Nonlinear Electron-phonon Coupling Research Articles

Optical manipulation of the charge-density-wave state in RbV3Sb5.

Broken time-reversal symmetry in the absence of spin order indicates the presence of unusual phases such as orbital magnetism and loop currents1-4. The recently discovered kagome superconductors AV3Sb5 (where A is K, Rb or Cs)5,6 display an exotic charge-density-wave (CDW) state andhave emerged as astrong candidate for materialshosting a loop currentphase. The idea that the CDW breaks time-reversal symmetry7-14 is, however, being intensely debated due to conflicting experimental data15-17. Here we use laser-coupled scanning tunnelling microscopy to study RbV3Sb5. By applying linearly polarized light along high-symmetry directions, we show that the relative intensities of the CDW peaks can be reversibly switched, implying a substantial electro-striction response, indicative of strong nonlinear electron-phonon coupling. A similar CDW intensity switching is observed with perpendicular magnetic fields, which implies an unusual piezo-magnetic response that, in turn, requires time-reversal symmetry breaking. We show that the simplest CDW that satisfies these constraints is an out-of-phase combination of bond charge order and loop currents that we dub a congruent CDW flux phase. Our laser scanning tunnelling microscopy data open the door to the possibility of dynamic optical control of complex quantum phenomenon in correlated materials.

Optical Manipulation of Bipolarons in a System with Nonlinear Electron-Phonon Coupling.

We investigate full quantum mechanical evolution of two electrons nonlinearly coupled to quantum phonons and simulate the dynamical response of the system subject to a short spatially uniform optical pulse that couples to dipole-active vibrational modes. Nonlinear electron-phonon coupling can either soften or stiffen the phonon frequency in the presence of electron density. In the former case, an external optical pulse tuned just below the phonon frequency generates attraction between electrons and leads to a long-lived bound state even after the optical pulse is switched off. It originates from a dynamical modification of the self-trapping potential that induces a metastable state. By increasing the pulse frequency, the attractive electron-electron interaction changes to repulsive. Two sequential optical pulses with different frequencies can switch between attractive and repulsive interaction. Finally, we show that the pulse-induced binding of electrons is shown to be efficient also for weakly dispersive optical phonons, in the presence anharmonic phonon spectrum and in two dimensions.

Phonon modulated hopping polarons: x -representation technique

We report a breakthrough development allowing one to solve a broad class of polaron problems with highly nonlinear electron-phonon coupling that were considered unsolvable without uncontrolled simplifications in the past using a Monte Carlo technique formulated in the coordinate representation for both the particle and the atomic displacements. The only condition is the sign positivity of the hopping amplitude. The technique dramatically simplifies (with the corresponding efficiency gains) for models with dispersionless phonons. Our study sheds important light on the nature and universality of the most striking qualitative and quantitative effects demonstrated by the ``standard'' (Peierls/Su-Schrieffer-Heeger) model based on the linearized displacement-modulated hopping.

Cavity engineering of Hubbard U via phonon polaritons

Pump-probe experiments have suggested the possibility to control electronic correlations by driving infrared-active (IR-active) phonons with resonant midinfrared laser pulses. In this work we study two possible microscopic nonlinear electron-phonon interactions behind these observations, namely coupling of the squared lattice displacement either to the electronic density or to the double occupancy. We investigate whether photon-phonon coupling to quantized light in an optical cavity enables similar control over electronic correlations. We first show that inside a dark cavity electronic interactions increase, ruling out the possibility that T c in superconductors can be enhanced via effectively decreased electron-electron repulsion through nonlinear electron-phonon coupling in a cavity. We further find that upon driving the cavity, electronic interactions decrease. Two different regimes emerge: (i) a strong coupling regime where the phonons show a delayed response at a time proportional to the inverse coupling strength, and (ii) an ultra-strong coupling regime where the response is immediate when driving the phonon polaritons resonantly. We further identify a distinctive feature in the electronic spectral function when electrons couple to phonon polaritons involving an IR-active phonon mode, namely the splitting of the shake-off band into three bands. This could potentially be observed by angle-resolved photoemission spectroscopy.

Phonon-induced disorder in dynamics of optically pumped metals from nonlinear electron-phonon coupling

The non-equilibrium dynamics of matter excited by light may produce electronic phases, such as laser-induced high-transition-temperature superconductivity, that do not exist in equilibrium. Here we simulate the dynamics of a metal driven at initial time by a spatially uniform pump that excites dipole-active vibrational modes which couple nonlinearly to electrons. We provide evidence for rapid loss of spatial coherence, leading to emergent effective disorder in the dynamics, which arises in a system unitarily evolving under a translation-invariant Hamiltonian, and dominates the electronic behavior as the system evolves towards a correlated electron-phonon long-time state, possibly explaining why transient superconductivity is not observed. Our framework provides a basis within which to understand correlation dynamics in current pump-probe experiments of vibrationally coupled electrons, highlight the importance of the evolution of phase coherence, and demonstrate that pumped electron-phonon systems provide a means of realizing dynamically induced disorder in translation-invariant systems.

Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model

Determining the range of validity of Migdal’s approximation for electron-phonon (e-ph) coupled systems is a long-standing problem. Many attempts to answer this question employ the Holstein Hamiltonian, where the electron density couples linearly to local lattice displacements. When these displacements are large, however, nonlinear corrections to the interaction must also be included, which can significantly alter the physical picture obtained from this model. Using determinant quantum Monte Carlo and the self-consistent Migdal approximation, we compared superconducting and charge-density-wave correlations in the Holstein model with and without second-order nonlinear interactions. We find a disagreement between the two cases, even for relatively small values of the e-ph coupling strength, and, importantly, that this can occur in the same parameter regions where Migdal’s approximation holds. Our results demonstrate that questions regarding the validity of Migdal’s approximation go hand in hand with questions of the validity of a linear e-ph interaction.

Quantum nonlinear phononics route towards nonequilibrium materials engineering: Melting dynamics of a ferrielectric charge density wave

Negative nonlinear electron-phonon coupling involving an infrared-active phonon mode can lead to an instability towards the formation of a polar lattice distortion with ferrielectric (FE) moments accompanied by an electronic charge-density wave (CDW). Analyzing a small model system in and out of thermal equilibrium, we investigate the FE-CDW and its melting dynamics following an ultrashort laser pulse that drives the ionic dipoles. We observe nonequilibrium coherent phonon amplitude mode oscillations that soften towards the transition to the normal phase. Our case study serves as a first step towards a microscopic understanding of quantum nonlinear phononics as a basis for nonequilibrium control in quantum materials.

Light-enhanced electron-phonon coupling from nonlinear electron-phonon coupling

We investigate an exact nonequilibrium solution of a two-site electron-phonon model, where an infrared-active phonon that is nonlinearly coupled to the electrons is driven by a laser field. The time-resolved electronic spectrum shows coherence-incoherence spectral weight transfer, a clear signature of light-enhanced electron-phonon coupling. The present study is motivated by recent evidence for enhanced electron-phonon coupling in pump-probe TeraHertz and angle-resolved photoemission spectroscopy in bilayer graphene when driven near resonance with an infrared-active phonon mode [E.~Pomarico et al., Phys.~Rev.~B 95, 024304 (2017)], and by a theoretical study suggesting that transient electronic attraction arises from nonlinear electron-phonon coupling [D.~M.~Kennes et al., Nature Physics (2017), 10.1038/nphys4024]. We show that a linear scaling of light-enhanced electron-phonon coupling with the pump field intensity emerges, in accordance with a time-nonlocal self-energy based on a mean-field decoupling using quasi-classical phonon coherent states. Finally we demonstrate that this leads to enhanced double occupancies in accordance with an effective electron-electron attraction. Our results suggest that materials with strong phonon nonlinearities provide an ideal playground to achieve light-enhanced electron-phonon coupling and possibly light-induced superconductivity.

Resonant interactions between discrete phonons in quinhydrone driven by nonlinear electron-phonon coupling

This study reports experimental, computational, and theoretical evidence for a previously unobserved coherent phonon-phonon interaction in an organic solid that can be described by the application of Fano's analysis to a case without the presence of a continuum. Using Raman spectroscopy of the hydrogen-bonded charge-transfer material quinhydrone, two peaks appear near $700{\mathrm{cm}}^{\ensuremath{-}1}$ we assign as phonons whose position and line-shape asymmetry depend on the sample temperature and light scattering excitation energy. Density functional theory calculations find two nearly degenerate phonons possessing frequencies near the values found in experiment that share similar atomic motion out of the aromatic plane of electron donor and acceptor molecules of quinhydrone. Further analytical modeling of the steady-state light scattering process using the Peierls-Hubbard Hamiltonian and time-dependent perturbation theory motivates assignment of the physical origin of the asymmetric features of each peak's line shape to an interaction between two discrete phonons via nonlinear electron-phonon coupling. In the context of analytical model results, characteristics of the experimental spectra upon 2.33 eV excitation of the Raman scattering process are used to qualify the temperature dependence of the magnitude of this coupling in the valence band of quinhydrone. These results broaden the range of phonon-phonon interactions in materials in general while also highlighting the rich physics and fundamental attributes specific to organic solids that may determine their applicability in next generation electronics and photonics technologies.

Modeling of the processes of laser-nanoparticle interaction taking into account temperature dependences of parameters

Absorption, electron-phonon coupling and heating of nanoparticles (NPs) under action of short laser pulses on NPs and their cooling after the end of laser action usually has nonlinear character. Nonlinear electron-phonon coupling under action of pico- and femtosecond pulses on metal NPs depends on electron and lattice parameters. Optical (absorption, scattering, extinction) and thermo-physical (coefficient of thermal conductivity, heat capacity, etc.) parameters of different materials of NPs (metals, oxides, semiconductors, etc.) and environments (water, liquids, dielectrics, etc.) depend on temperature and determine nonlinear dynamics of NPs heating and cooling. It is very important to take into account the temperature dependence of optical and thermophysical parameters of NPs and surrounding media under investigation of absorption of laser radiation, electron-phonon coupling, nanoparticle (NP) heating, heat transfer and its cooling after the end of laser pulse action. Theoretical modeling of the processes of laser-NP interaction taking into account temperature dependences of parameters of NPs and environments was carried out. Influence of temperature dependences of these parameters on values and dynamics of the processes is determined.

Pressure dependence of superconducting transition temperature of MgB2 up to 8 GPa

AbstractThe pressure dependence of electronic structure, phonon frequencies, electron–phonon coupling constant, and the superconducting transition temperature Tc in MgB2 are calculated via zone‐center frozen phonon modes calculations using the FP‐LAPW method. The calculations are performed from pressure dependent lattice parameters measured experimentally up to 8 GPa. Under quasi‐hydrostatic pressure, Tc is found to decrease with an approximately quadratic dependence, deviating significantly from the linearity. It is shown that the pressure‐induced anisotropic change of lattice parameters, the increasing E2g phonon frequency, and nonlinear electron–phonon coupling are three key factors of producing nonlinear Tc(P) observed in MgB2. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling the Effects of Torsional Disorder on the Spectra of Poly- and Oligo-(p-phenyleneethynylenes)

The absorption spectra of phenyleneethynylene oligomers show an unusual change in shape with oligomer length. The unusual aspects of the spectra arise from rotation of the phenylene rings about the long axis of the oligomer. In the ground electronic state, the barrier to this rotation is low and the spectra in room temperature come from an ensemble of different structures. In the excited electronic state, the barrier to rotation is substantially higher, giving rise to strong nonlinear electron-phonon coupling. A multidimensional semiempirical model that includes these effects is developed for the photophysics of phenyleneethynylene oligomers. The ground-state energy is modeled with a molecular mechanics expression, and the excitation energy is modeled with an exciton model. Intermediate Neglect of Differential Overlap/Singles Configuration Interaction (INDO/SCI) calculations verify the exciton model and provide initial estimates of the model parameters. These parameters generate the qualitative features seen in experimental spectra. Inclusion of entropy effects from the multiple torsional coordinates is essential. Refinement of the parameters yields quantitative agreement with experiment. This agreement shows that coupling to torsional motion is a major factor in the spectroscopy and photophysics of these conjugated polymers.

Interpretation of high pressure experimental data in mgb2: a challenge to current theories

We review various anomalies seen in Raman spectroscopy, superconducting transition temperature T c and electrical resistance at room temperature and high pressure in the new high temperature superconductor MgB2. In order to explore the possibility of the anomalies being caused by an electronic topological transition (ETT), we have carried out detailed electronic structure studies of the band structure under pressure. Our calculations are done in the presence of a frozen-in phonon displacement that mimics the effects of thermal vibrations of the B-atoms at room temperature. Our results clearly establish the occurrence of a phonon-assisted ETT near 18 GPa. The dimensionless electron–phonon coupling λ is also found to be anomalous in its pressure variation at the same pressure. We also indicate why a detailed explanation of the phonon Raman anomaly needs the inclusion of effects arising from a non-linear electron–phonon coupling.

Giant infrared intensity of the Peierls mode at the neutral-ionic phase transition.

We present exact diagonalization results on a modified Peierls-Hubbard model for the neutral-ionic phase transition. The ground state potential energy surface and the infrared intensity of the Peierls mode point to a strong, nonlinear electron-phonon coupling, with effects that are dominated by the proximity to the electronic instability rather than by electronic correlations. The huge infrared intensity of the Peierls mode at the ferroelectric transition is related to the temperature dependence of the dielectric constant of mixed-stack organic crystals.

Giant anharmonicity and nonlinear electron-phonon coupling in MgB2: a combined first-principles calculation and neutron scattering study.

First-principles calculations of the electronic band structure and lattice dynamics for the new superconductor MgB (2) are carried out and found to be in excellent agreement with our inelastic neutron scattering measurements. The numerical results reveal that the E(2g) in-plane boron phonons near the zone center are very anharmonic and strongly coupled to the planar B sigma bands near the Fermi level. This giant anharmonicity and nonlinear electron-phonon coupling is key to quantitatively explaining the observed high T(c) and boron isotope effect in MgB (2).

Two-dimensional localized modes in conjugated polymers: the nonlinear electron–phonon coupling effect

The two-dimensional localized modes around a soliton have been investigated by using an extension of Su–Shrieffer–Heeger model, in which is included the nonlinear term of electron–phonon interaction. The results show that there appears an additional localized mode, and the two modes obtained in the previous work without the nonlinear term disappear. Furthermore, the frequencies of the modes are shifted and their localizations are changed after turning on the nonlinear term.

Nonlinear dynamics of a two-dimensional lattice

The dynamics of the nonlinear excitations in a two-dimensional (2D) φ4-diatomic lattice, with nonlinear on-site electron-phonon coupling at the polarizable ion site has been presented, without considering the self consistent phonon approximation. One of the major results obtained from our calculations is in the understanding of continuous structural phase transition, where we have obtained the minimum in soft mode frequency at a soft mode temperatureT s (>T c), not at critical temperatureT c. This occurs due to the anisotropy of such 2D systems.

The influence of structural instabilities and non-linear electron-phonon coupling on the isotope effect

In the framework of a two-component Φ 4-lattice model structural phase transitions are considered. It was found that both long-range ordered phases and glassy-like states can be described in this model. On the basis of the standard Eliashberg theory the phonon-driven superconducting transition of electrons in a single band is investigated. To do this, the electron-phonon coupling is taken linear and quadratic in the fluctuations of the lattice order parameters. The dependence of the superconducting transition temperature and the isotope effect on the defect concentration is discussed for various parameter sets. Different qualitative features are obtained. Tje La 2− x Sr x CuO 4 is taken as a reference system.

Effect of a site-dependent nonlinear electron-phonon coupling on the character of coherent and dissipative dynamics of a molecular dimer.

The dynamics of particle or quasiparticle motion in a molecular adiabatic dimer with site-dependent nonlinear polaronic coupling has been investigated in both coherent and dissipative regimes. An analysis of equations of motion for the Bloch-vector components has been performed. Our results show that the character of coherent dynamics is strongly influenced by nonlinear coupling. Exact conditions for self-trapping and transfer oscillations have been derived. It was shown that dissipative dynamics, particularly the character of the steady state, is determined by the condition of detailed balance in accordance with thermodynamics

On superconductivity in systems with non-linear electron-phonon coupling and structural instabilities

A model for the linear and quadratic coupling of an anharmonic optical phonon branch producing a structural phase transition at T=T0 with a band of free electrons has been treated within an extended Eliashberg theory. The quadratic coupling causes a critical behaviour of Tc(T0) as Tc to T0 due to a renormalization of the linear coupling constant by a non-vanishing lattice order parameter for T<T0. The parameter of the isotope effect alpha shows an unusual behaviour. Zero or even negative values of alpha are obtained if the superconducting transition is near the structural one.