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1. Intermediate polaronic charge transport in organic crystals from a many-body first-principles approach

   Chang, Benjamin K.; Zhou, Jin-Jian; Lee, Nien-En; Bernardi, Marco (December 2022, npj Computational Materials)

   Abstract Charge transport in organic molecular crystals (OMCs) is conventionally categorized into two limiting regimes − band transport, characterized by weak electron-phonon (e-ph) interactions, and charge hopping due to localized polarons formed by strong e-ph interactions. However, between these two limiting cases there is a less well understood intermediate regime where polarons are present but transport does not occur via hopping. Here we show a many-body first-principles approach that can accurately predict the carrier mobility in this intermediate regime and shed light on its microscopic origin. Our approach combines a finite-temperature cumulant method to describe strong e-ph interactions with Green-Kubo transport calculations. We apply this parameter-free framework to naphthalene crystal, demonstrating electron mobility predictions within a factor of 1.5−2 of experiment between 100 and 300 K. Our analysis reveals the formation of a broad polaron satellite peak in the electron spectral function and the failure of the Boltzmann equation in the intermediate regime. 

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2. Ab initio electron-two-phonon scattering in GaAs from next-to-leading order perturbation theory

   https://doi.org/10.1038/s41467-020-15339-0  

   Lee, Nien-En; Zhou, Jin-Jian; Chen, Hsiao-Yi; Bernardi, Marco (March 2020, Nature Communications)

   Abstract Electron-phonon (e–ph) interactions are usually treated in the lowest order of perturbation theory. Here we derive next-to-leading ordere–ph interactions, and compute from first principles the associated electron-two-phonon (2ph) scattering rates. The derivations involve Matsubara sums of two-loop Feynman diagrams, and the numerical calculations are challenging as they involve Brillouin zone integrals over two crystal momenta and depend critically on the intermediate state lifetimes. Using Monte Carlo integration together with a self-consistent update of the intermediate state lifetimes, we compute and converge the 2ph scattering rates, and analyze their energy and temperature dependence. We apply our method to GaAs, a weakly polar semiconductor with dominant optical-mode long-rangee–ph interactions. We find that the 2ph scattering rates are as large as nearly half the value of the one-phonon rates, and that including the 2ph processes is necessary to accurately predict the electron mobility in GaAs from first principles. 

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3. First-principles electron-phonon interactions and polarons in the parent cuprate ${\mathrm{La}}_2{\mathrm{CuO}}_4$

   https://doi.org/10.1103/PhysRevResearch.7.L012073  

   Chang, Benjamin K; Timrov, Iurii; Park, Jinsoo; Zhou, Jin-Jian; Marzari, Nicola; Bernardi, Marco (March 2025, Physical Review Research)

   Understanding electronic interactions in high-temperature superconductors is an outstanding challenge. In the widely studied cuprate materials, experimental evidence points to strong electron-phonon ( $e$-ph) coupling and broad photoemission spectra. Yet, the microscopic origin of this behavior is not fully understood. Here, we study $e$-ph interactions and polarons in a prototypical parent (undoped) cuprate, ${\mathrm{La}}_2{\mathrm{CuO}}_4$(LCO), by means of first-principles calculations. Leveraging parameter-free Hubbard-corrected density functional theory, we obtain a ground state with the band gap and Cu magnetic moment in nearly exact agreement with experiments. This enables a quantitative characterization of $e$-ph interactions. Our calculations reveal two classes of longitudinal optical (LO) phonons with strong $e$-ph coupling to hole states. These modes consist of bond stretching and bond bending in the Cu-O plane as well as vibrations of apical O atoms. The hole spectral functions, obtained with a cumulant method that can capture strong $e$-ph coupling, exhibit broad quasiparticle peaks with a small spectral weight ( $Z\approx 0.25$) and pronounced LO-phonon sidebands characteristic of polaron effects. Our calculations predict features observed in photoemission spectra, including a 40-meV peak in the $e$-ph coupling distribution function not explained by existing models. These results show that the universal strong $e$-ph coupling found experimentally in doped lanthanum cuprates is also present in the parent compound, and elucidate its microscopic origin. 

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4. Efficient GPU Parallelization of Electronic Transport and Nonequilibrium Dynamics from Electron-Phonon Interactions in the Perturbo Code

   Peng, Shiyu; Pinkston, Donnie; Yao, Jia; Kliavinek, Sergei; Maliyov, Ivan; Bernardi, Marco (November 2025, arXivorg)

   The Boltzmann transport equation (BTE) with electron-phonon (e-ph) interactions computed from first principles is widely used to study electronic transport and nonequilibrium dynamics in materials. Calculating the e-ph collision integral is the most important step in the BTE, but it remains computationally costly, even with current MPI+OpenMP parallelization. This challenge makes it difficult to study materials with large unit cells and to achieve high resolution in momentum space. Here, we show acceleration of BTE calculations of electronic transport and ultrafast dynamics using graphical processing units (GPUs). We implement a novel data structure and algorithm, optimized for GPU hardware and developed using OpenACC, to process scattering channels and efficiently compute the collision integral. This approach significantly reduces the overhead for data referencing, movement, and synchronization. Relative to the efficient CPU implementation in the open-source package Perturbo (v2.2.0), used as a baseline, this approach achieves a speed-up of 40 times for both transport and nonequilibrium dynamics on GPU hardware, and achieves nearly linear scaling up to 100 GPUs. The novel data structure can be generalized to other electron interactions and scattering processes. We released this GPU implementation in the latest public version (v3.0.0) of Perturbo. The new MPI+OpenMP+GPU parallelization enables sweeping studies of e-ph physics and electron dynamics in conventional and quantum materials, and prepares Perturbo for exascale supercomputing platforms. 

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5. Data-driven low-rank approximation for the electron-hole kernel and acceleration of time-dependent GW calculations

   https://doi.org/10.1038/s41524-025-01680-9  

   Hou, Bowen; Wu, Jinyuan; Chang_Lee, Victor; Guo, Jiaxuan; Liu, Luna Y; Qiu, Diana Y (December 2025, npj Computational Materials)

   Many-body interactions are essential for understanding non-linear optics and ultrafast spectroscopy of materials. Recent first principles approaches based on nonequilibrium Green’s function formalisms, such as the time-dependent adiabatic GW (TD-aGW) approach, can predict nonequilibrium dynamics of excited states including electron-hole interactions. However, the high-dimensionality of the electron-hole kernel poses significant computational challenges. Here, we develop a data-driven low-rank approximation for the electron-hole kernel, leveraging localized excitonic effects in the Hilbert space of crystalline systems to achieve significant data compression through singular value decomposition (SVD). We show that the subspace of non-zero singular values remains small even as the k-grid grows, ensuring computational tractability with extremely dense k-grids. This low-rank property enables at least 95% data compression and an order-of-magnitude speedup of TD-aGW calculations. Our approach avoids intensive training processes and eliminates time-accumulated errors, seen in previous approaches, providing a general framework for high-throughput, nonequilibrium simulation of light-driven dynamics in materials. 

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