling is relevant to explain the optical properties of β-Sr0.17V2O5. The optical response along the conducting direction is assigned to an adiabatic small polaron absorption, in intermediate or strong electron-phonon coupling regime. In this framework, the optical conductivity is in qualitative agreement with recent Dynamical Mean Field Theory results over a wide temperature range.

Optical conductivity in thet−JHolstein model

Using a recently developed numerical method we compute charge stiffness and optical conductivity of the $t\text{\ensuremath{-}}J$ model coupled to optical phonons. Coherent hole motion is most strongly influenced by the electron-phonon coupling within the physically relevant regime of the exchange interaction. We find unusual nonmonotonous dependence of the charge stiffness as a function of the exchange coupling near the crossover to the strong electron-phonon coupling regime. Optical conductivity in this regime shows a two-peak structure. The low-frequency peak represents local magnetic excitation, attached to the hole, while the higher-frequency peak corresponds to the mid-infrared band that originates from coupling to spin-wave excitations, broadened and renormalized by phonon excitations. We observe no separate peak at or slightly above the phonon frequency. This finding suggests that in the framework of the $t\text{\ensuremath{-}}J$ Holstein model the two-peak structure seen in recent optical measurements is due to magnetic excitations coupled to lattice degrees of freedom via doped charge carriers.

GREEN FUNCTION CALCULATIONS FOR THE THREE-DIMENSIONAL HOLSTEIN MODEL

The many-body Green functions for the three-dimensional electron–phonon Holstein model are calculated via the Feynman diagram technique. The lowest-order contributions to the one-electron self-energy are considered (the Hartree–Fock approximation). The chemical potential is adjusted to yield the desired band-filling. The temperature dependence of the chemical potential has the correct asymptotic form in the non-interacting limit. The behavior of the one-electron occupancy factor is examined for various parameter values of the model. Tian's theorem is satisfied at half-filling. Luttinger liquid behavior is observed in the strong electron–phonon coupling regime.

Pair tunneling and shot noise through a single molecule in a strong electron-phonon coupling regime

We investigate the electronic transport through a single molecule in a strong electron-phonon coupling regime. Based on a particle-hole transformation, which is made suitable for a nonequilibrium situation, we treat the pair tunneling and cotunneling on an equal footing. We propose an experimental setup to enhance the visibility of pair tunneling, which has no Franck-Condon suppression. We also discuss the shot noise characteristics.

Magnetoconductance through a vibrating molecule in the Kondo regime

The effect of a magnetic field on the equilibrium spectral and transport properties of a single-molecule junction is studied using the numerical renormalization group method. The molecule is described by the Anderson-Holstein model in which a single vibrational mode is coupled to the electron density. The effect of an applied magnetic field on the conductance in the Kondo regime is qualitatively different in the weak and strong electron-phonon coupling regimes. In the former case, the Kondo resonance is split and the conductance is strongly suppressed by a magnetic field $g mu_B B \gtrsim k_BT_K$, with $T_K$ the Kondo temperature. In the strong electron-phonon coupling regime a charge analog of the Kondo effect develops. In this case the Kondo resonance is not split by the field and the conductance in the Kondo regime is enhanced in a broad range of values of $B$.

Polaron states in InAs/GaAs quantum dots: strong electron–phonon coupling regime

We report on the magneto-optical evidence and theoretical modelling of polaron effects in self-assembled InAs/GaAs quantum dots. Using far-infrared magneto-transmission experiments performed up to 28 T at T=2 K in doped QDs samples, we investigate the electronic transitions between the ground and first excited states. We observe very large anticrossings in the B-dispersion of the magneto-optical transitions, whose existence cannot be explained by a purely electronic model. We thus calculate the coupling between the mixed electron-lattice states using the Fröhlich Hamiltonian and determine the polaron states and the energies of the dipolar electric transitions. An excellent agreement between the calculations and the experimental data is obtained, demonstrating that the magneto-optical transitions occur between polaron states. The time dependence of the survival probability is calculated for the various non-interacting electron–phonon states. Such probabilities are found to oscillate and do not show an exponential decay as it would be the case for a weak coupling regime. This last argument confirms that the electrons and the LO-phonons experience a strong coupling regime in QDs.

Electron-phonon quantum kinetics in the strong-coupling regime

Summary form only given. While ultrafast semiconductor spectroscopy has investigated scattering times, i.e. the time between different scattering events, for many years, quantum kinetics asks for the duration of one scattering process, i.e. for the memory time. For the electron-LO-phonon quantum kinetics in the weak coupling regime (GaAs), quantum kinetics shows up as an oscillation in the coherent four-wave mixing (FWM) signal. This observation was interpreted as an oscillation of a band electron back and forth between its initial and a final state it scatters into (for long times) due to the emission of n=1 phonon. We discuss the strong electron-phonon coupling regime, in which n>1 phonon scattering processes are expected to become important as well. Bulk ZnSe is used as a model system, in which the Frohlich-constant is about one order of magnitude larger than in GaAs. In our experiments, the band edge of an antireflection-coated, 100 nm thin film of ZnSe at low temperatures is excited with blue, transform-limited 13 fs pulses. Two-pulse, three-pulse FWM-experiments and coherent control experiments are performed and discussed.

Polaron theory of mid-infrared conductivity a numerical cluster solution

Mid-infrared spectra are obtained with numerical calculations of the optical conductivity σ(ω) of a finite-size Holstein model. The results show that the analytic formula of Reik for the optical conductivity is valid only in a strong electron-phonon coupling regime. σ(ω) shows a number of peaks corresponding to the bound states of polarons with a different number of phonons. Calculation of σ(ω) has also been done in the adiabatic limit in the one-dimensional case. It is found that for intermediate coupling the peak in σ(ω) is strongly asymmetric. The optical conductivity of the two-site model in the presence of two electrons is studied. Numerical results show a shift of the peak in σ(ω) to the low-energy region with an increasing Hubbard U for the strong electron-phonon interaction (E p>U) whereas the peak moves to the high-energy region for U>E p high-energy region starts to develop in the large U limit in the presence of phonons. The significance of these calculations for the experimental observations of the mid-infrared spectra of high- T c cuprates is discussed.