A Full Minimal Coupling GW-BSE Framework for Circular Dichroism in Solids: Applications to Chiral 2D Perovskites

Abstract

Circular dichroism (CD) and other chiroptical responses are a key probe of both chirality and momentum-space geometry in solids, but first-principles calculations are still challenging in periodic systems with strong exciton effects. Here, we develop a gauge-invariant first-principles framework for CD including exciton effects based on full minimal coupling (FMC) within the GW plus Bethe-Salpeter equation (GW-BSE) formalism. In contrast to standard multipole expansion and sum-over-states (SOS) approaches, which require careful gauge-fixing, converge slowly, and suffer origin ambiguities, FMC evaluates optical matrix elements directly at finite photon wavevector, naturally including intraband and near-degenerate transitions while placing electric-dipole (ED), magnetic-dipole (MD), and electric-quadrupole (EQ) contributions on equal footing. Applied to two prototypical two-dimensional chiral hybrid perovskites, (S-NEA)2PbBr4 and (S-MBA)2PbI4, our calculations reveal that MD and EQ channels contribute equally to the CD signal. Crucially, intraband and quasi-degenerate transitions only captured within FMC can significantly modify CD spectra, especially in systems with dense band degeneracies. The FMC framework, therefore, offers a computationally efficient and numerically robust way for predicting chiral optoelectronic phenomena in complex solids.

Figures (3)

• Figure 1: SOS CD calculations for S-NPB.a Spectra at the GW independent-particle level. showing (i) the imaginary part of the dielectric function $\epsilon"$, and (ii) the differential imaginary response computed with MD-only, EQ-only, and both contributions. b Same as a at the GW-BSE level including excitons. c, Contribution of independent-particle bands (VBM=highest valence band; CBM=lowest conduction band) to the four lowest energy excitons (D, X, Y, Z); the optically bright X and Y states are highlighted in red. The size of the circles scales with $\sum_{c\mathbf{k}}|A^S_{vc\mathbf{k}}|^2$ for valence states or $\sum_{v\mathbf{k}}|A^S_{vc\mathbf{k}}|^2$ for conduction states. d, Convergence of the excitonic CD spectrum with respect to the number of bands in the SOS summation.
• Figure 2: FMC CD calculations for 2D-HOIPs.a, CD spectra for S‑MPI (with excitons) obtained via SOS using different energy thresholds (Rydbergs) to identify degenerate states. b, Contributions of independent‑particle bands to excitons near the first bright peak. X, Y, Z label the brightest states for the corresponding linear polarizations; D denotes the lowest dark state. Bright X and Y are highlighted in red. c,d, CD spectra from SOS and FMC at the independent‑particle level (lower panels) and including excitonic effects (upper panels) for c S-NPB and c S-MPI.
• Figure 3: Analysis of SOS and FMC.a,b. Spatially dependent part of the transition matrix element D of S-NPB from the SOS and FMC approaches. c,d. Diagonal elements of the electron orbital-angular-momentum matrix for S-MPI evaluated with (c) SOS and (d) FMC.