arXiv subjects

Shilpa Paul

Publications and source records attributed to Shilpa Paul.

4 recordsLinked to original sources

arXiv2026

Accurate computation of the electron-phonon interaction contribution to the total energy

The standard Hamiltonian of a coupled electron-phonon system is based on second-order perturbation theory. The EPI contribution in the standard Hamiltonian consists of two terms, the EPI contribution to the band-structure energy and the partial-Fan-Migdal (FM)-occupied contribution. Within the non-adiabatic approximation, we derive a new expression for the partial-FM-occ contribution and show that it has the structure of a higher-order term, and not a second-order term. Along similar lines, we derive new expressions for the computation of the partial-FM-occ term. The new expressions for the partial-FM-occ term must be preferred over the standard expressions, in theoretical and computational studies, because they incorporate the complete physics underlying this term. Unlike the EPI contribution to individual eigenstates, the EPI contribution to the total energy must be computed in the non-adiabatic approximation for all materials, Infra-red (IR) active and IR-inactive. We report the computation of the standard Hamiltonian, for the first time, for Carbon polymorphs (diamond and hexagonal lonsdaleite) by including the EPI contribution to the total energy. This is the most accurate ab initio total energy reported till date. The present work also opens the way to compute the ab initio free-energy more accurately at finite temperatures by including the EPI contribution.

cond-mat.mtrl-sci↗

arXiv2025

Theoretical issues in the accurate computation of the electron-phonon interaction contribution to the total energy

We report the computation of the Standard Hamiltonian of a coupled electron-phonon system by accurately computing the electron-phonon interaction (EPI) contribution to the total energy. This gives the most accurate ab initio total energy till date. However, our results show that the per-atom EPI energy is unit-cell-size dependent due to the partial-Fan-Migdal term that arises from the antisymmetric nature of the crystal wavefunction. Due to this, only energy differences between polytypes, in supercells with identical number of atoms, are meaningful, rather than per-atom total energy. This violates our understanding of Quantum Mechanics applied to periodic solids and raises serious theoretical questions. In his original (1951) paper, Fan suggested, without specifying any reason, that second-order perturbation theory applied to the whole crystal is of questionable validity. Our results support Fan's suggestion for the reason that the partial-FM term makes the per-atom total energy unit-cell-size dependent. This leads to a new fundamental problem in condensed matter physics, viz. second-order perturbation theory is invalid for whole crystals, an entire class. It is essential to resolve this problem, especially because it causes the standard Hamiltonian, the starting point of EPI studies and the most accurate ab initio total energy, to be of questionable validity.

cond-mat.mtrl-sci↗

arXiv2023

Electron-phonon interaction contribution to the total energy of group IV semiconductor polymorphs: evaluation and implications

In density functional theory (DFT) based total energy studies, the van der Waals (vdW) and zero-point vibrational energy (ZPVE) correction terms are included to obtain energy differences between polymorphs. We propose and compute a new correction term to the total energy, due to electron-phonon interactions (EPI). We rely on Allen's general formalism, which goes beyond the Quasi-Harmonic Approximation (QHA), to include the free energy contributions due to quasiparticle interactions. We show that, for semiconductors and insulators, the EPI contributions to the free energies of electrons and phonons are the corresponding zero-point energy contributions. Using an approximate version of Allen's formalism in combination with the Allen-Heine theory for EPI corrections, we calculate the zero-point EPI corrections to the total energy for cubic and hexagonal polytypes of Carbon, Silicon and Silicon Carbide. The EPI corrections alter the energy differences between polytypes. In SiC polytypes, the EPI correction term is more sensitive to crystal structure than the vdW and ZPVE terms and is thus essential in determining their energy differences. It clearly establishes that the cubic SiC-3C is metastable and hexagonal SiC-4H is the stable polytype. Our results are consistent with the experimental results of Kleykamp. Our study enables the inclusion of EPI corrections as a separate term in the free energy expression. This opens the way to go beyond the QHA by including the contribution of EPI on all thermodynamic properties.

cond-mat.mtrl-sci↗

arXiv2022

Critical role of electron-phonon interactions in determining the relative stability of Boron Nitride polymorphs

Despite several first principles studies, the relative stability of BN polymorphs remains controversial. The stable polymorph varies between the cubic (c-BN) and hexagonal (h-BN) depending on the van der Waals (vdW) dispersion approximation used. These studies are unable to explain the main experimental results, c-BN is stable, the relative stability order and the large energy difference between h-BN and c-BN (greater than 150 meV/formula unit). In this study, we introduce contributions from electron-phonon interactions (EPI) to the total energy of BN polymorphs. This clearly establishes c-BN is the stable polymorph irrespective of the vdW approximation. Only by including EPI contributions do the ab initio results match, for the first time, the main experimental results mentioned above. The EPI contribution to the total energy is strongly sensitive to chemical bonding (approximately twice in $sp^2$-bonded layered over $sp^3$-bonded polymorphs) and to crystal structure. The crucial role of EPI contributions is seen in $sp^2$-bonded layered BN polymorphs where it is greater than the vdW contribution. Given that h-BN is a prototype layered material, in bulk or 2D form, our results have a broader relevance, that is, including EPI correction, along with vdW approximation, is vital for the study of energetics in layered materials.

cond-mat.mtrl-sci↗