Band gap renormalization, carrier mobilities, and the electron-phonon self-energy in crystalline naphthalene

Abstract

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 firstprinciples calculations and an analysis of the electron-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.

ABINIT: Overview and focus on selected capabilities

“…Both approaches are implemented in ABINIT although it should be noted that, according to recent works, the on-the-mass-shell approach provides results that are closer to those obtained with more advanced techniques based on the cumulant expansion 122 or self-energy calculations employing an eigenvalue-self-consistent cycle. 123 Accurate calculations of e-ph renormalization are still challenging even by present standards because the e-ph self-energy is quite sensitive to the q-point sampling. Moreover, a large number of empty states m are usually required to converge the real part of the self-energy.…”

“…Furthermore, this upper-band contribution to Σ converges quickly with respect to q-point sampling, and it can be safely computed on a coarse q-grid. 123,129 The code can compute QP corrections and lifetimes due to e-ph scattering as well as spectral functions. The lifetimes obtained from the imaginary part of Eq.…”

Fröhlich polaron effective mass and localization length in cubic materials: Degenerate and anisotropic electronic bands

“…Such features can only be addressed by first-principles approaches, that have seen an impressive development during the last two decades. Existing first-principles approaches consider polarons either in the self-trapped adiabatic state [1,[11][12][13][14][15], corresponding to the strong-coupling limit, or from many-body perturbation theory, corresponding to the weak-coupling limit, e.g., the Allen-Heine-Cardona (AHC) approach [16][17][18][19][20][21][22][23][24][25][26][27]. In the first case, the polaron formation energy is computed from the associated collective atomic displacement pattern and frozen electronic density, and the mobility is estimated through the computation of barriers for transitioning the localized polaron from one site to another.…”

First-principles predictions of Hall and drift mobilities in semiconductors

“…Due to the complexity of computing carrier mobilities fully from first principles, the first calculation appeared only in 2009 10 . Since then, only 19 bulk semiconductors have been investigated: Si [10][11][12][13][14][15][16] , Diamond 17 , GaAs 13,[18][19][20][21][22] , GaN [23][24][25] , 3C-SiC 26,27 , GaP 22 , GeO 2 28 , SnSe 29 , SnSe 2 30 , BAs 31,32 , PbTe 33,34 , naphtalene 35,36 , Bi 2 Se 3 37 , Ga 2 O 3 [38][39][40][41] , TiO 2 42 , SrTiO 3 43,44 , PbTiO 3 15 , Rb 3 AuO 45 , and CH 3 NH 3 PbI 3 46 .…”