Circular dichroism of crystals from first principles

Christian Multunas, Andrew Grieder, Junqing Xu, Yuan Ping, and Ravishankar Sundararaman

Phys. Rev. Materials 7, 123801 – Published 4 December 2023

Abstract

Chiral crystals show promise for spintronic technologies on account of their high spin selectivity, which has led to significant recent interest in quantitative characterization and first-principles prediction of their spin-optoelectronics properties. Here, we outline a computational framework for efficient ab initio calculations of circular dichroism (CD) in crystalline materials. We leverage direct calculations of orbital angular momentum and quadrupole matrix element calculations in density-functional theory (DFT) and Wannier interpolation to calculate CD in complex materials, removing the need for band convergence and accelerating Brillouin-zone convergence compared to prior approaches. We find strong agreement with measured CD signals in molecules and crystals ranging in complexity from small bulk unit cells to 2D hybrid perovskites, and show the importance of the quadrupole contribution to the anisotropic CD in crystals. Spin-orbit coupling affects the CD of crystals with heavier atoms, as expected, but this is primarily due to changes in the electronic energies, rather than due to direct contributions from the spin matrix elements. We showcase the capability to predict CD for complex structures on a 2D hybrid perovskite, finding strong orientation dependence and identifying the eigen-directions of the unit cell with the strongest CD. We additionally decompose CD into separate contributions from inorganic, organic, and mixed organic-inorganic transitions, finding the chiral molecules to dominate the CD, with the inorganic lattice contributing at higher frequencies in specific directions. This unprecedented level of detail in CD predictions in crystals will facilitate experimental development of complex chiral crystals for spin selectivity.

Received 22 June 2023
Revised 5 October 2023
Accepted 8 November 2023

DOI:https://doi.org/10.1103/PhysRevMaterials.7.123801

Physics Subject Headings (PhySH)

Optical activity

Chiral symmetry

First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Christian Multunas¹, Andrew Grieder ², Junqing Xu^3,4, Yuan Ping^2,5,*, and Ravishankar Sundararaman ^1,6,†

¹Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
²Department of Materials Science and Engineering, University of Wisconsin-Madison, Wisconsin 53706, USA
³Department of Physics, Hefei University of Technology, Hefei, Anhui 230009, China
⁴Department of Chemistry and Biochemistry, University of California, Santa Cruz, California 95064, USA
⁵Department of Physics, University of California, Santa Cruz, California 95064, USA
⁶Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA

^*yping3@wisc.edu
^†sundar@rpi.edu

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Issue

Vol. 7, Iss. 12 — December 2023

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Images

Figure 1
Band convergence of CD computed purely from momentum $p$ matrix elements using Eq. (14), compared to the direct DFT evaluation of $L$ and $Q_{μ ν}$ matrix elements without the additional sum over bands, for (a) camphor and (b) Te, which additionally shows the Wannier prediction for comparison. More than 1000 bands are necessary to converge the result for the camphor molecule, while 100 bands achieve adequate convergence for the Te crystal. (c) Convergence of direct DFT prediction of CD for Te with number of $k$ -points for Brillouin zone integration.
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Figure 2
Calculated CD spectra for (a) camphor and (b) norcamphor agree well with measurements [29]. The HOMO-LUMO gap is corrected using the scissor operator (shift unoccupied energy levels) to match experiment, but the CD spectrum is matched quantitatively without any scaling.
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Figure 3
(a) Predicted CD for cubic chiral semimetal CoSi is entirely from the magnetic dipole (MD) terms, with no contribution from the electric quadrupole (EQ) terms. The CD is equal and opposite for enantiomers with the ${P 2}_{1} 3$ (R) and ${P 2}_{1} \bar{3}$ (S) space groups, and (b) is unaffected by spin-orbit coupling (SOC). (c) Computed optical conductivity (OC) for CoSi shows good agreement with experiment in the location of the absorption peaks, and the differential absorption for CD also peaks at the same frequencies. (d, e) Same as panels (a, b) for MgPt, showing a nonnegligible impact of SOC. (f) Spin contributions do not change the CD of MgPt, and the impact of SOC is instead due to band energy changes. (g) Band structure of CoSi is largely unchanged by SOC, while (h) that of MgPt shows spin-splits $\sim 0.1 - 0.2$ eV.
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Figure 4
Calculated CD tensor of hexagonal crystals quartz, Te, and Se shows strong anisotropy between in-plane ( $xx$ = $yy$ ) and out-of-plane ( $zz$ ) directions. The total CD ( $MD + EQ$ ) is substantially modified by the electric quadrupole (EQ) contributions compared to the magnetic-dipole-only CD (MD).
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Figure 5
(a) Predicted CD for Se matches experiment well [37], after using a scissor to correct the band gap, assuming path length $l = 0.01$ mm not reported in Ref. [37]. (b) Optical rotation (OR) for Te, obtained by Kramers-Kronig integration of predicted CD, matches experimental measurements quantitatively [38]. The electric quadrupole term is critical to even get the correct sign as experiment for the OR of Te.
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Figure 6
(a) Predicted CD agrees with measurements [43] for hybrid perovskite (S)-NPB (1-(1-naphthyl)ethylammonium lead bromide) beyond the first excitonic peak not captured in our DFT calculations. Since experimental data is polycrystalline and does not report path length, we show the isotropic average ( $Tr Δ α$ /3) and fit path length $l = 0.02$ mm to match the predicted magnitude. (b) Atomic structure of (S)-NPB, where the chiral molecules distort the inorganic lattice to induce chirality throughout, indicating eigendirections $α$ and $β$ in the $x z$ plane that lead to maximal CD magnitude. (c) Angular dependence of CD in the $x z$ and $x y$ planes, showing maximum magnitudes along the $α$ and $β$ directions for all frequencies, almost an an order of magnitude higher than that along the optical axis ( $y$ direction). (d) Orbital decomposition of CD along the eigendirections at two peak frequencies $A$ and $B$ : each heat map is split into quadrants based on transitions from initial and final states in the organic molecule and inorganic lattice components. The intramolecular contributions dominate the CD, with mixed and inorganic contributions becoming important only for higher frequencies in the $y$ direction.
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