Title: Solving the Bethe-Salpeter equation on a subspace: Approximations and consequences for low-dimensional materials

Abstract

It is well known that the ambient environment can dramatically renormalize the quasiparticle gap and exciton binding energies in low-dimensional materials, but the effect of the environment on the energy splitting of the spin-singlet and spin-triplet exciton states is less understood. A prominent effect is the renormalization of the exciton binding energy and optical strength (and hence the optical spectrum) through additional screening of the direct Coulomb term describing the attractive electron-hole interaction in the kernel of the Bethe-Salpeter equation. The repulsive exchange interaction responsible for the singlet-triplet splitting, on the other hand, is unscreened within formal many-body perturbation theory. However, Benedict argued that in practical calculations restricted to a subspace of the full Hilbert space, the exchange interaction should be appropriately screened by states outside of the subspace, the so-called S approximation [L. X. Benedict, Phys. Rev. B 66, 193105 (2002)PRBMDO0163-182910.1103/PhysRevB.66.193105]. Here, we systematically explore the accuracy of the S approximation for different confined systems, including a molecule and heterostructures of semiconducting and metallic layered materials. We show that the S approximation is actually exact in the limit of small exciton binding energies (i.e., small direct term) and can be used to significantly accelerate convergence of the exciton energiesmore » with respect to the number of empty states, provided that a particular effective screening consistent with the conventional Tamm-Dancoff approximation is employed. We further find that the singlet-triplet splitting in the energy of the excitons is largely unaffected by the external dielectric environment for most quasi-two-dimensional materials.« less

Authors:

Qiu, Diana Y.  ^[1];

• Search DOE PAGES for author "Qiu, Diana Y."
• Search DOE PAGES for ORCID "0000-0003-3067-6987"

da Jornada, Felipe H. ^[2]; Louie, Steven G.  ^[3]

• Search DOE PAGES for author "Louie, Steven G."
• Search DOE PAGES for ORCID "0000-0003-0622-0170"

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+ Show Author Affiliations

1. Yale Univ., New Haven, CT (United States); Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Stanford Univ., Palo Alto, CA (United States)
3. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Publication Date:

Fri Jan 15 00:00:00 EST 2021

Research Org.:

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division

OSTI Identifier:

1823051

Grant/Contract Number:  

AC02-05CH11231

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review B

Additional Journal Information:

Journal Volume: 103; Journal Issue: 4; Journal ID: ISSN 2469-9950

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Dielectric properties; Electronic structure; Electronic structure of atoms & molecules; Excitons; First-principles calculations; Quasiparticles & collective excitations