The Feynman path-integral variational approach to the polaron problem, along with the associated Feynman-Hellwarth-Iddings-Platzman (FHIP) linear-response mobility theory, provides a computationally amenable method to predict the frequency-resolved temperature-dependent charge-carrier mobility, and other experimental observables in polar semiconductors. We show that the FHIP mobility theory predicts non-Drude transport behavior, and shows remarkably good agreement with the recent diagrammatic Monte Carlo mobility simulations of Mishchenko et al. [Phys. Rev. Lett. 123, 076601 (2019)] for the abstract Fr\"ohlich Hamiltonian. We extend this method to multiple phonon modes in the Fr\"ohlich model action. This enables a slightly better variational solution, as inferred from the resulting energy. We carry forward this extra complexity into the mobility theory, which shows a richer structure in the frequency and temperature-dependent mobility, due to the different phonon modes activating at different energies. The method provides a computationally efficient and fully quantitative method of predicting polaron mobility and response in real materials.
The Feynman path-integral variational approach to the polaron problem, along with the associated Feynman-Hellwarth-Iddings-Platzman (FHIP) linear-response mobility theory, provides a computationally amenable method to predict the frequency-resolved temperature-dependent charge-carrier mobility, and other experimental observables in polar semiconductors. We show that the FHIP mobility theory predicts non-Drude transport behavior, and shows remarkably good agreement with the recent diagrammatic Monte Carlo mobility simulations of Mishchenko et al. [Phys. Rev. Lett. 123, 076601 (2019)] for the abstract Fr"ohlich Hamiltonian. We extend this method to multiple phonon modes in the Fr"ohlich model action. This enables a slightly better variational solution, as inferred from the resulting energy. We carry forward this extra complexity into the mobility theory, which shows a richer structure in the frequency and temperature-dependent mobility, due to the different phonon modes activating at different energies. The method provides a computationally efficient and fully quantitative method of predicting polaron mobility and response in real materials.
In a number of physical situations, from polarons to Dirac liquids and to non-Fermi liquids, one encounters the "beyond quasiparticles" regime, in which the inelastic scattering rate exceeds the thermal energy of quasiparticles. Transport in this regime cannot be described by the kinetic equation. We employ the diagrammatic Monte Carlo method to study the mobility of a Fröhlich polaron in this regime and discover a number of nonperturbative effects: a strong violation of the Mott-Ioffe-Regel criterion at intermediate and strong couplings, a mobility minimum at T∼Ω in the strong-coupling limit (Ω is the optical mode frequency), a substantial delay in the onset of an exponential dependence of the mobility for T<Ω at intermediate coupling, and complete smearing of the Drude peak at strong coupling. These effects should be taken into account when interpreting mobility data in materials with strong electron-phonon coupling.
In the present work, the problem of an all-coupling analytic description for the optical conductivity of the Fr\"ohlich polaron is treated, with the goal being to bridge the gap in the validity range that exists between two complementary methods: on the one hand, the memory-function formalism and, on the other hand, the strong-coupling expansion based on the Franck-Condon picture for the polaron response. At intermediate coupling, both methods were found to fail as they do not reproduce diagrammatic quantum Monte Carlo results. To resolve this, we modify the memory-function formalism with respect to the Feynman-Hellwarth-Iddings-Platzman approach in order to take into account a nonquadratic interaction in a model system for the polaron. The strong-coupling expansion is extended beyond the adiabatic approximation by including in the treatment nonadiabatic transitions between excited polaron states. The polaron optical conductivity that we obtain at T=0 by combining the two extended methods agrees well, both qualitatively and quantitatively, with the diagrammatic quantum Monte Carlo results in the whole available range of the electron-phonon coupling strength.
Polarons—quantum particles dressed by a cloud of bath excitations—arise whenever a particle interacts strongly with its host medium. Electron and hole polarons, formed when carriers bind to a phonon cloud through electron-phonon (e-ph) interactions, govern charge transport in transition metal oxides, organic semiconductors, and halide perovskites. The concept generalizes to exciton-phonon interactions, giving rise to exciton polarons that produce the large Stokes shifts and broad photoluminescence (PL) lineshapes central to light-emitting applications. A predictive treatment of polarons has remained elusive. Numerically exact methods such as diagrammatic Monte Carlo (DMC) have been restricted to simplified model Hamiltonians, while first-principles approaches based on density functional theory provide material-specific e-ph interactions but treat the e-ph correlation approximately. This thesis bridges that gap by developing first-principles diagrammatic Monte Carlo (FPDMC), which stochastically sums all e-ph Feynman diagrams using accurate ab-initio interactions, yielding numerically exact polaron properties in real materials. Two methodological advances make FPDMC possible. A matrix-product formalism sums over electronic band indices exactly, alleviating the multi-band sign problem in realistic band structures. A data-driven compression of e-ph interactions based on singular-value decomposition (SVD) in the Wannier basis then accelerates the method by more than 10³×. The SVD compression also reveals a hidden low-dimensional structure of quantum interactions, maintaining accuracy across charge transport, spin relaxation, band renormalization, and superconductivity calculations. Extending this philosophy to phonon-phonon interactions via a permanent CP (PCP) decomposition yields 10³–10⁴× compression of anharmonic force constants and orders-of-magnitude speedups in thermal conductivity calculations. Applying FPDMC, we study polarons in LiF, SrTiO₃, and TiO₂, finding excellent agreement with experimental mobilities and resolving the contrasting small- and large-polaron transport in the two TiO₂ polymorphs. To make the microscopic picture concrete, we introduce an e-ph correlation function that visualizes lattice distortion and polaron orbital character. Extending FPDMC to exciton polarons, we obtain first-principles exciton-phonon interactions from finite-momentum Bethe-Salpeter equation calculations and derive a Fermi-golden-rule PL theory. Applied to CrBr₃, FPDMC predicts a broad PL spectrum agreeing with experiment in both peak position and lineshape.
Including the effect of lattice anharmonicity on electron-phonon interactions has recently garnered attention due to its role as a necessary and significant component in explaining various phenomena, including superconductivity, optical response, and temperature dependence of mobility. This study focuses on analytically treating the effects of anharmonic electron-phonon coupling on the polaron self-energy, combined with numerical Diagrammatic Monte Carlo (DiagMC) data. Specifically, we incorporate a quadratic interaction into the method of squeezed phonon states, which has proven effective for analytically calculating the polaron parameters. Additionally, we extend this method to nonparabolic finite-width conduction bands while maintaining the periodic translation symmetry of the system. Our results are compared with those obtained from Diagrammatic Monte Carlo, partially reported in a recent study [S. Ragni et al., Phys. Rev. B 107, L121109 (2023)], covering a wide range of coupling strengths for the nonlinear interaction. Remarkably, our analytic method predicts the same features as the Diagrammatic Monte Carlo simulation.
The path-integral approach to the tight-binding polaron is extended to multiple optical phonon modes of arbitrary dispersion and polarization. The nonlinear lattice effects are neglected. Only one electron band is considered. The electron-phonon interaction is of the density-displacement type, but can be of arbitrary spatial range and shape. Feynman's analytical integration of ion trajectories is performed by transforming the electron-ion forces to the basis in which the phonon dynamical matrix is diagonal. The resulting polaron action is derived for the periodic and shifted boundary conditions in imaginary time. The former can be used for calculating polaron thermodynamics while the latter for the polaron mass and spectrum. The developed formalism is the analytical basis for numerical analysis of such models by path-integral Monte Carlo methods.
The Fröhlich polaron model describes a ubiquitous class of problems concerned with understanding properties of a single mobile particle interacting with a bosonic reservoir. Originally introduced in the context of electrons interacting with phonons in crystals, this model found applications in such diverse areas as strongly correlated electron systems, quantum information, and high energy physics. In the last few years this model has been applied to describe impurity atoms immersed in Bose-Einstein condensates of ultracold atoms. The tunability of microscopic parameters in ensembles of ultracold atoms and the rich experimental toolbox of atomic physics should allow to test many theoretical predictions and give us new insights into equilibrium and dynamical properties of polarons. In these lecture notes we provide an overview of common theoretical approaches that have been used to study BEC polarons, including Rayleigh-Schrödinger and Green's function perturbation theories, self-consistent Born approximation, mean-field approach, Feynman's variational path integral approach, Monte Carlo simulations, renormalization group calculations, and Gaussian variational ansatz. We focus on the renormalization group approach and provide details of analysis that have not been presented in earlier publications. We show that this method helps to resolve striking discrepancy in polaron energies obtained using mean-field approximation and Monte Carlo simulations. We also discuss applications of this method to the calculation of the effective mass of BEC polarons. As one experimentally relevant example of a non-equililbrium problem we consider Bloch oscillations of Bose polarons and demonstrate that one should find considerable deviations from the commonly accepted phenomenological Esaki-Tsu model. We review which parameter regimes of Bose polarons can be achieved in various atomic mixtures.