arXiv subjects

Stefano Ragni

Publications and source records attributed to Stefano Ragni.

7 recordsLinked to original sources

arXiv2026

Anomalous temperature dependence of polaron mobility in a nonlinear double-well potential: unbiased X-propagator approach

We develop an unbiased X-propagator method for calculating finite-temperature optical conductivity $σ(ω)$ and dc mobility $μ$ for arbitrary nonlinear electron-phonon interaction. We apply it to a polaron coupled to a double-well lattice potential, a minimal model for strongly anharmonic polar materials. At moderate coupling, the mobility exhibits three temperature regimes associated with confinement within one well, thermal competition with the barrier, and barrier-insensitive high-temperature dynamics. This sequence produces a concave temperature dependence of the mobility that is absent in conventional linear-coupling polaron models. At strong coupling, the mobility becomes nonmonotonic, and its temperature evolution is reflected in a characteristic redistribution of optical spectral weight. For parameters relevant to SrTiO$_3$, our results qualitatively reproduce both the anomalous concave mobility and the onset of violation of the Mott-Ioffe-Regel limit, thereby supporting nonlinear coupling to a soft anharmonic lattice mode as a microscopic mechanism for anomalous transport in dilute polar metals.

cond-mat.str-el↗

arXiv2026

Polaron formation as the vertex function problem: From Dyck's paths to self-energy Feynman diagrams

We present an iterative method for generating the complete set of self-energy Feynman diagrams at arbitrary order for the single-polaron problem with arbitrary linear coupling to the lattice. The approach combines a combinatorial representation of noncrossing diagrams, based on Dyck paths associated with Stieltjes-Rogers polynomials, with the constraints of the Ward-Takahashi identity to systematically incorporate vertex corrections. This construction yields a one-to-one correspondence between terms in the expansion based on Stieltjes-Rogers polynomials and diagrammatic contributions, and provides, through a sequence of simple steps, a closed, algorithmic framework for generating all diagrams of a given order, together with their relative weights. The method enables efficient, unbiased evaluation of diagrammatic series and improves the convergence of diagrammatic Monte Carlo by eliminating the need for stochastic weighting between different topologies. We further outline how the construction can be generalized to finite-density electron systems.

cond-mat.str-el↗

arXiv2025

Polarons with arbitrary nonlinear electron-phonon interaction

We develop an exact computational method based on numerical X-propagators for solving polaron models with arbitrary nonlinear couplings of local vibration modes to the electron density and magnitude of the hopping amplitude. Our approach covers various polaron models, some of which were impossible to treat by any existing approximation-free techniques. Moreover, it remains efficient in the most relevant but computationally challenging regime of phonon frequencies much smaller than the electron bandwidth. As a case study, we consider the double-well type nonlinear model with quadratic ($g_2<0$) and quartic ($g_4>0$) interactions describing a broad class of technologically important materials, such as quantum paraelectric compounds and halide perovskites. We observe, depending on the model parameters, three qualitatively different regimes: (i) quantum interplay of quartic and quadratic interactions which suppresses effects of the quadratic coupling, (ii) intermediate-coupling regime with exponential $\propto \exp(αg_2 Ω^{-1/4})$ scaling of the quasiparticle weight and mass renormalization, and (iii) strong-coupling asymptotic behavior.

cond-mat.str-el↗

arXiv2025

First-principles theory of nonlinear long-range electron-phonon interaction

Describing electron-phonon interactions in a solid requires knowledge of the electron-phonon matrix elements in the Hamiltonian. State-of-the-art first-principles calculations for the electron-phonon interaction are limited to the 1-electron-1-phonon matrix element, which is suitable for harmonic materials. However, there is no first-principles theory for 1-electron-2-phonon interactions, which occur in anharmonic materials with significant electron-phonon interaction such as halide perovskites and quantum paraelectrics. Here, we derive an analytical expression for the long-range part of the 1-electron-2-phonon matrix element, written in terms of microscopic quantities that can be calculated from first principles. We show that the long-range 1-electron-2-phonon interaction is described by the derivative of the phonon dynamical matrix with respect to an external electric field. We calculate the quasiparticle energy of a large polaron including 1-electron-2-phonon interaction, and show that it can be written in terms of a 1-electron-2-phonon spectral function $\mathcal{T}_{αβ}(ω)$. We demonstrate how to calculate this spectral function and its temperature dependence for the benchmark materials LiF and KTaO$_3$, where it turns out that the effect is very small. The first-principles framework developed in this article is general, paving the way for future calculations of 1-electron-2-phonon interactions in materials where the effect may be larger.

cond-mat.mtrl-sci↗

arXiv2025

First-principles theory of nonlinear long-range electron-phonon interaction

Electron-phonon interactions in solids are crucial for understanding many interesting phenomena, such as conventional superconductivity, temperature-dependent band-gap renormalization, and polarons. For harmonic materials, the linear interaction of one electron with one phonon is sufficient to quantitatively describe these properties. However, in anharmonic materials such as quantum paraelectrics, halide perovskites, and high-pressure hydrides, the nonlinear electron-phonon interactions may play an important role. Currently, the only available Hamiltonians for nonlinear electron-phonon interaction are model Hamiltonians, written in terms of phenomenological parameters. Here, we present a microscopic theory for long-range nonlinear electron-phonon interactions, which can be combined with first-principles calculations. We provide a semi-analytical expression for the long-range part of the 1-electron-2-phonon matrix element. We show that in contrast to the long-range 1-electron-1-phonon interaction, the continuum approximation is not sufficient and the entire phonon dispersion must be taken into account. Additionally, we show that the quasiparticle energies can be written in terms of a 1-electron-2-phonon spectral function. To demonstrate the method, we calculate the 1-electron-2-phonon spectral function for LiF and KTaO$_3$ from first principles. Our framework is a step forward toward complete first-principles calculations of nonlinear electron-phonon interactions in solids.

cond-mat.mtrl-sci↗

arXiv2024

Analytic method for quadratic polarons in nonparabolic bands

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 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.

cond-mat.other↗

arXiv2022

Polaron with Quadratic Electron-phonon Interaction

We present the first numerically exact study of a polaron with quadratic coupling to the oscillator displacement, using two alternative methodological developments. Our results cover both anti-adiabatic and adiabatic regimes and the entire range of electron-phonon coupling $g_2$, from the system's stability threshold at attractive $g_2=-1$ to arbitrary strong repulsion at $g_2 \gg 1$. Key properties of quadratic polarons prove dramatically different from their linear counterparts. They (i) are insensitive even to large quadratic coupling except in the anti-adiabatic limit near the threshold of instability at attraction; (ii) depend only on the adiabatic ratio but are insensitive to the electron dispersion and dimension of space; (iii) feature weak lattice deformations even at the instability point. Our results are of direct relevance to properties of electrons at low densities in polar materials, including recent proposals for their superconducting states.

cond-mat.str-el↗