Electron-phonon System Research Articles

Colossal phonon drag enhanced thermopower in lightly doped diamond

Diamond is one of the most studied materials because of its unique combination of remarkable electrical, mechanical, thermal and optical properties. Using a fully self-consistent ab initio theory of coupled electron-phonon transport, we reveal another striking behavior: a huge drag enhancement of the thermopower of lightly doped diamond. Thermopower values of around 100,000 μV K−1 are found at 100 K, significantly exceeding the highest previously measured value in the correlated metal FeSb2, and occurring at much higher temperatures. The enormous thermopower in diamond arises primarily from exceptionally weak anharmonic phonon decay around and below 100 K that facilitates efficient momentum exchange between charge carriers and phonons through electron-phonon interactions. Exceedingly large thermoelectric power factors are also identified. This work gives insights into the physics of the coupled electron-phonon system in solids and advances our understanding of thermoelectric transport in the regime of strong drag.

Zigzag HgTe Nanowires Modify the Electron-Phonon Interaction in Chirality-Refined Single-Walled Carbon Nanotubes.

Atomically thin nanowires (NWs) can be synthesized inside single-walled carbon nanotubes (SWCNTs) and feature unique crystal structures. Here we show that HgTe nanowires formed inside small-diameter (<1 nm) SWCNTs can advantageously alter the optical and electronic properties of the SWCNTs. Metallic purification of the filled SWCNTs was achieved by a gel column chromatography method, leading to an efficient extraction of the semiconducting and metallic portions with known chiralities. Electron microscopic imaging revealed that zigzag HgTe chains were the dominant NW geometry in both the semiconducting and metallic species. Equilibrium-state and ultrafast spectroscopy demonstrated that the coupled electron–phonon system was modified by the encapsulated HgTe NWs, in a way that varied with the chirality. For semiconducting SWCNTs with HgTe NWs, Auger relaxation processes were suppressed, leading to enhanced photoluminescence emission. In contrast, HgTe NWs enhanced the Auger relaxation rate of metallic SWCNTs and created faster phonon relaxation, providing experimental evidence that encapsulated atomic chains can suppress hot carrier effects and therefore boost electronic transport.

Energy, Momentum, and Angular Momentum Transfer between Electrons and Nuclei.

The recently developed exact factorization approach condenses all electronic effects on the nuclear subsystem into scalar and vector potentials that appear in an effective time dependent Schrödinger equation. Starting from this equation, we derive subsystem Ehrenfest identities characterizing the energy, momentum, and angular momentum transfer between electrons and nuclei. An effective electromagnetic force operator induced by the electromagnetic field corresponding to the effective scalar and vector potentials appears in all three identities. The effective magnetic field has two components that can be identified with the Berry curvature calculated with (a)different Cartesian coordinates of the same nucleus and (b)arbitrary Cartesian coordinates of two different nuclei. (a)has a classical interpretation as the induced magnetic field felt by the nucleus, while (b)has no classical analog. Subsystem Ehrenfest identities are ideally suited for quantifying energy transfer in electron-phonon systems. With two explicit examples we demonstrate the usefulness of the new identities.

Dynamics of photoinduced entanglement generation between remote electron-phonon systems

We numerically study the dynamics of quantum entanglement generation between remote electron-phonon systems by photoirradiation employing a model of multiple spins and boson modes. The Schmidt decomposition on the time-dependent wavefunction enables us to discuss the mechanism of the entanglement generation as dynamical behaviors of the singular vectors. The calculated results show that an effective entanglement source will be provided by an appropriate measurement on the phonon state.

Devil's staircase of topological Peierls insulators and Peierls supersolids

We consider a mixture of ultracold bosonic atoms on a one-dimensional lattice described by the XXZ-Bose-Hubbard model, where the tunneling of one species depends on the spin state of a second deeply trapped species. We show how the inclusion of antiferromagnetic interactions among the spin degrees of freedom generates a Devil's staircase of symmetry-protected topological phases for a wide parameter regime via a bosonic analog of the Peierls mechanism in electron-phonon systems. These topological Peierls insulators are examples of symmetry-breaking topological phases, where long-range order due to spontaneous symmetry breaking coexists with topological properties such as fractionalized edge states. Moreover, we identify a region of supersolid phases that do not require long-range interactions. They appear instead due to a Peierls incommensurability mechanism, where competing orders modify the underlying crystalline structure of Peierls insulators, becoming superfluid. Our work show the possibilities that ultracold atomic systems offer to investigate strongly-correlated topological phenomena beyond those found in natural materials.

Resonant Raman scattering in UO2 revisited

Due to ${\mathrm{UO}}_{2}$ being a strong electron-phonon interaction system, resonant Raman scattering is particularly helpful in exploring the relationship between its optical properties and electronic structure. Fr\"ohlich interaction induced resonant 2LO(\ensuremath{\Gamma}) phonon Raman scattering exhibits excitation energy $({E}_{i}=1.58--3.06\phantom{\rule{0.16em}{0ex}}\mathrm{eV})$, temperature (77--873 K), and pressure (\ensuremath{\le}29 GPa) dependent weighted contributions of two resonances. The first (incoming) resonance occurs when the incident photon energy equals the energy of an optical transition positioned at \ensuremath{\delta} \ensuremath{\sim} 0.19 above the \ensuremath{\sim}2.1 eV band gap. The second (outgoing) resonance occurs when the scattered-photon energy is equal to that of the optical transition. The energy of this transition is proposedly related to the Brillouin zone \ensuremath{\Gamma} point electronic density of states, positioned to be slightly above the band gap, by recent density functional theory calculations. The interplay between the simultaneous temperature dependent effects of tuning the band gap and altering the lifetime broadening of the excited electronic state is elucidated and demonstrated to strongly depend on the excitation energy and its position with respect to the band gap. The core difference between pressure and temperature dependent Raman response is mostly attributed to the ``resonant-suppressing'' role played by excited-state lifetime shortening, which becomes increasingly dominant at increased temperatures.

Ultrafast carrier dynamics at organic donor–acceptor interfaces—a quantum-based assessment of the hopping model

We investigate the charge transfer dynamics of photogenerated excitons at the donor–acceptor interface of an organic solar cell blend under the influence of molecular vibrations. This is examined using an effective Hamiltonian, parametrized by density functional theory calculations, to describe the full quantum behaviour of the relevant molecular orbitals, which are electronically coupled with each other and coupled to over 100 vibrations (via Holstein coupling). This electron–phonon system is treated in a numerically quasi-exact fashion using the matrix-product-state (MPS) ansatz. We provide insight into different mechanisms of charge separation and their relation to the electronic driving energy for the separation process. We find ultrafast electron transfer, which for small driving energy is dominated by kinetic processes and at larger driving energies by dissipative phonon emission connected to the prevalent vibration modes. Using this fully quantum mechanical model we perform a benchmark comparison to a recently developed semi-classical hopping approach, which treats the hopping and vibration time scales consistently. We find qualitatively and quantitatively good agreement between the results of the sophisticated MPS based quantum dynamics and the simple and fast time-consistent-hopping approach.

Quantum entanglement control of electron–phonon systems by light irradiation

We numerically study the dynamics of quantum entanglement between interacting electron-phonon and qubit-spin systems under photoirradiation, employing a model of multiple spins and boson modes. The interplay of the antiferromagnetic exchange and electron-phonon interactions provides us with a phase diagram, wherein each phase is characterized by the ground state property of the electron-phonon system. Light irradiation of the electron-phonon system facilitates the generation of quantum entanglement, according to the spin configuration and the phonon state in the ground state. Analyses using the quantum mutual information and the singular values of the reduced density matrix indicate that the quantum mechanical effect of the irradiated light appears in the state of the material.

Fluctuating Nature of Light-Enhanced d -Wave Superconductivity: A Time-Dependent Variational Non-Gaussian Exact Diagonalization Study

Engineering quantum phases using light is a novel route to designing functional materials, where light-induced superconductivity is a successful example. Although this phenomenon has been realized experimentally, especially for the high-$T_c$ cuprates, the underlying mechanism remains mysterious. Using the recently developed variational non-Gaussian exact diagonalization method, we investigate a particular type of photoenhanced superconductivity by suppressing a competing charge order in a strongly correlated electron-electron and electron-phonon system. We find that the $d$-wave superconductivity pairing correlation can be enhanced by a pulsed laser, consistent with recent experiments based on gap characterizations. However, we also find that the pairing correlation length is heavily suppressed by the pump pulse, indicating that light-enhanced superconductivity may be of fluctuating nature. Our findings also imply a general behavior of nonequilibrium states with competing orders, beyond the description of a mean-field framework.

Two-step Dynamics of Photoinduced Phonon Entanglement Generation between Remote Electron–Phonon Systems

The generation of quantum entanglement between phonons in photoirradiated remote electron-phonon systems is numerically studied. Upon excitation by a visible/ultraviolet laser pulse, the entanglement of electrons is immediately generated and that of phonons follows via electron-phonon interactions, i.e., the entanglement generation of phonons is a two-step process. Therefore, it is important to design the temporal properties of incident optical pulses in order to control the entanglement of electrons and/or phonons. These features are revealed by the quantum mutual information and the composite modes derived from the Heisenberg equation of motion. The calculated results also show that the dynamics of the phonon entanglement can be observed by time-resolved spectroscopy on the scattered light.

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.

Chebyshev Matrix Product States with Canonical Orthogonalization for Spectral Functions of Many-Body Systems.

We propose a method to calculate the spectral functions of many-body systems by Chebyshev expansion in the framework of matrix product states coupled with canonical orthogonalization (coCheMPS). The canonical orthogonalization can improve the accuracy and efficiency significantly because the orthogonalized Chebyshev vectors can provide an ideal basis for constructing the effective Hamiltonian in which the exact recurrence relation can be retained. In addition, not only the spectral function but also the excited states and eigenenergies can be directly calculated, which is usually impossible for other MPS-based methods such as time-dependent formalism or correction vector. The remarkable accuracy and efficiency of coCheMPS over other methods are demonstrated by calculating the spectral functions of spin chain and ab initio hydrogen chain. For the first time we demonstrate that Chebyshev MPS can be used to deal with ab initio electronic Hamiltonian effectively. We emphasize the strength of coCheMPS to calculate the low excited states of systems with sparse discrete spectrum. We also caution the application for electron-phonon systems with dense density of states.

Defect effects and electronic structure regulation in low-dimensional materials

Low-dimensional materials have been drawing increasing interest due to the unique structures and fascinating properties which are quite promising for wide-range application ranging from new energy resources to information technology. The exotic electronic states of the low-dimensional materials which arise from the quantum-confinement effects of electrons render a potential strategy to overcome the size-limitation of traditional semiconducting materials and continue the Moores’ law which is difficult for the conventional bulk materials. The electronic structure modulation of low-dimensional materials to meet the relevant requirements serves as the key to reach this goal. Notably, in low-dimensional materials, the defect effects are more remarkable than those in bulk materials due to the high specific surface area and quantum confinement effects. Moreover, the compatibility of low-dimensional materials to nanoscaled devices is crucial for the next-generation device applications. Here, we focus on the role of defects in electronic structure modulation of one- (1D) and two-dimensional (2D) materials to summarize works of our group relevant to this topic in recent years. The point defects, such as vacancies and adatoms (or functional groups) are revealed to have significant contribution to the electron spin-polarization and excited states. The ferromagnetism of the metal-free materials is demonstrated in wide range of materials, such as graphite, hexagonal boron nitride and silicon carbide both theoretically and experimentally. The spin-polarization of p electrons in these materials enriches the family of ferromagnetic materials and offers a promising strategy for spintronics device applications. The hollow structure of carbon nanotubes provides an ideal platform for the study of atomic reaction, diffusion and condensation processes confined in nanospace. The electronic band structures of carbon nanotubes can be effectively regulated by encapsulating metal or hydrogen nanowires. Ultrahigh density of hydrogen nanowires can be confined inside carbon nanotubes, thanks to the excellent mechanical properties, which lead to metallization or superconductivity of the 1D hydrogen systems at relative low pressure and high temperature, due to the “physical compression” effect of carbon nanotubes. The superconducting hydrogen can be well explained in terms of the Eliashberg superconductivity theory for electron-phonon strong-coupling system. The metallization and superconducting phase of hydrogen nanowires encapsulated in carbon nanotubes open a promising platform for study of low-dimensional superconductivity at high pressure. Additionally, metal-organic frameworks (MOFs) which are composed of transition metal (TM) atoms and organic ligands emerged as a new family of 2D materials. Compared with traditional 2D materials, MOFs have the advantages of structural diversity, porous configurations, tunable electronic band structures. Some lattice models, such as Kagome, Lieb and Ruby lattice models can be achieved in 2D MOFs. The synergistic effect of TM atoms and organic ligands leads to exotic properties, such as Kane fermions, topological electronic states (quantum spin Hall effects and quantum anomalous Hall effect), superconductivity, high catalytic activity, etc. The well-distributed TM atoms in the porous structures of 2D MOFs facilitate the catalysis in hydrogen evolution reaction (HER), oxygen evolution reaction (OER) and oxygen reduction reaction (ORR), which hold great promise in water splitting and fuel cells. In view of the experimental progresses on the synthesis of diverse 2D MOFs, the fascinating properties of 2D MOFs bring about new concepts for electronic devices and catalysis design.

Quantum dynamics of electric-dipole coupled defect centers in solids

We investigate the quantum dynamics of two defect centers in solids, which are coupled by vacuum-induced dipole–dipole interactions. When the interaction between defects and phonons is taken into account, the two coupled electron–phonon systems make up two equivalent multilevel atoms. By making Born–Markov and rotating wave approximations, we derive a master equation describing the dynamics of the coupled multilevel atoms. The results indicate the concepts of subradiant and superradiant states can be applied to these systems and the population transfer process presents different behaviors from those of the two dipolar-coupled two-level atoms due to the participation of phonons.

Variational Approach for Many-Body Systems at Finite Temperature.

We introduce an equation for density matrices that ensures a monotonic decrease of the free energy and reaches a fixed point at the Gibbs thermal. We build a variational approach for many-body systems that can be applied to a broad class of states, including all bosonic and fermionic Gaussian, as well as their generalizations obtained by unitary transformations, such as polaron transformations in electron-phonon systems. We apply it to the Holstein model on 20×20 and 50×50 square lattices, and predict phase separation between the superconducting and charge-density wave phases in the strong interaction regime.

Charge-density-wave melting in the one-dimensional Holstein model

We study the Holstein model of spinless fermions, which at half-filling exhibits a quantum phase transition from a metallic Tomonaga-Luttinger liquid phase to an insulating charge-density-wave (CDW) phase at a critical electron-phonon coupling strength. In our work, we focus on the real-time evolution starting from two different types of initial states that are CDW ordered: (i) ideal CDW states with and without additional phonons in the system and (ii) correlated ground states in the CDW phase. We identify the mechanism for CDW melting in the ensuing real-time dynamics and show that it strongly depends on the type of initial state. We focus on the far-from-equilibrium regime and emphasize the role of electron-phonon coupling rather than dominant electronic correlations, thus complementing a previous study of photo-induced CDW melting [H. Hashimoto and S. Ishihara, Phys. Rev. B 96, 035154 (2017)]. The numerical simulations are performed by means of matrix-product-state based methods with a local basis optimization (LBO). Within these techniques, one rotates the local (bosonic) Hilbert spaces adaptively into an optimized basis that can then be truncated while still maintaining a high precision. In this work, we extend the time-evolving block decimation (TEBD) algorithm with LBO, previously applied to single-polaron dynamics, to a half-filled system. We demonstrate that in some parameter regimes, a conventional TEBD method without LBO would fail. Furthermore, we introduce and use a ground-state density-matrix renormalization group method for electron-phonon systems using local basis optimization. In our examples, we account for up to $M_{\rm ph} = 40$ bare phonons per site by working with $O(10)$ optimal phonon modes.

Coupled electron-impurity and electron-phonon systems as trivial non-Fermi liquids

We consider an electron gas, both in two (2D) and three (3D) dimensions, interacting with quenched impurities and phonons within leading order finite-temperature many body perturbation theories, calculating the electron self-energies, spectral functions, and momentum distribution functions at finite temperatures. The resultant spectral function is in general highly non-Lorentzian, indicating that the system is not a Fermi liquid in the usual sense. The calculated momentum distribution function cannot be approximated by a Fermi function at any temperature, providing a rather simple example of a non-Fermi liquid with well-understood properties.

Enhancement of superconductivity by frustrating the charge order

We study the superconductivity of strongly coupled electron-phonon systems where the geometry of the lattice frustrates the charge order by the sign-problem-free Quantum Monte Carlo(QMC) method. The results suggest that with charge order frustrated, the superconductivity can benefit from strong electron-phonon interaction in a wide range of coupling strengths.

Finite frequency noise in a chiral Luttinger liquid coupled to phonons

We study transport between Quantum Hall (QH) edge states at filling factor $\nu = 1$ in the presence of electron-acoustic-phonon coupling. Performing a Bogoliubov-Valatin (BV) trasformation the low-energy spectrum of interacting electron-phonon system is presented. The electron-phonon interaction splits the spectrum into charged and neutral "downstream" and neutral "upstream" modes with different velocities. In the regimes of dc and periodic ac biases the tunelling current and non-equilibrium finite frequency non-symmetrized noise are calculated perturbatively in tunneling coupling of quantum point contact (QPC). We show that the presence of electron-phonon interaction strongly modifies noise and current relations compared to free-fermion case.

Quantum Monte Carlo with the Langevin Equation: Coupled Bose-Fermi Systems

We describe the algorithmic details and a performance evaluation of a Langevin approach to a strongly interacting electron-phonon system, and show it has a near linear scaling with lattice size Ns. Many of the limitations of previous attempts to employ such methods to condensed matter lattice Hamiltonians are absent. In particular, the iterative linear algebra solution remains well behaved at strong coupling and low temperatures. The use of Fourier Acceleration is crucial for efficiency, and its use makes the method competitive with the widely-used local update methods, which scale as for on-site interactions and for long range electron-phonon coupling, even on rather small lattice sizes.