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Visualization of atomistic optical waves in crystals

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Inside SiC, the refractive index stops being a single number.

desk verdict A well-illustrated application of the authors' own eigen-decomposition framework to 3C-SiC, but the quantitative claims are not yet backed by converged or benchmarked calculations. read the letter →

arxiv 2411.09876 v1 pith:JJQFKNVZ submitted 2024-11-15 physics.optics cond-mat.other

Jungho Mun , Sathwik Bharadwaj , Zubin Jacob This is my paper · ORCID
classification physics.opticscond-mat.other PACS 78.20.Ci71.45.Gm
keywords refractiveindexmicroscopicopticalbandstructuredielectricmatrixnonlocalitysiliconcarbideeigenmodeslocal-fieldeffectsatomisticelectrodynamics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that the classical refractive index is only an approximation that holds for uniform planewaves in a homogeneous medium. At the atomistic level, a crystal's optical response is a nonlocal, multi-modal object: diagonalizing the inverse dielectric matrix yields a deep microscopic optical band structure with many eigenwaves, each carrying its own screening strength. For silicon carbide, the authors compute these eigenwaves and show that the dominant one resembles a planewave, while higher-order ones are nonplanar and inhomogeneous even near the optical limit. They reconstruct the macroscopic dielectric constant as a mode-weighted average of screening strengths, obtaining ε_eff = 4.908, and conclude that the refractive index of a crystal depends on the spatial structure of the field inside it.

What carries the argument

The central object is the deep microscopic optical band structure, obtained by the eigen-decomposition of the dielectric matrix: ε̄(q,ω) = Σ_λ |E_λ⟩ π_λ ⟨E_λ|. Here π_λ(q,ω) is the microscopic optical index (whose screening strength is 1 − $π_λ^{{-1}}$) and |E_λ⟩ is the microscopic optical eigenwave. Below the bandgap the dielectric matrix is Hermitian, so the eigenwaves form an orthonormal basis; this lets an arbitrary external field be decomposed into these eigenwaves, and the effective screening strength follows as $ε_eff^{{-1}}$ = Σ_λ w_λ $π_λ^{{-1}}$ with weights w_λ = Σ_g |E_{λg}† E_g|^2. This decomposition is what turns the refractive index from a scalar into a mode-dependent quantity.

What would settle it

Repeat the dielectric-matrix calculation with a larger reciprocal-space cutoff and denser k-mesh (for instance a 101×101 matrix and a 25×25×25 k-mesh) and compare the resulting mode-weighted ε_eff to the experimental electronic dielectric constant of 3C-SiC; if the converged value moves substantially away from 4.908 toward the measured value, the quantitative claim that local fields lower the dielectric constant to this degree is called into question, although the qualitative existence of nonplanar higher-order eigenwaves could still survive.

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Extended reading notes

Core claim

The central discovery is that the dielectric response of a crystal decomposes into a discrete set of microscopic optical eigenwaves, and that the effective screening felt by any field is a weighted average over these eigenwaves, with weights determined by the field's overlap with each mode. In SiC, the eigenvalue decomposition of the Hermitian dielectric matrix at q = 2π/a (0.1,0,0) and ω = 10 THz yields a dominant eigenwave (λ = 0) that is nearly a planewave, plus higher-order eigenwaves (λ = 1,2,3,4) with rapidly varying polarization textures at the lattice level. The macroscopic dielectric constant ε_eff = 4.908 is obtained from the eigenmode overlaps and screening strengths 1 − $π_λ^{{-1}}$, and it is lower than the value ε_00 = 5.435 that ignores local-field effects, consistent with the known tendency of local fields to lower the dielectric constant. The paper therefore claims that the refractive index is not a uniquely determined material constant but depends on the structure of the light inside the medium.

Load-bearing premise

The quantitative results rest on the accuracy of the empirical-pseudopotential RPA dielectric matrix computed on a 51×51 reciprocal-space grid with a 15×15×15 k-mesh, and the paper reports no convergence study and does not benchmark its ε_eff = 4.908 (or ε_00 = 5.435) against the measured electronic dielectric constant of 3C-SiC (about 6.5).

Editorial extensions

If this is right

  • Near the Γ-point, higher-order eigenwaves remain nonplanar and inhomogeneous, so atomistic nonlocal optical response persists even in the small-momentum limit.
  • Structured or localized light that couples strongly to high-order eigenwaves will experience a lower effective screening strength than a macroscopic planewave.
  • The paper predicts hidden optical eigenwaves that do not couple to macroscopic planewaves, and suggests they may carry topological optical invariants.
  • The macroscopic dielectric constant is lowered by local-field effects: for SiC at 10 THz, the mode-weighted value is 4.908 versus 5.435 without local fields.
  • The framework is intended to extend beyond SiC to other materials, including two-dimensional materials and transverse excitations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the mode-weighted picture is correct, far-field measurements (which approximate planewaves) and near-field probes (electron beams, optical antennas) will systematically report different effective refractive indices for the same crystal; this could be tested by comparing electron energy loss spectra with ellipsometry.
  • The nonplanar higher-order eigenwaves imply that a point emitter inside a crystal radiates into a structured near field that no local dielectric constant can describe, which would affect predicted Purcell factors and radiation patterns of quantum emitters in SiC.
  • One testable extension is to compute the same band structure with a larger reciprocal-space cutoff and denser k-mesh and compare the resulting ε_eff to the measured electronic dielectric constant of 3C-SiC; the quantitative claim about the lowering of the dielectric constant stands only if the converged value remains close to the mode-weighted result.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. This paper introduces a 'deep microscopic optical band structure' for crystalline solids by eigendecomposing the RPA dielectric matrix in reciprocal space, and applies it to 3C-SiC. The dominant eigenmode is shown to be approximately planewave-like while higher-order eigenmodes exhibit rapidly varying polarization textures. The paper derives an effective screening strength as a weighted average of the eigenvalues, and reports that for a macroscopic planewave the effective dielectric constant is ε_eff = 4.908, lower than the head element ε_00 = 5.435. The authors interpret this as evidence that the refractive index is not a unique material property but depends on the spatial structure of the optical field.

Significance. The conceptual framework of decomposing the dielectric response into microscopic eigenwaves is attractive and may offer new insight into nonlocal and local-field effects in crystals. The visualizations of the eigenmodes are evocative. However, the central quantitative claims are not supported by a convergence study or an independent benchmark, and the connection to the transverse refractive index is not established. The qualitative existence of higher-order eigenmodes is robust because any non-diagonal dielectric matrix has multiple eigenmodes, but the specific eigenvalues, weights, and the reported lowering of the dielectric constant require validation. The paper is a promising application of an existing formalism (ref. 26) rather than a fully validated new prediction.

major comments (3)
  1. [S1 (Eq. S1) and Fig. 4] The quantitative results—the eigenvalues πλ, the weights wλ, and the central values ε_eff = 4.908 and ε_00 = 5.435—are computed from a single RPA dielectric matrix with a 51×51 reciprocal-space cutoff, a 15×15×15 k-mesh, 4 valence and 20 conduction bands, and empirical pseudopotentials. No convergence study is reported, and there is no comparison to the measured high-frequency electronic dielectric constant of 3C-SiC (~6.5) or to converged first-principles results. Since the claimed local-field-induced lowering of the dielectric constant depends on the difference between ε_eff and ε_00, the accuracy of the underlying matrix is load-bearing. The authors should provide convergence tests in both the reciprocal-space cutoff and the k-mesh, and benchmark ε_00 against experiment or established DFT calculations.
  2. [Sec. II and Sec. V] The eigen-decomposition in Eq. (2) is performed on the longitudinal dielectric matrix, and the paper explicitly limits the treatment to longitudinal fields. Yet the abstract and conclusions claim a 'quantum generalization of refractive index', which is a property of transverse optical fields. The paper does not justify the connection between the longitudinal eigenmodes and the transverse refractive index; the standard equivalence in the long-wavelength limit for cubic crystals is not discussed. Unless this connection is established, the claim should be reframed as a generalization of longitudinal dielectric response, or the transverse treatment should be included.
  3. [Sec. IV, Eq. (4)] The effective screening formula ε_eff^(-1) = Σ_λ w_λ π_λ^(-1) for a macroscopic planewave is exactly (ε^(-1))_00, the head of the inverse dielectric matrix, which is the standard definition of the macroscopic dielectric function including local-field effects. The paper should state this relation explicitly, because otherwise the derivation appears circular: the eigenvalues and weights are constructed from the same matrix whose macroscopic response they are supposed to explain. With that clarification, the mathematical content is sound, but the predictive claim that 'the classical refractive index is not a unique quantity' (Sec. IV) is not demonstrated: no example of a structured field (e.g., a point source or a tightly focused beam) is given in which the effective screening is actually lowered, nor is the coupling of such fields to the high-order eigenmodes computed. Without such an example, this conclusion is speculative.
minor comments (4)
  1. [Sec. III] The notation n_hat(q+g) is used in Sec. III without definition; it is defined later in Eq. (S3) of the SI, but should be defined at first use in the main text.
  2. [Fig. 3 and SI figures] The figures lack scale bars and clear units; the 'a.u.' intensity scale is not defined.
  3. [SI S1] The SI text contains placeholder citation markers '[? ? ?]' in the reference to Adler-Wiser theory and to the symmetrized Coulomb kernel; these need to be replaced with proper references.
  4. [Sec. III] The paper states that the eigenwaves with λ = 2 and 3 are degenerate and related by a four-fold improper rotation, but this is not shown explicitly; a symmetry analysis or a statement about the irreducible representations would strengthen the claim.

Circularity Check

2 steps flagged · score 4.0 of 10

The field-dependent effective screening and the 'hidden eigenwave' claims are partly built into the definitions; the numeric planewave result is a basis re-expression of the input dielectric matrix, but the RPA calculation itself is not a fitted closed loop.

  1. self definitional [Section IV, Effective dynamic screening (equations after Fig. 4a and concluding paragraph)]
    "The effective screening strength can be obtained as ε−1 eff = Σλ wλ π−1 λ , where the weight is determined by the overlap between the external field and the eigenwaves as wλ = Σg|E†λ gEg|2 ... Therefore, a field experiences an effective screening strength in a crystal ... The refractive index of a matter is not a uniquely determined quantity, but depends on the structure of light inside the media."

    The central qualitative conclusion is entailed by the definition: ε_eff is defined as a weighted average of the eigenvalues of the same dielectric matrix, with field-dependent weights wλ. Thus the statement that the effective screening (and hence the 'refractive index') depends on the spatial structure of the field is true by construction, not an independent prediction. The computation of πλ and wλ still requires the input RPA matrix, so the numerical values are not vacuous, but the conceptual 'field-dependence' claim is a restatement of the defining formula.

  2. renaming known result [Section IV, equations for planewave weights and paragraph reporting εeff = 4.908]
    "For a macroscopic planewave, the weight is given as wλ = Σg|E†λ gδg0|2 ... the macroscopic dielectric constant obtained in this way, εeff = 4.908, is smaller than the macroscopic dielectric constant obtained without the local-field effect, ε00 = 5.435."

    Because the eigenbasis is complete and orthonormal, the planewave weighted average Σλ wλ πλ^{-1} exactly equals the 00 element of the inverse dielectric matrix, (ε^{-1})_{00}. Therefore ε_eff for a planewave is the standard local-field-corrected macroscopic dielectric constant expressed in the eigenbasis; it is a unitary basis change of the input matrix, not an independent physical prediction. The paper presents this linear-algebra identity as a new way to 'obtain' the macroscopic dielectric constant, which is a re-expression rather than a derivation from new physics.

full rationale

The paper does not exhibit the most severe form of circularity: the eigenvalues and eigenvectors are obtained by an explicit eigen-decomposition of a stated RPA dielectric matrix (Eq. S1), and no parameter is fitted to the predicted effective constant or to the experimental dielectric constant. Self-citation to Ref. [26] introduces the 'deep microscopic optical band structure' concept, but the calculation in this paper is spelled out, so the self-citation is not the load-bearing element. However, two central interpretive claims are partly definitional. First, the field-dependent effective screening is defined as an overlap-weighted average of the input matrix's eigenvalues, so the conclusion that the refractive index is not unique but field-dependent follows from the definition rather than from an external test. Second, the planewave value ε_eff = 4.908 is exactly the 00 element of the inverse dielectric matrix rewritten in the eigenbasis, i.e., the standard local-field-corrected macroscopic dielectric constant; the eigen-decomposition is a basis change, not an independent calculation. The missing benchmark against the measured electronic dielectric constant of 3C-SiC (about 6.5) and the absence of a convergence study are correctness risks, not circularity. Overall, the numerical workflow is a real computation, but the framing of field-dependent refractive index and of the macroscopic constant as new predictions is partially circular, giving a score of 4.

Assumptions & free parameters 1 free parameters · 4 assumptions · 1 invented entities

The central claim rests on the empirical-pseudopotential RPA dielectric matrix, the choice of longitudinal-only fields, and the eigen-decomposition of that same matrix. The quantitative outputs inherit fitted pseudopotential parameters and unvalidated numerical cutoffs. The only invented entity is the eigenwave basis itself, which is derived rather than postulated but is presented as a fundamental physical quantity without independent experimental evidence.

free parameters (1)
  • Empirical pseudopotential form factors for SiC = not stated in the paper
    The band structure used in the RPA dielectric matrix (Eq. S1) is obtained from the empirical pseudopotential method; these form factors are fitted to prior experimental or ab initio band structure data and directly control the eigenvalues pi_lambda and the resulting dielectric constant values.
assumptions (4)
  • standard math The dielectric matrix is Hermitian for frequencies below the bandgap, so eigen-decomposition yields orthonormal eigenwaves
    Used in Section II to justify treating eigenwaves as an orthonormal basis for the optical response.
  • domain assumption The Adler-Wiser RPA formula (Eq. S1) correctly describes the longitudinal dielectric response including local field effects
    The entire optical band structure is computed from this formula; no benchmarking is given in the paper.
  • domain assumption Longitudinal fields only; transverse parts are neglected
    The framework defines eigenwaves for longitudinal fields (Eq. 3) and defers transverse excitation to future work; the claim of a general 'refractive index' is therefore restricted to longitudinal probes like EELS.
  • domain assumption The empirical pseudopotential band structure with 4 valence and 20 conduction bands on a 15x15x15 k-mesh is converged enough for the optical response
    No convergence study is provided; the quantitative results (epsilon_eff = 4.908) depend on these numerical choices.
invented entities (1)
  • Deep microscopic optical band structure and microscopic optical eigenwaves
    purpose: Provides a basis to decompose the dielectric response and to define a 'quantum generalization of refractive index' for crystals
    These are mathematical constructs from the eigen-decomposition of the dielectric matrix (Eq. 2); no direct experimental observable or falsifiable prediction is demonstrated beyond the computed images, and the claim of topological properties is speculative.

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Pith. "Pith review of Visualization of atomistic optical waves in crystals." pith.science (2026). https://pith.science/paper/JJQFKNVZ

@misc{pith2026241109876,
  author       = {Pith},
  title        = {Pith review of: Visualization of atomistic optical waves in crystals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JJQFKNVZ}},
  note         = {Machine review of arXiv:2411.09876}
}
read the original abstract

The refractive index of a matter is foundational to quantify the light-matter interaction of the medium. However, the classical description of refractive index is based on macroscopic homogenization and is limited to describing the local optical response of materials. A complete quantum description of light-matter interaction should consider nonlocality and multiple-scattering of optical responses at the atomistic lattice level. Recently, the deep microscopic optical band structure was introduced as a quantum generalization of refractive index of a medium. This quantum description unveils multiple optical eigenmodes in crystalline solids and hidden microscopic optical waves at the lattice level. In this work, we unravel the microscopic optical waves in silicon carbide. We predict and visualize hidden microscopic optical eigenwaves, which can be nonplanar and inhomogeneous even near the optical limit. Also, the nonlocal macroscopic dielectric constant of the crystal is analyzed using the microscopic optical waves as the basis. Our work establishes a general framework for picoscale electrodynamics applicable to other materials including two-dimensional materials.

Figures

Figures reproduced from arXiv: 2411.09876 by the authors.

Figure 1
Figure 1. FIG. 1. Concept of refractive index in a crystalline solid. (a) Clas [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Light inside lattices of a crystalline solid. (a) The unit-cell and (b) the Brillouin zone of SiC with zincblende crystal structure. (c) [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Distributions of atomistic lights and local polarization tex [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Schematics of the effective screening process experienced [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

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Works this paper leans on

38 extracted references · 33 canonical work pages

  1. [1]

    J. D. Jackson, Classical electrodynamics; 3rd ed. (Wiley, New York, NY , 1999)

    work page 1999

  2. [2]

    Andreoli, M

    F. Andreoli, M. J. Gullans, A. A. High, A. Browaeys, and D. E. Chang, Maximum refractive index of an atomic medium, Phys. Rev. X 11, 011026 (2021)

    2021

  3. [3]

    H. Shim, F. Monticone, and O. D. Miller, Fundamental limits to the refractive index of transparent optical materials, Adv. Mater. 33, 2103946 (2021)

    2021

  4. [4]

    V . M. Shalaev, Optical negative-index metamaterials, Nature photonics 1, 41 (2007)

    work page 2007

  5. [5]

    J. Mun, M. Kim, Y . Yang, T. Badloe, J. Ni, Y . Chen, C.-W. Qiu, and J. Rho, Electromagnetic chirality: from fundamentals to nontraditional chiroptical phenomena, Light: Science & Ap- plications 9, 139 (2020)

    work page 2020

  6. [6]

    D. Lee, S. So, G. Hu, M. Kim, T. Badloe, H. Cho, J. Kim, H. Kim, C.-W. Qiu, and J. Rho, Hyperbolic metamaterials: fusing artificial structures to natural 2d materials, ELight 2, 1 (2022)

    work page 2022

  7. [7]

    Liberal and N

    I. Liberal and N. Engheta, Near-zero refractive index photonics, Nature Photonics 11, 149 (2017)

    work page 2017

  8. [8]

    Galfsky, H

    T. Galfsky, H. Krishnamoorthy, W. Newman, E. Narimanov, Z. Jacob, and V . Menon, Active hyperbolic metamaterials: en- hanced spontaneous emission and light extraction, Optica 2, 62 (2015)

    work page 2015

Show all 38 references
  1. [9]

    Gonçalves, T

    P. Gonçalves, T. Christensen, N. Rivera, A.-P. Jauho, N. A. Mortensen, and M. Solja ˇci´c, Plasmon–emitter interactions at the nanoscale, Nat. Commun. 11, 366 (2020)

    2020

  2. [10]

    Tsukerman, Classical and non-classical effective medium the- ories: New perspectives, Phys

    I. Tsukerman, Classical and non-classical effective medium the- ories: New perspectives, Phys. Lett. A 381, 1635 (2017)

    2017

  3. [11]

    A. A. Orlov, P. M. V oroshilov, P. A. Belov, and Y . S. Kivshar, Engineered optical nonlocality in nanostructured metamateri- als, Phys. Rev. B 84, 045424 (2011)

    2011

  4. [12]

    Torquato and J

    S. Torquato and J. Kim, Nonlocal effective electromagnetic wave characteristics of composite media: Beyond the qua- sistatic regime, Phys. Rev. X 11, 021002 (2021)

    2021

  5. [13]

    Lobet, I

    M. Lobet, I. Liberal, L. Vertchenko, A. V . Lavrinenko, N. En- gheta, and E. Mazur, Momentum considerations inside near- zero index materials, Light Sci. Appl. 11, 110 (2022)

    2022

  6. [14]

    N. A. Mortensen, Mesoscopic electrodynamics at metal sur- faces: —from quantum-corrected hydrodynamics to micro- scopic surface-response formalism, Nanophotonics 10, 2563 (2021)

    2021

  7. [15]

    J. J. Baumberg, J. Aizpurua, M. H. Mikkelsen, and D. R. Smith, Extreme nanophotonics from ultrathin metallic gaps, Nat. Mater. 18, 668 (2019)

    2019

  8. [16]

    Boroviks, Z.-H

    S. Boroviks, Z.-H. Lin, V . A. Zenin, M. Ziegler, A. Dellith, P. Gonçalves, C. Wolff, S. I. Bozhevolnyi, J.-S. Huang, and N. A. Mortensen, Extremely confined gap plasmon modes: when nonlocality matters, Nat. Commun. 13, 3105 (2022)

    2022

  9. [17]

    King-Smith and D

    R. King-Smith and D. Vanderbilt, Theory of polarization of crystalline solids, Phys. Rev. B 47, 1651 (1993)

    1993

  10. [18]

    Resta, Macroscopic electric polarization as a geometric quantum phase, Europhys

    R. Resta, Macroscopic electric polarization as a geometric quantum phase, Europhys. Lett. 22, 133 (1993)

    1993

  11. [19]

    Aspnes, Local-field effects and effective-medium theory: A microscopic perspective, Am

    D. Aspnes, Local-field effects and effective-medium theory: A microscopic perspective, Am. J. Phys. 50, 704 (1982)

    1982

  12. [20]

    T. Wang, Z. Gui, A. Janotti, C. Ni, and P. Karandikar, Strong effect of electron-phonon interaction on the lattice thermal con- ductivity in 3C-SiC, Phys. Rev. Mater.1, 034601 (2017)

    2017

  13. [21]

    S. L. Adler, Quantum theory of the dielectric constant in real solids, Phys. Rev. 126, 413 (1962)

    1962

  14. [22]

    Wiser, Dielectric constant with local field effects included, Phys

    N. Wiser, Dielectric constant with local field effects included, Phys. Rev. 129, 62 (1963)

    1963

  15. [23]

    Gajdoš, K

    M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, and F. Bech- stedt, Linear optical properties in the projector-augmented wave methodology, Phys. Rev. B73, 045112 (2006)

    2006

  16. [24]

    P. T. Mahon, R. A. Muniz, and J. Sipe, Microscopic polarization and magnetization fields in extended systems, Phys. Rev. B 99, 235140 (2019)

    2019

  17. [25]

    Andreoli, B

    F. Andreoli, B. Windt, S. Grava, G. M. Andolina, M. J. Gullans, A. A. High, and D. E. Chang, The maximum refractive index of an atomic crystal - from quantum optics to quantum chemistry (2023), arXiv:2303.10998 [quant-ph]

    2023 arXiv

  18. [26]

    Bharadwaj and Z

    S. Bharadwaj and Z. Jacob, Unraveling picophotonics of crys- talline materials (2024), arXiv:2407.15189 [physics.optics]

    2024 arXiv

  19. [27]

    Castelletto, B

    S. Castelletto, B. Johnson, V . Ivády, N. Stavrias, T. Umeda, A. Gali, and T. Ohshima, A silicon carbide room-temperature single-photon source, Nat. Mater. 13, 151 (2014). 6

    2014

  20. [28]

    Widmann, S.-Y

    M. Widmann, S.-Y . Lee, T. Rendler, N. T. Son, H. Fedder, S. Paik, L.-P. Yang, N. Zhao, S. Yang, I. Booker,et al., Coherent control of single spins in silicon carbide at room temperature, Nat. Mater. 14, 164 (2015)

    2015

  21. [29]

    R. Nagy, M. Niethammer, M. Widmann, Y .-C. Chen, P. Ud- varhelyi, C. Bonato, J. U. Hassan, R. Karhu, I. G. Ivanov, N. T. Son, et al., High-fidelity spin and optical control of single silicon-vacancy centres in silicon carbide, Nat. Commun. 10, 1 (2019)

    2019

  22. [30]

    H. C. Po, A. Vishwanath, and H. Watanabe, Symmetry-based indicators of band topology in the 230 space groups, Nat. Com- mun. 8, 50 (2017)

    2017

  23. [31]

    D. Lu, F. Gygi, and G. Galli, Dielectric properties of ice and liquid water from first-principles calculations, Phys. Rev. Lett. 100, 147601 (2008)

    2008

  24. [32]

    Poursoti, W

    Z. Poursoti, W. Sun, S. Bharadwaj, M. Malac, S. Iyer, F. Khos- ravi, K. Cui, L. Qi, N. Nazemifard, R. Jagannath, et al., Deep ultra-violet plasmonics: exploiting momentum-resolved elec- tron energy loss spectroscopy to probe germanium, Opt. Ex- press 30, 12630 (2022)

    2022

  25. [33]

    Van Mechelen, W

    T. Van Mechelen, W. Sun, and Z. Jacob, Optical n-invariant of graphene’s topological viscous hall fluid, Nat. Commun. 12, 4729 (2021)

    2021

  26. [34]

    Van Mechelen, S

    T. Van Mechelen, S. Bharadwaj, Z. Jacob, and R.-J. Slager, Op- tical n-insulators: Topological obstructions to optical wannier functions in the atomistic susceptibility tensor, Phys. Rev. Res. 4, 023011 (2022)

    2022

  27. [35]

    Supplemental Movies 1 and 2 contain the temporal evolutions of the microscopic optical eigenwaves corresponding to Fig

    See Supplemental Material at http://link.aps.org/supplemental/xxx for (1) the notes of the calculation of the microscopic optical band structure and eigenwaves, (2) the real-space distributions of higher-order microscopic optical eigenwaves at Gamma point, and (3) the dominant...

  28. [36]

    Sangalli, J

    D. Sangalli, J. Berger, C. Attaccalite, M. Grüning, and P. Ro- maniello, Optical properties of periodic systems within the current-current response framework: Pitfalls and remedies, Phys. Rev. B 95, 155203 (2017)

    2017

  29. [37]

    Sipe and A

    J. Sipe and A. Shkrebtii, Second-order optical response in semi- conductors, Phys. Rev. B 61, 5337 (2000)

    2000

  30. [38]

    Marzari, A

    N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, and D. Vander- bilt, Maximally localized wannier functions: Theory and appli- cations, Rev. Mod. Phys. 84, 1419 (2012). Supplementary information for Visualization of atomistic optical waves in crystals Jungho Mun, 1, 2 Sathwik...

    2012 arXiv

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