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arXiv:1812.10336 · Physical Review Letters

Polaron Mobility in the “Beyond Quasiparticles” Regime

Andrei S. Mishchenko, Lode Pollet, Nikolay V. Prokof'ev, Abhishek Kumar, Dmitrii L. Maslov, Naoto Nagaosa

Published Aug 12, 2019• 39 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.123.076601

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•Oct 4, 1999•0 citations
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.
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 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=0T=0T=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.
A detailed study of the Fr\"ohlich polaron model is performed on the basis of diagrammatic quantum Monte Carlo method [N. V. Prokof'ev and B. V. Svistunov, Phys. Rev. Lett. 81,81,81, 2514 (1998)]. The method is further developed both quantitatively (performance) and qualitatively (new estimators), and is enhanced by spectral analysis of the polaron Green's function, within an approach developed in the present paper. We present up to date results for the binding energy, and make available precise data for the effective mass, including the region of intermediate and strong couplings. We look at the structure of the polaron cloud and answer such questions as the average number of phonons in the cloud and their number/momentum distribution. The spectral analysis reveals nontrivial structure of the spectral density at intermediate and large coupling: the spectral continuum features pronounced peaks that we attribute to unstable excited states of the polaron.
We introduce the first bold diagrammatic Monte Carlo approach to deal with polaron problems at a finite electron density nonperturbatively, i.e., by including vertex corrections to high orders. Using the Holstein model on a square lattice as a prototypical example, we demonstrate that our method is capable of providing accurate results in the thermodynamic limit in all regimes from a renormalized Fermi liquid to a single polaron, across the nonadiabatic region where Fermi and Debye energies are of the same order of magnitude. By accounting for vertex corrections, the accuracy of the theoretical description is increased by orders of magnitude relative to the lowest-order self-consistent Born approximation employed in most studies. We also find that for the electron-phonon coupling typical for real materials, the quasiparticle effective mass increases and the quasiparticle residue decreases with increasing the electron density at constant electron-phonon coupling strength.
The Fr\"ohlich model describes the interaction of a mobile impurity with a surrounding bath of phonons which leads to the formation of a quasiparticle, the polaron. In this paper an efficient renormalization group approach is presented which provides a description of Fr\"ohlich polarons in all regimes ranging from weak to strong coupling. The extended renormalization group approach introduced here is capable of predicting ground state properties for arbitrarily small impurity masses. This allows us to obtain the full phase diagram of the Fr\"ohlich Hamiltonian, which we present concretely for the Bogoliubov-Fr\"ohlich model originally introduced to describe ultracold impurities in a Bose-Einstein condensate. For this model, whose regime of validity in ultracold quantum gases is the subject of debate, we benchmark our method by comparison of the ground state energy to recent diagrammatic quantum Monte Carlo calculations.
A detailed study of the Frohlich polaron model is performed on the basis of diagrammatic quantum Monte Carlo method. The method is further developed both quantitatively (performance) and qualitatively (new estimators), and is enhanced by spectral analysis of the polaron Green function, within a novel approach. We present the best up to date results for the binding energy, and for the first time make available precise data for the effective mass, including the region of intermediate and strong couplings. We look at the structure of the polaron cloud and answer such questions as the average number of phonons in the cloud and their number/momentum distribution. The spectral analysis reveals non-trivial structure of the spectral density at intermediate and large coupling: the spectral continuum features pronounced peaks that we attribute to unstable excited states of the polaron.