Organic molecular crystals are expected to feature appreciable electron-phonon interactions that influence their electronic properties at zero and finite temperature. In this work, we report first-principles calculations and an analysis of the electr
on-phonon self-energy in naphthalene crystals. We compute the zero-point renormalization and temperature dependence of the fundamental band gap, and the resulting scattering lifetimes of electronic states near the valence- and conduction-band edges employing density functional theory. Further, our calculated phonon renormalization of the $GW$-corrected quasiparticle band structure predicts a fundamental band gap of 5 eV for naphthalene at room temperature, in good agreement with experiments. From our calculated phonon-induced electron lifetimes, we obtain the temperature-dependent mobilities of electrons and holes in good agreement with experimental measurements at room temperatures. Finally, we show that an approximate energy self-consistent computational scheme for the electron-phonon self-energy leads to the prediction of strong satellite bands in the electronic band structure. We find that a single calculation of the self-energy can reproduce the self-consistent results of the band gap renormalization and electrical mobilities for naphthalene, provided that the on-the-mass-shell approximation is used, i.e., if the self-energy is evaluated at the bare eigenvalues.
A topological phase transition from a trivial insulator to a $mathbb{Z}_2$ topological insulator requires the bulk band gap to vanish. In the case of noncentrosymmetric materials, these phases are separated by a gapless Weyl semimetal phase. However,
at finite temperature, the gap is affected by atomic motion, through electron-phonon interaction, and by thermal expansion of the lattice. As a consequence, the phase space of topologically nontrivial phases is affected by temperature. In this paper, the pressure and temperature dependence of the indirect band gap of BiTeI is investigated from first principles. We evaluate the contribution from both electron-phonon interaction and thermal expansion, and show that their combined effect drives the topological phase transition towards higher pressures with increasing temperature. Notably, we find that the sensitivity of both band extrema to pressure and topology for electron-phonon interaction differs significantly according to their leading orbital character. Our results indicate that the Weyl semimetal phase width is increased by temperature, having almost doubled by 100 K when compared to the static lattice results. Our findings thus provide a guideline for experimental detection of the nontrivial phases of BiTeI and illustrate how the phase space of the Weyl semimetal phase in noncentrosymmetric materials can be significantly affected by temperature.
We present a new first-principles linear-response theory of changes due to perturbations in the quasiparticle self-energy operator within the $GW$ method. This approach, named $GW$ perturbation theory ($GW$PT), is applied to calculate the electron-ph
onon ($e$-ph) interactions with the full inclusion of the $GW$ non-local, energy-dependent self-energy effects, going beyond density-functional perturbation theory. Avoiding limitations of the frozen-phonon technique, $GW$PT gives access to $e$-ph matrix elements at the $GW$ level for all phonons and scattering processes, and the computational cost scales linearly with the number of phonon modes (wavevectors and branches) investigated. We demonstrate the capabilities of $GW$PT by studying the $e$-ph coupling and superconductivity in Ba$_{0.6}$K$_{0.4}$BiO$_3$. We show that many-electron correlations significantly enhance the $e$-ph interactions for states near the Fermi surface, and explain the observed high superconductivity transition temperature of Ba$_{0.6}$K$_{0.4}$BiO$_3$ as well as its doping dependence.
The absorption spectra of single-layer GaSe and GaTe in the hexagonal phase feature exciton peaks with distinct polarization selectivity. We investigate these distinct features from first-principle calculations using the GW-BSE formalisms. We show th
at the brightness of the exciton absorption peaks is tunable with the polarization of the light. Due to the symmetry of the bands under z-axis mirror symmetry, the bound exciton states selectively couple to either in-plane or out-of-plane polarization of the light. In particular, for a p-polarized light absorption experiment, the absorption peaks of the s-like excitons emerge at large angle of incidence, while the overall absorbance reduces over the rest of the spectrum.
The electron-phonon interaction causes thermal and zero-point motion shifts of electron quasiparticle (QP) energies $epsilon_k(T)$. Other consequences of interactions, visible in angle-resolved photoemission spectroscopy (ARPES) experiments, are broa
dening of QP peaks and appearance of sidebands, contained in the electron spectral function $A(k,omega)=-{Im m}G_R(k,omega) /pi$, where $G_R$ is the retarded Greens function. Electronic structure codes (e.g. using density-functional theory) are now available that compute the shifts and start to address broadening and sidebands. Here we consider MgO and LiF, and determine their nonadiabatic Migdal self energy. The spectral function obtained from the Dyson equation makes errors in the weight and energy of the QP peak and the position and weight of the phonon-induced sidebands. Only one phonon satellite appears, with an unphysically large energy difference (larger than the highest phonon energy) with respect to the QP peak. By contrast, the spectral function from a cumulant treatment of the same self energy is physically better, giving a quite accurate QP energy and several satellites approximately spaced by the LO phonon energy. In particular, the positions of the QP peak and first satellite agree closely with those found for the Frohlich Hamiltonian by Mishchenko $textit{et al.}$ (2000) using diagrammatic Monte Carlo. We provide a detailed comparison between the first-principles MgO and LiF results and those of the Frohlich Hamiltonian. Such an analysis applies widely to materials with infra-red active phonons. We also compare the retarded and time-ordered cumulant treatments: they are equivalent for the Frohlich Hamiltonian, and only slightly differ in first-principles electron-phonon results for wide-band gap materials.
The effect of electron-phonon interactions on optical absorption spectra requires a special treatment in materials with strong electron-hole interactions. We conceptualize these effects as exciton-phonon coupling. Through phonon absorption and emissi
on, the optically accessible excitons are scattered into dark finite-momentum exciton states. We derive a practical expression for the exciton-phonon self-energy that relates to the temperature dependence of the optical transitions and their broadening. This expression differs qualitatively from previous approximated expressions found in literature.
We determine the topological phase diagram of BiTl(S$_{1-delta}$Se$_{delta}$)$_2$ as a function of doping and temperature from first-principles calculations. Due to electrontextendash phonon interaction, the bands are renormalized at finite temperatu
re, allowing for a transition between the trivial ($Z_2=0$) and non-trivial ($Z_2=1$) topological phase. We find two distinct regions of the phase diagram with non-trivial topology. In BiTlS$_2$, the phonons promote the crystal to the topological phase at high temperature, while in BiTlSe$_2$, the topological phase exists only at low temperature. This behaviour is explained by the symmetry of the phonon coupling potential, whereby the even phonon modes (whose potential is even under inversion) promote the topological phase and the odd phonon modes promote the trivial phase.
The renormalization of the band structure at zero temperature due to electron-phonon coupling is investigated in diamond, BN, LiF and MgO crystals. We implement a dynamical scheme to compute the frequency-dependent self-energy and the resulting quasi
particle electronic structure. Our calculations reveal the presence of a satellite band below the Fermi level of LiF and MgO. We show that the renormalization factor (Z), which is neglected in the adiabatic approximation, can reduce the zero-point renormalization (ZPR) by as much as 40%. Anharmonic effects in the renormalized eigenvalues at finite atomic displacements are explored with the frozen-phonon method. We use a non-perturbative expression for the ZPR, going beyond the Allen-Heine-Cardona theory. Our results indicate that high-order electron-phonon coupling terms contribute significantly to the zero-point renormalization for certain materials.
The renormalization of electronic eigenenergies due to electron-phonon interactions (temperature dependence and zero-point motion effect) is important in many materials. We address it in the adiabatic harmonic approximation, based on first principles
(e.g. Density-Functional Theory), from different points of view: directly from atomic position fluctuations or, alternatively, from Janaks theorem generalized to the case where the Helmholtz free energy, including the vibrational entropy, is used. We prove their equivalence, based on the usual form of Janaks theorem and on the dynamical equation. We then also place the Allen-Heine-Cardona (AHC) theory of the renormalization in a first-principle context. The AHC theory relies on the rigid-ion approximation, and naturally leads to a self-energy (Fan) contribution and a Debye-Waller contribution. Such a splitting can also be done for the complete harmonic adiabatic expression, in which the rigid-ion approximation is not required. A numerical study within the Density-Functional Perturbation theory framework allows us to compare the AHC theory with frozen-phonon calculations, with or without the rigid-ion terms. For the two different numerical approaches without rigid-ion terms, the agreement is better than 7 $mu$eV in the case of diamond, which represent an agreement to 5 significant digits. The magnitude of the non rigid-ion terms in this case is also presented, distinguishing specific phonon modes contributions to different electronic eigenenergies.
