Exact Coulomb cutoff technique for supercell calculations

Abstract

We present a reciprocal space analytical method to cut off the long range interactions in supercell calculations for systems that are infinite and periodic in one or two dimensions, generalizing previous work to treat finite systems. The proposed cutoffs are functions in Fourier space, that are used as a multiplicative factor to screen the bare Coulomb interaction. The functions are analytic everywhere except in a subdomain of the Fourier space that depends on the periodic dimensionality. We show that the divergences that lead to the nonanalytical behavior can be exactly canceled when both the ionic and the Hartree potential are properly screened. This technique is exact, fast, and very easy to implement in already existing supercell codes. To illustrate the performance of the scheme, we apply it to the case of the Coulomb interaction in systems with reduced periodicity ͑as one-dimensional chains and layers͒. For these test cases, we address the impact of the cutoff on different relevant quantities for ground and excited state properties, namely: the convergence of the ground state properties, the static polarizability of the system, the quasiparticle corrections in the GW scheme, and the binding energy of the excitonic states in the Bethe-Salpeter equation. The results are very promising and easy to implement in all available first-principles codes.

Plasmons in metallic monolayer and bilayer transition metal dichalcogenides

“…In order to remove the interaction between supercells, the Coulomb interaction was truncated in the direction perpendicular to the layers. 26 If this is not done, the plasmons in neighboring layers will interact for in-plane wave vectors q < 2π/L, where L is the distance between the layers. In particular, the plasmon energy will incorrectly tend to a finite energy in the q → 0 limit.…”

A First-Principles Time-Dependent Density Functional Theory Framework for Spin and Time-Resolved Angular-Resolved Photoelectron Spectroscopy in Periodic Systems

“…In our implementation we used the exact cutoff method described in Ref. 46 along the non-periodic dimension and employed non-orthogonal grids 47 , optimized according to the lattice symmetries, on the periodic ones. Our implementation is fully parallel in grid points, k-points, bands and spin dimension.…”

Quasiparticle energy and optical excitations of gated bilayer graphene

“…To solve this problem, we deliberately employ the mini Brillouin zone (BZ) sampling scheme to account for this sharply-varying character as motivated by Refs. 26,27 , and use it to both evaluate the QP energies and solve the BSE (Ref. 28 ).…”

“…To eliminate the spurious interaction between neighboring BLG, the slab-truncation scheme is applied to mimic isolated GBLG 26,27 . The electric field is applied, via periodic sawtooth potential, perpendicular to graphene layers.…”