Electron-phonon System Research Articles

Bose-Einstein-condensate polaron in harmonic trap potentials in the weak-coupling regime: Lee-Low-Pines–type approach

We have calculated the zero-temperature binding energy of a single impurity atom immersed in a Bose-Einstein condensate of ultracold atoms that are trapped in an axially symmetric harmonic potential, where the impurity interacts with bosonic atoms in the condensate via a low-energy s-wave scattering. In this case, bosons are excited around the impurity to form a quasiparticle, namely, a BEC polaron. We have developed a variational method, {\it a la} Lee-Low-Pines (LLP) theory for electron-phonon systems, for description of the polaron with a conserved angular momentum around the symmetric axis. It is found in numerical results that the binding energy between the impurity and the excited bosons break the degeneracy with respect to the total angular momentum of the polaron. The angular momentum is partially shared by the excited bosons, which is due to a mechanism similar to the drag effect on the polaron momentum by a phonon cloud in the LLP theory.

Normal state of metallic hydrogen sulfide

Generalized theory of the normal properties of the metal in the case of the electron-phonon (EP) systems with not constant density of electronic states is used to examine the normal state of the SH3 and SH2 phase of the hydrogen sulfide at different pressures. The frequency dependence of the real and imaginary part of the self-energy part (SP) of the electron Green's function, the real and imaginary part of the complex renormalization of the electron mass, the real and imaginary part of the complex renormalization of the chemical potential, as well as the renormalized with the strong electron-phonon interaction the electron density of states are calculated. The calculations are performed for the stable orthorhombic IM-3M hydrogen sulfide SH3 structure at three pressures P = 170 GPa, P = 180 GPa, P = 225 GPa and SH2 structure with the symmetry I4/MMM (D4H-17) for the three values of pressure P = 150 GPa , P = 180 GPa, P = 225 GPa at the temperature of T = 200K. Key words: hydrogen sulfide, electron-phonon system, the pressure, the electronic properties.

Metal hydrogen sulfide superconducting temperature

AbstractÉliashberg theory is generalized to the electronphonon (EP) systems with the not constant density of electronic states. The phonon contribution to the anomalous electron Green’s function (GF) is considered. The generalized Éliashberg equations with the variable density of electronic states are resolved for the hydrogen sulphide SHThe results of the solution of the Eliashberg equations for the Im-3m (170 GPa), Im-3m (200 GPa) and R3m (120 GPa) phases are presented. A peak value T

Critical temperature of metallic hydrogen sulfide at 225-GPa pressure

The Eliashberg theory generalized for electron—phonon systems with a nonconstant density of electron states and with allowance made for the frequency behavior of the electron mass and chemical potential renormalizations is used to study T c in the SH3 phase of hydrogen sulfide under pressure. The phonon contribution to the anomalous electron Green’s function is considered. The pairing within the total width of the electron band and not only in a narrow layer near the Fermi surface is taken into account. The frequency and temperature dependences of the complex mass renormalization ReZ(ω), the density of states N(e) renormalized by the electron—phonon interactions, and the electron—phonon spectral function obtained computationally are used to calculate the anomalous electron Green’s function. A generalized Eliashberg equation with a variable density of electron states has been solved. The frequency dependence of the real and imaginary parts of the order parameter in the SH3 phase has been obtained. The value of T c ≈ 177 K in the SH3 phase of hydrogen sulfide at pressure P = 225 GPa has been determined by solving the system of Eliashberg equations.

Reconstruction of the electron spectrum in a metal hydrogen sulfide

Generalized Eliashberg theory of the normal properties of a metal electron-phonon system with a non constant electron density of states has been used to study the effect of the conduction band reconstruction. The electron density of states of the metallic phase of the hydrogen sulfide renormalized by the strong electron-phonon coupling at a pressure of P = 225 GPa has been calculated. It has been found that the reconstructed conduction band contains a series of narrow energy pockets.

Dynamical Cooper pairing in nonequilibrium electron-phonon systems

We analyze Cooper pairing instabilities in strongly driven electron-phonon systems. The light-induced non-equilibrium state of phonons results in a simultaneous increase of the superconducting coupling constant and the electron scattering. We demonstrate that the competition between these effects leads to an enhanced superconducting transition temperature in a broad range of parameters. Our results may explain the observed transient enhancement of superconductivity in several classes of materials upon irradiation with high intensity pulses of terahertz light, and may pave new ways for engineering high-temperature light-induced superconducting states.

Quasi-one Dimensional Topological Insulator: Möbius Molecular Devices in Peierls Transition**Supported by the National Natural Science Foundation of China under Grant No. 11504241 and the Natural Science Foundation of Shenzhen University under Grant No. 201551

We show that, assisted by the Peierls transition of lattice, as a quasi-one dimensional (Q1D) tight binding system, a Möbius molecular device can behave as a simple topological insulator. With the Peierls phase transition to form a domain wall, the solitonary zero modes exist as the ground state of this electron-phonon hybrid system, which is protected by the Z2 topology of the Möbius strip. The robustness of the ground state prevents these degenerate zero modes from their energy spectrum splitting caused by any perturbation.

Critical temperature of metallic hydrogen at a pressure of 500 GPa

The Eliashberg theory generalized for electron–phonon systems with a variable electron density of states is used to study Tc in the I41/AMD phase of metallic hydrogen under compression taking into account the frequency behavior of the renormalization of the mass of the electron and the chemical potential. The phonon contribution to the anomalous electron Green’s function is considered. Pairing is taken into account within the entire electron band rather than in a narrow region near the Fermi surface. The frequency and temperature dependences of the complex renormalization of the mass Re Z(ω), as well as the density of states N(ω) renormalized by the electron–phonon coupling and the spectral function of the electron–phonon coupling, which are obtained in calculations, are used to calculate the anomalous electron Green’s function. The frequency dependence of the real and imaginary parts of the order parameter in the I41/AMD phase is obtained. The solution of the system of Eliashberg equations gives the value Tc = 217 K in the I41/AMD phase of hydrogen at a pressure of 500 GPa.

Reconstruction of the conduction band in metallic hydrogen sulfide

The theory of the normal properties of a metal generalized to the case of particular properties of an electron band with a finite width for electron–phonon systems with a varying electron density of states has been used to study the normal state of the SH3 phase of hydrogen sulfide at a pressure of 225 GPa and a temperature of 200 K. The frequency dependences of the real, ReΣ(ω), and imaginary, ImΣ(ω), parts of the selfenergy part of the Green’s function of the electron Σ(ω), as well as the electron density of states N(e) of the Im–3m stable orthorhombic structure of SH3 hydrogen sulfide at a pressure of P = 225 GPa, which is renormalized by the strong electron–phonon coupling, have been calculated. It has been established that a part of the electron conduction band of the SH3 phase of hydrogen sulfide adjacent to the Fermi level undergoes renormalization-induced reconstruction in the form of a number of energy pockets with the widths equal to fractions of the characteristic phonon energies of the system.

Density matrix embedding theory for interacting electron-phonon systems

We describe the extension of the density matrix embedding theory (DMET) framework to coupled interacting fermion-boson systems. This provides a frequency-independent, entanglement embedding formalism to treat bulk fermion-boson problems. We illustrate the concepts within the context of the one-dimensional Hubbard-Holstein model, where the phonon bath states are obtained from the Schmidt decomposition of a self-consistently adjusted coherent state. We benchmark our results against accurate density matrix renormalization group calculations.

Multiple amplitude modes in strongly coupled phonon-mediated superconductors

We study collective amplitude modes of the superconducting order parameter in strongly-coupled electron-phonon systems described by the Holstein model using the nonequilibrium dynamical mean-field theory with the self-consistent Migdal approximation as an impurity solver. The frequency of the Higgs amplitude mode is found to coincide with the superconducting gap even in the strongly-coupled (beyond BCS) regime. Besides the Higgs mode, we unravel another collective mode involving the dynamics of both the phonons and the superconducting order parameter. The frequency of this mode, higher than twice the renormalized phonon frequency in the superconducting phase, is shown to reflect a strong electron-mediated phonon-phonon interaction. Both types of collective excitations contribute to time-resolved photoemission spectra after a strong laser pump as vertex corrections to produce resonance peaks, which allows one to distinguish them from quasiparticle excitations.

Matrix-product-state method with a dynamical local basis optimization for bosonic systems out of equilibrium

We present a method for simulating the time evolution of one-dimensional correlated electron-phonon systems which combines the time-evolving block decimation algorithm with a dynamical optimization of the local basis. This approach can reduce the computational cost by orders of magnitude when boson fluctuations are large. The method is demonstrated on the nonequilibrium Holstein polaron by comparison with exact simulations in a limited functional space and on the scattering of an electronic wave packet by local phonon modes. Our study of the scattering problem reveals a rich physics including transient self-trapping and dissipation.

Nonequilibrium kinetics of the electron–phonon sybsystem of a crystal in a strong electric field as a base of the electroplastic effect

We present the results of a kinetic analysis of nonequilibrium dynamics of the electron–phonon system of a crystal in a strong electric field based on the proposed method of numerically solving a set of Boltzmann equations for electron and phonon distribution functions without expanding the electron distribution function into a series in the phonon energy. It is shown that the electric field action excites the electron subsystem, which by transferring energy to the phonon subsystem creates a large amount of short-wave phonons that effectively influence the lattice defects (point, lines, boundaries of different phases), which results in a redistribution of and decrease in the lattice defect density, in damage healing, in a decrease in the local peak stress, and a decrease in the degradation level of the construction material properties.

Reasons for high-temperature superconductivity in the electron–phonon system of hydrogen sulfide

We have calculated the electron and phonon spectra, as well as the densities of the electron and phonon states, of the stable orthorhombic structure of hydrogen sulfide SH2 in the pressure interval 100–180 GPa. It is found that at a pressure of 175 GPa, a set of parallel planes of hydrogen atoms is formed due to a structural modification of the unit cell under pressure with complete accumulation of all hydrogen atoms in these planes. As a result, the electronic properties of the system become quasi-two-dimensional. We have also analyzed the collective synphase and antiphase vibrations of hydrogen atoms in these planes, leading to the occurrence of two high-energy peaks in the phonon density of states.

High T c in cuprates as a universal property of the electron–phonon system

The Eliashberg theory, which is generalized due to peculiar properties of the finite-width electron band for electron–phonon (EP) systems with a variable electron density of states (DOS), as well as with allowance for the electron–hole nonequivalence of the frequency behavior of the chemical potential renormalization depending on the doping level and electron correlations in the vertex function, is used to study Tc in cuprates. The phonon contribution to the nodal anomalous electron Green’s function (GF) is considered. Pairing within the total width of the electron band, and not only in a narrow layer at the Fermi surface, is taken into account. The calculated frequency and temperature dependences, as well as the dependence on the doping level of the complex renormalization ReZ, ImZ of the mass, complex renormalization Reχ(ω), Imχ(ω) of the chemical potential, and DOS N(e) renormalized due to the EP interaction are used to calculate the electron nodal anomalous GF. It is found that the effect of suppressing the high-frequency contribution to the Eliashberg equations derived anew for the EP system with a finite width of the electron band is a decisive factor for the manifestation of the effect of high-temperature superconductivity (HTSC). It is shown that in the vicinity of the optimal hole-type doping level in cuprates, the high value of Tc is reproduced by the spectral function of the electron–phonon interaction, which is obtained from tunneling experiments. Upon an increase in the doping level, leading to an increase in the degree of electron–hole nonequivalence, the new logarithmic term appearing in the equations for Tc has a tendency to increase Tc, while intensification of damping of charge carriers (especially suppression of the cutoff factor) leads to a decrease in Tc.

Effects of electron–acoustic phonon interaction in the presence of spin–orbit couplings in graphene

We investigate the effects of electron-zone center acoustic phonon interaction on spin–orbit couplings in pristine graphene. We examine the polaron formation and analyse the effects of spin–orbit couplings on polaron formation and electron–phonon couplings. Fröhlich type Hamiltonian within the continuum limit is used to describe the electron–phonon system. With theoretical analysis, we show that, in the presence of electron–phonon interaction, the intrinsic and Rashba spin–orbit couplings of graphene become k dependent and Rashba spin–orbit coupling exhibits different characters with respect to spin orientation. Even there is a symmetry between electron–hole states if only one spin–orbit mechanism is present, electron–phonon coupling induces symmetry breaking between electron–hole states. Moreover, polaronic effect is decreased for both spin states, but it is increased beyond the some critical values of k for spin-up states in the presence of spin–orbit couplings.

High-temperature superconductivity in two-band materials with interband pairing

Eliashberg theory is generalized with account of the specific properties of two-band electron-phonon (EP) systems. The superconducting transition temperature T c is examined in two-band materials, one of the representatives of which are pnictides. The strong EP coupling and the pairing within the full width of the electron band and not only in a narrow region near the Fermi surface are taken into account. It is found that the effect of the pairing of electrons belonging to different bands is crucial to the appearance of high T c in these materials. It is shown that the high T c value in the materials, such as pnictides, is displayed with the use of a two-band spectral function of the EP interaction derived from calculations and from tunnel experiments. The existence of specific conditions for the high T c appearance in the two-band materials is established.

Effective temperature of the non-equilibrium electrons in a degenerate semiconductor at low lattice temperature

The energy balance equation for the electron–phonon system is recast taking the degeneracy of the carrier ensemble into account. The effect of degeneracy on the field dependence of the temperature of the non-equilibrium carriers has been studied by solving the same equation. The high field distribution function of the carriers is assumed to be given by the Fermi Dirac function at the field dependent carrier temperature. The distribution function has been approximated in a way that facilitates analytical solution of the problem without any serious loss of accuracy. The field dependence of the electron temperature thus obtained seems to be significantly different from what follows had the degeneracy not been taken into account. The agreement of the results obtained from the present analysis with the available experimental data for Ge and InSb are quite satisfactory. The scope of further refinement of the present theory is highlighted.

General theory of intraband relaxation processes in heavily doped graphene

The frequency and wave-vector-dependent memory function in the longitudinal conductivity tensor of weakly interacting electronic systems is calculated by using an approach based on quantum transport equations. In this paper, we show that there is a close relation between the single-electron self-energy, the electron-hole pair self-energy, and the memory function. It is also shown in which way singular long-range Coulomb interactions, together with other $\mathbf{q}\ensuremath{\approx}\mathbf{0}$ scattering processes, drop out of both the memory function and the related transport equations. The theory is illustrated on heavily doped graphene, which is the prototype of weakly interacting single-band electron-phonon systems. A steplike increase of the width of the quasiparticle peak in angle-resolved photoemission spectra at frequencies of the order of the frequency of in-plane optical phonons is shown to be consistent with the behavior of an intraband plasmon peak in the energy loss spectroscopy spectra. Both anomalies can be understood as a direct consequence of weak electron scattering from in-plane optical phonons.

Negative-Temperature State Formed and Interactions Inverted by Symmetric Monocycle Optical Pulse Excitation

The excited state dynamics of correlated electron and electron-phonon systems triggered by an oscillating electric-field pulse of large amplitude are theoretically investigated. A "negative-temperature" state and inversion of electron-electron and electron-phonon interactions are induced even by a symmetric monocycle pulse. This fact is numerically demonstrated, using the exact diagonalization method, in a band-insulator phase of one-dimensional three-quarter-filled strongly dimerized extended Peierls-Hubbard and Holstein models. When the total-energy increment is maximized as a function of the electric field amplitude, the occupancy of the bonding and antibonding orbitals is inverted to produce a negative-temperature state. Around this state, the dependences of time-averaged electron-electron and electron-phonon correlation functions on interaction parameters are opposite to those in the ground state.