We study polarons in the one-dimensional Bond-Peierls electron-phonon model, in which phonons on bonds of a lattice modulate the hopping of electrons between lattice sites, and contrast the results to those known for the Breathing-Mode Peierls problem. By inspecting the atomic limit, we show that polaronic dressing and mass enhancement of Bond-Peierls polarons depend on the momentum dependence of the phonons. For dispersionless phonons, Bond-Peierls polarons are perfectly localized in the atomic limit, unlike their Breathing-mode counterparts, because the carrier creates a string of phonon excitations that can only be annihilated via processes that retrace the carrier to its original site. However, inclusion of phonon dispersion leads to a non-divergent polaron mass even in the atomic limit and depending on the form of the phonon dispersion may lead to a transition to a non-zero-momentum ground state akin to that found in the Breathing-mode Peierls model.
We study polarons in the one-dimensional Bond-Peierls electron-phonon model, in which phonons on bonds of a lattice modulate the hopping of electrons between lattice sites, and contrast the results to those known for the Breathing-Mode Peierls problem. By inspecting the atomic limit, we show that polaronic dressing and mass enhancement of Bond-Peierls polarons depend on the momentum dependence of the phonons. For dispersionless phonons, Bond-Peierls polarons are perfectly localized in the atomic limit, unlike their Breathing-mode counterparts, because the carrier creates a string of phonon excitations that can only be annihilated via processes that retrace the carrier to its original site. However, inclusion of phonon dispersion leads to a non-divergent polaron mass even in the atomic limit and depending on the form of the phonon dispersion may lead to a transition to a non-zero-momentum ground state akin to that found in the Breathing-mode Peierls model.
We study polarons in the one-dimensional Bond-Peierls electron-phonon model in which phonons on bonds of a lattice modulate the hopping of electrons between lattice sites and contrast the results to those known for the breathing-mode Peierls problem. By inspecting the atomic limit, we show that polaronic dressing and mass enhancement of Bond-Peierls polarons depend on the momentum dependence of the phonons. For dispersionless phonons, Bond-Peierls polarons are perfectly localized in the atomic limit, unlike their breathing-mode counterparts because the carrier creates a string of phonon excitations that can only be annihilated via processes that retrace the carrier to its original site. However, inclusion of phonon dispersion leads to a nondivergent polaron mass even in the atomic limit and depending on the form of the phonon dispersion may lead to a transition to a non-zero-momentum ground state akin to that found in the breathing-mode Peierls model.
Polarons with different types of electron-phonon coupling have fundamentally different properties. When the dominant interaction is between the electron density and lattice displacement, the momentum of the ground state does not change and the polaron gets exponentially heavy at strong coupling. In contrast, one-dimensional Peierls/Su-Schrieffer-Heeger (PSSH) polarons with interaction originating from displacement-modulated hopping feature a shift of the ground-state momentum to finite values and moderate values of effective mass as coupling is increased [D. J. J. Marchand et al., Phys. Rev. Lett. 105, 266605 (2010)]. Based on Diagrammatic Monte Carlo method, we investigate whether unusual properties of PSSH polarons depend on the type of the displacement-modulated hopping and to what degree they survive in higher dimension. We study two different PSSH models: with bosonic degrees of freedom residing on sites (model A) and bonds (model B) of the two-dimensional square lattice. For model A, we find that in both adiabatic and intermediate regimes, the momentum of the ground state experiences a continuous transition from zero to a finite value as a function of coupling strength. The transition is driven by quadratic instability of the dispersion function, implying that effective mass diverges at the critical point, and then decreases in an anisotropic fashion with increasing coupling. Unexpectedly, for model B, the momentum of the ground state always stays at zero and the effective mass increases monotonously with coupling. The increase is far from exponential and tends to level off at strong interaction, resulting in relatively light polarons. Having light polarons in the strong coupling regime is crucial for the bipolaron mechanism of high-temperature superconductivity [J. Sous, M. Chakraborty, R. V. Krems, and M. Berciu, Phys. Rev. Lett. 121, 247001 (2018).]
We calculate the spectral properties of the one-dimensional Holstein and breathing polarons using the self-consistent Born approximation. The Holstein model electron-phonon coupling is momentum independent while the breathing coupling increases monotonically with the phonon momentum. We find that for a linear or tight binding electron dispersion: (i) for the same value of the dimensionless coupling the quasiparticle renormalization at small momentum in the breathing polaron is much smaller, (ii) the quasiparticle renormalization at small momentum in the breathing polaron increases with phonon frequency unlike in the Holstein model where it decreases, and (iii) in the Holstein model the quasiparticle dispersion displays a kink and a small gap at an excitation energy equal to the phonon frequency ${\ensuremath{\omega}}_{0}$ while in the breathing model it displays two gaps, one at excitation energy ${\ensuremath{\omega}}_{0}$ and another one at $2{\ensuremath{\omega}}_{0}$. These differences have two reasons: first, the momentum of the relevant scattered phonons increases with increasing polaron momentum and second, the breathing bare coupling is an increasing function of the phonon momentum. These result in an effective electron-phonon coupling for the breathing model which is an increasing function of the total polaron momentum, such that the small momentum polaron is in the weak coupling regime while the large momentum one is in the strong coupling regime. However, the first reason does not hold if the free electron dispersion has low energy states separated by large momentum, as in a higher dimensional system, for example, in this situation the difference between the two models becomes less significant.
Many condensed matter problems involve a particle coupled to its environment. The polaron, originally introduced to describe electrons in a polarizable medium, describes a particle coupled to a bosonic field. The Holstein polaron model, although simple, including only optical Einstein phonons and an interaction that couples them to the electron density, captures almost all of the standard polaronic properties. We herein investigate polarons that differ significantly from this behaviour. We study a model with phonon-modulated hopping, and find a radically different behaviour at strong couplings. We report a sharp transition, not a crossover, with a diverging effective mass at the critical coupling. We also look at a model with acoustic phonons, away from the perturbative limit, and again discover unusual polaron properties. Our work relies on the Bold Diagrammatic Monte Carlo (BDMC) method, which samples Feynman diagrammatic expansions efficiently, even those with weak sign problems. Proposed by Prokof'ev and Svistunov, it is extended to lattice polarons for the first time here. We also use the Momentum Average (MA) approximation, an analytical method proposed by Berciu, and find an excellent agreement with the BDMC results. A novel MA approximation able to treat dispersive phonons is also presented, along with a new exact solution for finite systems, inspired by the same formalism.
In most cases, as the strength of electron-phonon coupling increases, the effective mass of polarons typically increases. However, in this paper, we uncover a fascinating phenomenon: the presence of light polarons even within the strong coupling regime, where electron-phonon coupling includes both Holstein and bond types (electron-phonon coupling occurring on the hopping bonds). To investigate this, we employ a diagrammatic Monte Carlo method based on the path-integral formulation of the particle sector and the Fock-state representation of the phonon sector. Our study centers on analyzing the impact of bond electron-phonon coupling on the Holstein polaron's essential properties, including its effective mass, ground-state energy, and the average number of phonons. We examine two distinct scenarios: one where the phonon frequency of both Holstein and bond types is the same, and another where the phonon frequency of the Holstein type is twice as large as that of the bond type. In both of these cases, when the Holstein coupling falls within the light mass regime, we observe minimal changes in the effective mass as a function of bond coupling, compared to the case of the bare bond polaron. However, the behavior of the effective mass undergoes a significant change in the heavy mass regime. Most intriguingly, we discover a nonmonotonic dependence of the effective mass on the bond coupling gB when the Holstein coupling gH falls within the heavy mass regime. This finding holds promise, particularly in the context of bipolarons, where achieving a light effective mass and a large binding energy to get a compact size is crucial.
We study the small-polaron problem of a single electron interacting with the lattice for the Holstein model in the adiabatic limit on a comb lattice hen the electron-phonon interaction acts only on the base sites. The ground state properties can be easily deduced from the ones of a linear chain with a appropriate rescaling of the coupling constant. On the other hand, the dynamical properties, that involve the complete spectrum of the system, present an "exotic" behavior. In the weak coupling limit the Drude weight (zero-frequency-conductivity) is enhanced with respect to its free-case value, contrary to the linear chain case, where for every finite value one has suppression of the Drude peak. More interestingly, the loss of coherent electron motion and the polaronic localization of the carrier occurs for different coupling values. Thus for intermediate coupling, a different phase appears with large kinetic energy and no coherent motion. RI Capone, Massimo/A-7762-2008