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Symmetry Rules for Cavity Materials Engineering with Linearly Polarized Vacuum Fields

T0 review · 1 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read A dark, linearly polarized cavity breaks a crystal's symmetry by one rule: the electron–photon interaction is quadratic in electron momentum, so surviving symmetries are exactly those that leave the square of the momentum component along th

desk verdict Useful symmetry framework, but one central table entry (D2d) contradicts the paper's own rule; fix before this becomes the standard reference. read the letter →

arxiv 2607.28745 v1 pith:XWAZOVA3 submitted 2026-07-30 cond-mat.mtrl-sci

Jingkai Quan , Chongxiao Fan , Benshu Fan , I-Te Lu , Dante M. Kennes , Angel Rubio This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords cavitymaterialsengineeringQEDvacuumfluctuationspointgroupsymmetrybreakingpxLDABaTiO3MoS2
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 aims to establish a general symmetry principle for cavity materials engineering: when a crystal is placed in a dark, linearly polarized cavity, the effective light–matter interaction is proportional to the square of the electron momentum projected along the polarization axis, (Π·ε)^2. From this single quadratic form, the authors derive a complete classification of the symmetry-breaking patterns induced by such cavities for all 32 crystallographic point groups, with explicit tables telling which subgroup survives for each polarization direction. The classification matters because it turns cavity design into a group-theory problem: choosing the polarization axis selects the preserved symmetries, and with them the degeneracies, spectral selection rules, and allowed macroscopic responses of the coupled material. The framework is validated by quantum-electrodynamical density functional theory calculations showing that different cavity polarizations split the band degeneracies of cubic BaTiO3 in exactly the predicted patterns and that a y-polarized mode activates a new infrared peak and splits a degenerate mode in monolayer MoS2.

What carries the argument

The central object is the quadratic kernel (k·ε)^2, equivalently (Π·ε)^2, which appears both in the photon-free QED Hamiltonian and in the pxLDA exchange-correlation potential. Its invariance group is the criterion: a crystal point-group operation survives cavity coupling if and only if it leaves this squared momentum projection invariant. The same kernel also has a geometric reading as a renormalization of the canonical momentum metric—an effective mass renormalization along the polarization direction—which is how vacuum fluctuations enter the electronic structure. The subgroup tables are generated by applying this single invariance test to the uniaxial and polyhedral point groups.

What would settle it

Tune a cavity mode through an electronic resonance in a crystal such as BaTiO3 and measure the band-degeneracy splitting pattern on both sides of the resonance; the (Π·ε)^2 subgroup predictions should hold only in the far-off-resonance limit, and deviations near resonance would reveal the contribution of photon-number sectors omitted by the zero-photon downfolding. A second, cleaner test: drive the cavity to a nonzero photon amplitude and look for inversion-symmetry-breaking effects, which the paper's dark-cavity quadratic rule explicitly forbids.

Watch

Extended reading notes

Core claim

Within the photon-free QED Hamiltonian obtained by downfolding the Pauli–Fierz Hamiltonian to the zero-photon sector, a linearly polarized dark cavity contributes an effective interaction H_I ~ (Π·ε)^2. Because this is quadratic, it preserves any operation that maps Π to −Π or that leaves the ε axis invariant: inversion, time reversal, and PT survive, while rotation axes not parallel to ε, and mirror planes neither perpendicular to nor containing ε, are broken. The paper shows that the resulting symmetry reduction for a single mode polarized along ε is identical to that of two orthogonal modes polarized perpendicular to ε, and from this derives complete subgroup relations for all 32 crystall

Load-bearing premise

The entire classification collapses if the cavity is not in the regime where the dressed photon frequency far exceeds electronic transition energies, or if the photon field has a nonzero mean amplitude, because then the downfolded interaction is no longer exactly quadratic in electron momentum and the simple (Π·ε)^2 invariance rule stops being exact.

Editorial extensions

If this is right

  • Given any material point group and a cavity polarization axis, the surviving subgroup and hence the fate of each degenerate irrep can be read off before any numerical calculation.
  • Cavity modes can selectively break rotational symmetries while keeping inversion and time reversal, so degeneracy splittings are symmetry-controlled without introducing electric or magnetic parity-breaking effects.
  • Nonpolar point groups can be reduced to polar subgroups (e.g., D3 → C2), which makes a finite cavity-induced polarization symmetry-allowed even without external driving.
  • Symmetry lowering activates silent vibrational modes: in MoS2, the A1′ mode becomes infrared-active and the degenerate E′ mode splits, changing both IR and Raman spectra in a predictable way.
  • Breaking C3 in graphene shifts the Dirac cone away from K and K′ without opening a gap, because PT symmetry survives; the shift direction is set by the polarization axis.

Reading between the lines

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

  • The same (Π·ε)^2 rule implies a direct experimental diagnostic: measuring which degeneracies split under a linearly polarized cavity directly reveals the surviving subgroup, and any observed splitting inconsistent with the table would signal physics beyond the zero-photon downfolding.
  • An untested extension not pursued in the paper is the near-resonant regime: if the dressed photon frequency is lowered toward electronic transitions, photon-number sectors beyond zero will contribute linear or higher couplings, so the symmetry reduction should become polarization-direction dependent in a richer way; few-mode models could map where the quadratic rule fails.
  • The equivalence between one mode along ε and two orthogonal modes perpendicular to ε suggests that Fabry–Pérot setups with an unpolarized mode pair can be reliably modeled by a single effective axis, simplifying experimental design—but this is a corollary of the paper's own analysis, and its robustness to inhomogeneous mode profiles is not tested.
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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

1 major / 4 minor

Summary. The manuscript derives a symmetry rule for cavity materials engineering: after downfolding the Pauli–Fierz Hamiltonian to the zero-photon sector (Sec. II A), the effective light–matter interaction is proportional to (Π·ε)^2, Eq. (6). The symmetry of the coupled system is therefore the stabilizer of the quadratic form in the electron momentum, and the authors tabulate the resulting subgroups for all 32 crystallographic point groups (Tables II and III). The framework is demonstrated with QEDFT calculations for cubic BaTiO3, monolayer MoS2, and graphene using the pxLDA functional. The central derivation is standard and clearly presented; the numerical examples serve as consistency checks of the group-theoretical predictions.

Significance. If the classification is correct, the paper provides a genuinely useful reference: a parameter-free, group-theoretical design rule for how a dark linearly polarized cavity reduces the point-group symmetry of any crystal. The derivation from the Pauli–Fierz Hamiltonian is transparent, the stabilizer logic is simple, and the BaTiO3/MoS2 demonstrations are internally consistent with the stated subgroups. The high-frequency and dark-cavity limitations are acknowledged in Sec. IV B and do not by themselves undermine the central claim. The main product is the classification itself, so a single incorrect entry in the advertised 'complete' table is load-bearing.

major comments (1)
  1. [Table II, D2d row; Eqs. (6) and Tab. I] The entry D2d → C2 for a cavity mode along x/y is inconsistent with the paper's own criterion. By Tab. I, an operation survives exactly when it maps Π_x to ±Π_x, i.e. when it preserves the unoriented x-axis. For D2d with S4 along z, in the standard 4̄2m setting (C2' axes along x and y), the surviving elements are E, C2(z), C2'(x), C2'(y), which form D2, not C2. In the alternative 4̄m2 setting (C2' axes along [110], mirror planes xz/yz), the survivors are E, C2(z), σ_d(xz), σ_d(yz), which form C2v. Either way one does not obtain C2. The tabulated C2 would only follow if x/y are chosen along a generic, non-symmetry-adapted direction, but that is not a conventional crystallographic orientation and is not specified. Because Tables II–III are the central deliverable, this row must be corrected or the coordinate convention must be stated; if both tetragonal settings are intended, the table sho
minor comments (4)
  1. [Table III] The column headers C2P and C4P are never defined, which makes an independent check of the polyhedral table difficult. Please define these axes (or rename them) and state the convention used for T, Th, Td, O, and Oh.
  2. [Sec. II A, after Eq. (9)] The sentence 'g[ρ](k) ... cannot further lower the symmetry beyond what is imposed by the kernel' is stronger than symmetry alone guarantees: a degenerate ground state may spontaneously break a symmetry that the Hamiltonian preserves. The examples are consistent, but the general statement should be phrased in terms of Hamiltonian symmetry or restricted to nondegenerate ground states.
  3. [Eq. (10)] The 'canonical momentum metric' h is introduced but not defined explicitly. Writing the matrix h (or h^T h) would make the geometric interpretation clearer.
  4. [Appendix B] The coupling ratio for MoS2 and graphene is stated as λ/ω = 1.0, which is much larger than the BaTiO3 value and is also larger than the typical experimental range quoted in the main text. Please comment on whether such a large value is used only for numerical visibility and whether the spectral splittings persist at smaller coupling.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the symmetry classification follows directly from Eq. (6); self-citations occur only in the QEDFT implementation/application and are not load-bearing.

full rationale

The derivation chain is: Pauli-Fierz Hamiltonian Eq. (1) -> Bogoliubov-dressed form Eq. (3) -> high-frequency zero-photon downfolding Eq. (5) -> interaction kernel (Pi·epsilon)^2 Eq. (6) -> stabilizer criterion in Sec. IIB -> Tables II/III. Each step is either explicitly derived in the paper or a standard group-theoretic computation; no fitted parameter enters. The paper states that the light-matter interaction is quadratic in electron momentum and then that the effective Hamiltonian preserves exactly the operations that leave (Pi·epsilon)^2 invariant, so the classification is the stabilizer of that kernel rather than being defined in terms of the outputs it predicts. The QEDFT applications use the same pf Hamiltonian and the authors' pxLDA functional (Refs. 39,43), and Sec. IIB explicitly says 'Such agreement is expected, since the pxLDA functional provides a density-functional approximation to the underlying pf QED Hamiltonian'; they are consistency checks rather than external benchmarks. The high-frequency and dark-cavity assumptions are acknowledged limitations (Secs. IIA, IVB), not circular steps. The reviewer's D2d -> C2 table concern is an internal consistency/correctness question, not a circularity chain: even if a row is wrong, the claimed derivation does not reduce to its own output. No circular step meriting a nonzero score was identified beyond minor self-referential validation style, hence score 2.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central claim has no fitted constants: the only inputs are the model Hamiltonian and the assumption that one or two effective modes capture the cavity. The applications choose λ/ω for visibility rather than fitting. No new particles, forces, or dimensions are introduced; the 'dressed photon' modes are a standard Bogoliubov transformation.

free parameters (2)
  • coupling ratio λ/ω (per cavity mode) = 0.2 (BaTiO3), 1.0 (MoS2 and graphene)
    Chosen for numerical visibility, not fitted to experiment; not needed for the central symmetry classification. At λ/ω=1.0 the calculation is in the ultra-strong-coupling regime, where the high-frequency pf-QED downfolding is less secure.
  • cavity mode frequencies ω and polarizations ε = selected per configuration, e.g., ε1=1/√2(1,-1,0), ε2=(0,0,1) for the (110) plane
    Inputs from cavity geometry; the classification depends only on the polarization axis, not on the specific values.
assumptions (6)
  • domain assumption The Pauli-Fierz Hamiltonian in the Coulomb gauge and long-wavelength approximation describes the cavity-coupled material.
    Used in Sec. IIA, Eq. (1). The entire analysis is built on this model.
  • domain assumption The high-frequency limit permits projection onto the zero-photon sector, giving the pf QED Hamiltonian with interaction ~(Π·ε)^2.
    Sec. IIA, Eq. (5). If the photon frequency is not much larger than electronic transitions, additional photon sectors contribute and the quadratic form is not exact.
  • domain assumption The cavity field is dark: ⟨a†+a⟩=0 and ⟨(a†+a)^2⟩≠0.
    Sec. IIB, bottom of p.3. This distinguishes pf QED from minimal coupling; a coherent amplitude would reintroduce a linear coupling term.
  • standard math Standard character tables and group-subgroup relations are used to compute the stabilizer of a direction.
    Used in Sec. IIB and Tables II/III via the Bilbao Crystallographic Server.
  • domain assumption The pxLDA potential kernel (k·ε)^2/k^2 determines and cannot further lower the symmetry of the coupled system.
    Sec. IIA, Eq. (9) and following paragraph. Plausible for non-degenerate ground states, but spontaneous symmetry breaking could in principle lower the symmetry further; the paper does not prove this rigorously.
  • domain assumption One or two effective photon modes are sufficient to represent realistic cavity configurations.
    Sec. IIB, top of p.4, citing Refs. 15 and 72. This restricts the classification to Fabry-Pérot-like settings.

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Cite this review

Pith. "Pith review of Symmetry Rules for Cavity Materials Engineering with Linearly Polarized Vacuum Fields." pith.science (2026). https://pith.science/paper/XWAZOVA3

@misc{pith2026260728745,
  author       = {Pith},
  title        = {Pith review of: Symmetry Rules for Cavity Materials Engineering with Linearly Polarized Vacuum Fields},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XWAZOVA3}},
  note         = {Machine review of arXiv:2607.28745}
}
abstract

Cavity materials engineering, aiming to manipulate material properties by coupling to vacuum fluctuations inside a cavity, is a rapidly advancing field. Despite significant progress, most studies to date have focused on specific materials and cavity configurations. Here, through a comprehensive group-theoretical analysis, we establish general symmetry rules for cavity materials engineering with linearly polarized cavity photon modes. By analyzing the symmetry of the effective photon-free quantum-electrodynamics Hamiltonian, we provide a complete classification of the symmetry-breaking patterns induced by cavity modes for all crystallographic point groups. The power of this framework is then demonstrated by quantum-electrodynamical density functional theory calculations. In particular, we explain the distinct cavity-induced lifting of band degeneracies in cubic BaTiO$_3$ for different cavity mode configurations, and the cavity-modified infrared and Raman spectra of monolayer MoS$_2$ due to symmetry breaking. Our results highlight the central role of symmetry in cavity materials engineering and provide general guidelines for future studies in this field.

Figures

Figures reproduced from arXiv: 2607.28745 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Schematic illustration of a body-centered cubic [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a)-(d) Band structures of cubic BaTiO [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Illustration of the crystal structure of MoS [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a)-(d) Illustration of the coordinate system of the [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Shift of the Dirac point in graphene calculated us [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Infrared spectra of MoS [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Raman spectra of MoS [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

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Works this paper leans on

97 extracted references · 4 linked inside Pith

  1. [1]

    De La Torre, D

    A. De La Torre, D. M. Kennes, M. Claassen, S. Gerber, J. W. McIver, and M. A. Sentef, Colloquium: Nonther- mal pathways to ultrafast control in quantum materials, Reviews of Modern Physics93, 041002 (2021)

    2021

  2. [2]

    C. Bao, P. Tang, D. Sun, and S. Zhou, Light-induced emergent phenomena in 2D materials and topological materials, Nature Reviews Physics4, 33 (2022)

    2022

  3. [3]

    Bloch, A

    J. Bloch, A. Cavalleri, V. Galitski, M. Hafezi, and A. Ru- bio, Strongly correlated electron–photon systems, Nature 606, 41 (2022)

    2022

  4. [4]

    A. Zong, B. R. Nebgen, S.-C. Lin, J. A. Spies, and M. Zuerch, Emerging ultrafast techniques for studying quantum materials, Nature Reviews Materials8, 224 (2023)

    2023

  5. [5]

    Fausti, R

    D. Fausti, R. Tobey, N. Dean, S. Kaiser, A. Dienst, M. C. Hoffmann, S. Pyon, T. Takayama, H. Takagi, and A. Cavalleri, Light-induced superconductivity in a stripe- ordered cuprate, science331, 189 (2011)

    2011

  6. [6]

    Mankowsky, A

    R. Mankowsky, A. Subedi, M. F¨ orst, S. O. Mariager, M. Chollet, H. T. Lemke, J. S. Robinson, J. M. Glow- nia, M. P. Minitti, A. Frano, M. Fechner, N. A. Spaldin, T. Loew, B. Keimer, A. Georges, and A. Cavalleri, Non- linear lattice dynamics as a basis for enhanced supercon- ductivity in YBa 2Cu3O6.5, Nature516, 71 (2014)

    2014

  7. [7]

    S. Fava, G. De Vecchi, G. Jotzu, M. Buzzi, T. Gebert, Y. Liu, B. Keimer, and A. Cavalleri, Magnetic field ex- pulsion in optically driven YBa 2Cu3O6.48, Nature632, 75 (2024)

    2024

  8. [8]

    Cavalleri, C

    A. Cavalleri, C. T´ oth, C. W. Siders, J. Squier, F. R´ aksi, P. Forget, and J. Kieffer, Femtosecond structural dynam- ics in VO2 during an ultrafast solid-solid phase transition, Physical review letters87, 237401 (2001)

    2001

Show all 97 references
  1. [9]

    A. S. Johnson, D. Perez-Salinas, K. M. Siddiqui, S. Kim, S. Choi, K. Volckaert, P. E. Majchrzak, S. Ulstrup, N. Agarwal, K. Hallman,et al., Ultrafast X-ray imag- ing of the light-induced phase transition in VO 2, Nature Physics19, 215 (2023)

    2023

  2. [10]

    Z. Zeng, M. F¨ orst, M. Fechner, M. Buzzi, E. Amuah, C. Putzke, P. Moll, D. Prabhakaran, P. Radaelli, and A. Cavalleri, Photo-induced chirality in a nonchiral crys- 12 tal, Science387, 431 (2025)

    2025

  3. [11]

    Oka and S

    T. Oka and S. Kitamura, Floquet engineering of quantum materials, Annual Review of Condensed Matter Physics 10, 387 (2019)

    2019

  4. [12]

    M. S. Rudner and N. H. Lindner, Band structure engi- neering and non-equilibrium dynamics in Floquet topo- logical insulators, Nat. Rev. Phys.2, 229 (2020)

    2020

  5. [13]

    Schlawin, D

    F. Schlawin, D. M. Kennes, and M. A. Sentef, Cavity quantum materials, Applied Physics Reviews9(2022)

    2022

  6. [14]

    F. J. Garcia-Vidal, C. Ciuti, and T. W. Ebbesen, Ma- nipulating matter by strong coupling to vacuum fields, Science373, eabd0336 (2021)

    2021

  7. [15]

    I.-T. Lu, D. Shin, M. Kamper Svendsen, S. Latini, H. H¨ ubener, M. Ruggenthaler, and A. Rubio, Cavity en- gineering of solid-state materials without external driv- ing, Advances in Optics and Photonics17, 441 (2025)

    2025

  8. [16]

    H. M. Bretscher, L. Graziotto, M. H. Michael, A. Mon- tanaro, I.-T. Lu, A. Grankin, J. W. McIver, J. Faist, D. Fausti, M. Eckstein, M. Ruggenthaler, A. Rubio, D. N. Basov, M. Hafezi, M. Claassen, D. M. Kennes, and M. A. Sentef, Fluctuation engineering in cavity quan- tum mater...

    2026 arXiv

  9. [17]

    Thomas, E

    A. Thomas, E. Devaux, K. Nagarajan, T. Chervy, M. Sei- del, G. Rogez, J. Robert, M. Drillon, T.-T. Ruan, S. Schlittenhardt,et al., Exploring superconductivity un- der strong coupling with the vacuum electromagnetic field, The Journal of Chemical Physics162(2025)

    2025

  10. [18]

    Keren, T

    I. Keren, T. A. Webb, S. Zhang, J. Xu, D. Sun, B. S. Kim, D. Shin, S. S. Zhang, J. Zhang, G. Pereira,et al., Cavity- altered superconductivity, Nature650, 864 (2026)

    2026

  11. [19]

    G. Jarc, S. Y. Mathengattil, A. Montanaro, F. Giusti, E. M. Rigoni, R. Sergo, F. Fassioli, S. Winnerl, S. Dal Zilio, D. Mihailovic,et al., Cavity-mediated ther- mal control of metal-to-insulator transition in 1T-TaS 2, Nature622, 487 (2023)

    2023

  12. [20]

    Appugliese, J

    F. Appugliese, J. Enkner, G. L. Paravicini-Bagliani, M. Beck, C. Reichl, W. Wegscheider, G. Scalari, C. Ciuti, and J. Faist, Breakdown of topological protection by cav- ity vacuum fields in the integer quantum hall effect, Sci- ence375, 1030 (2022)

    2022

  13. [21]

    Enkner, L

    J. Enkner, L. Graziotto, F. Appugliese, V. Rokaj, J. Wang, M. Ruggenthaler, C. Reichl, W. Wegscheider, A. Rubio, and J. Faist, Testing the renormalization of the von klitzing constant by cavity vacuum fields, Phys- ical Review X14, 021038 (2024)

    2024

  14. [22]

    Thomas, L

    A. Thomas, L. Lethuillier-Karl, K. Nagarajan, R. M. Ver- gauwe, J. George, T. Chervy, A. Shalabney, E. Devaux, C. Genet, J. Moran,et al., Tilting a ground-state reac- tivity landscape by vibrational strong coupling, Science 363, 615 (2019)

    2019

  15. [23]

    W. Ahn, J. F. Triana, F. Recabal, F. Herrera, and B. S. Simpkins, Modification of ground-state chemical reactiv- ity via light–matter coherence in infrared cavities, Science 380, 1165 (2023)

    2023

  16. [24]

    Q. Xie, H. Zhong, M. T. Batchelor, and C. Lee, The quantum rabi model: solution and dynamics, Journal of Physics A: Mathematical and Theoretical50, 113001 (2017)

    2017

  17. [25]

    Larson and T

    J. Larson and T. Mavrogordatos,The Jaynes–Cummings model and its descendants: modern research directions (IoP Publishing, 2021)

    2021

  18. [26]

    Kirton, M

    P. Kirton, M. M. Roses, J. Keeling, and E. G. Dalla Torre, Introduction to the dicke model: From equilibrium to nonequilibrium, and vice versa, Advanced Quantum Technologies2, 1800043 (2019)

    2019

  19. [27]

    C. J. Eckhardt, G. Passetti, M. Othman, C. Karrasch, F. Cavaliere, M. A. Sentef, and D. M. Kennes, Quan- tum Floquet engineering with an exactly solvable tight- binding chain in a cavity, Communications Physics5, 122 (2022)

    2022

  20. [28]

    Passetti, C

    G. Passetti, C. J. Eckhardt, M. A. Sentef, and D. M. Kennes, Cavity light-matter entanglement through quan- tum fluctuations, Physical Review Letters131, 023601 (2023)

    2023

  21. [29]

    Matousek, N

    M. Matousek, N. Vu, N. Govind, J. J. Foley IV, and L. Veis, Polaritonic chemistry using the density matrix renormalization group method, Journal of Chemical The- ory and Computation20, 9424 (2024)

    2024

  22. [30]

    Weber, L

    L. Weber, L. dos Anjos Cunha, M. A. Morales, A. Rubio, and S. Zhang, Phaseless auxiliary-field quantum Monte Carlo method for cavity-QED matter systems, Journal of Chemical Theory and Computation21, 2909 (2025)

    2025

  23. [31]

    McTague and J

    J. McTague and J. J. Foley, Non-Hermitian cavity quan- tum electrodynamics–configuration interaction singles approach for polaritonic structure with ab initio molecu- lar Hamiltonians, The Journal of Chemical Physics156 (2022)

    2022

  24. [32]

    N. Vu, D. Mejia-Rodriguez, N. P. Bauman, A. Panyala, E. Mutlu, N. Govind, and J. J. Foley IV, Cavity quan- tum electrodynamics complete active space configuration interaction theory, Journal of Chemical Theory and Com- putation20, 1214 (2024)

    2024

  25. [33]

    T. S. Haugland, E. Ronca, E. F. Kjønstad, A. Rubio, and H. Koch, Coupled cluster theory for molecular polaritons: Changing ground and excited states, Physical Review X 10, 041043 (2020)

    2020

  26. [34]

    A. E. DePrince, Cavity-modulated ionization potentials and electron affinities from quantum electrodynamics coupled-cluster theory, The Journal of Chemical Physics 154(2021)

    2021

  27. [35]

    Ruggenthaler, J

    M. Ruggenthaler, J. Flick, C. Pellegrini, H. Appel, I. V. Tokatly, and A. Rubio, Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory, Physical Review A90, 012508 (2014)

    2014

  28. [36]

    Flick, C

    J. Flick, C. Sch¨ afer, M. Ruggenthaler, H. Appel, and A. Rubio, Ab initio optimized effective potentials for real molecules in optical cavities: Photon contributions to the molecular ground state, ACS photonics5, 992 (2018)

    2018

  29. [37]

    Flick, Simple exchange-correlation energy functionals for strongly coupled light-matter systems based on the fluctuation-dissipation theorem, Phys

    J. Flick, Simple exchange-correlation energy functionals for strongly coupled light-matter systems based on the fluctuation-dissipation theorem, Phys. Rev. Lett.129, 143201 (2022)

    2022

  30. [38]

    Sch¨ afer, F

    C. Sch¨ afer, F. Buchholz, M. Penz, M. Ruggenthaler, and A. Rubio, Making ab initio QED functional(s): Non- perturbative and photon-free effective frameworks for strong light–matter coupling, Proceedings of the National Academy of Sciences118, e2110464118 (2021)

    2021

  31. [39]

    I.-T. Lu, M. Ruggenthaler, N. Tancogne-Dejean, S. La- tini, M. Penz, and A. Rubio, Electron-photon exchange- correlation approximation for quantum-electrodynamical density-functional theory, Physical Review A109, 052823 (2024)

    2024

  32. [40]

    Flick, M

    J. Flick, M. Ruggenthaler, H. Appel, and A. Rubio, Atoms and molecules in cavities, from weak to strong coupling in quantum-electrodynamics (QED) chemistry, Proceedings of the National Academy of Sciences114, 13 3026 (2017)

    2017

  33. [41]

    Ruggenthaler, D

    M. Ruggenthaler, D. Sidler, and A. Rubio, Understand- ing polaritonic chemistry from ab initio quantum electro- dynamics, Chemical Reviews123, 11191 (2023)

    2023

  34. [42]

    Tasci, L

    C. Tasci, L. A. Cunha, and J. Flick, Photon many-body dispersion: Exchange-correlation functional for strongly coupled light-matter systems, Physical Review Letters 134, 073002 (2025)

    2025

  35. [43]

    Fan, I.-T

    B. Fan, I.-T. Lu, M. Ruggenthaler, and A. Rubio, Unified ab initio quantum-electrodynamical density-functional theory for cavity-modified electron-phonon-photon cou- pling in solids, arXiv preprint arXiv:2603.24095 (2026)

    2026 arXiv

  36. [44]

    I.-T. Lu, D. Shin, M. K. Svendsen, H. H¨ ubener, U. De Giovannini, S. Latini, M. Ruggenthaler, and A. Ru- bio, Cavity-enhanced superconductivity in MgB 2 from first-principles quantum electrodynamics (QEDFT), Pro- ceedings of the National Academy of Sciences121, e2415061121 (2024)

    2024

  37. [45]

    Nourmofidi, H

    O. Nourmofidi, H. H¨ ubener, E. Gross, and A. Rubio, Linking critical temperature with electron localization for cavity-enhanced superconductivity, Communications Physics (2026)

    2026

  38. [46]

    Shin, I.-T

    D. Shin, I.-T. Lu, B. Fan, E. V. Bostr¨ om, H. Liu, M. K. Svendsen, S. Latini, P. Tang, and A. Rubio, Multiple photon field-induced topological states in bulk HgTe, Sci. Adv.12, eaea5823 (2026)

    2026

  39. [47]

    H. Liu, S. Latini, I.-T. Lu, D. Shin, and A. Rubio, Mod- ifying electronic and structural properties of 2D van der Waals materials via cavity quantum vacuum fluctuations: a first-principles QEDFT study, Optical Materials Ex- press15, 2105 (2025)

    2025

  40. [48]

    M. S. Dresselhaus, G. Dresselhaus, and A. Jorio,Group theory: application to the physics of condensed matter (Springer Science & Business Media, 2007)

    2007

  41. [49]

    H. F. Jones,Groups, representations and physics(CRC Press, 2020)

    2020

  42. [50]

    Neufeld, M

    O. Neufeld, M. E. Tzur, G. Lerner, O. Kfir, A. Fleischer, and O. Cohen, Light symmetry, chirality, and their role in nonlinear optics and ultrafast phenomena, Advances in Optics and Photonics18, 160 (2026)

    2026

  43. [51]

    B. Fan, U. De Giovannini, H. H¨ ubener, S. Zhou, W. Duan, A. Rubio, and P. Tang, Floquet optical selec- tion rules in black phosphorus, Sci. Adv.11, eadw2744 (2025)

    2025

  44. [52]

    R. Li, B. Fan, U. De Giovannini, H. H¨ ubener, and A. Rubio, First-principles Floquet analysis from real-time propagation, arXiv preprint arXiv:2607.04269 (2026)

    2026 arXiv

  45. [53]

    Jiang and F

    Q.-D. Jiang and F. Wilczek, Quantum atmospherics for materials diagnosis, Physical Review B99, 201104 (2019)

    2019

  46. [54]

    Y. Ke, Z. Song, and Q.-D. Jiang, Vacuum-induced sym- metry breaking of chiral enantiomer formation in chem- ical reactions, Physical Review Letters131, 223601 (2023)

    2023

  47. [55]

    Cheng, E

    X. Cheng, E. V. Bostr¨ om, F. Y. Gao, E. Baldini, D. M. Kennes, and A. Rubio, Anyonic chern insulator in graphene induced by surface electromagnon vacuum fluctuations, arXiv preprint arXiv:2511.10836 (2025)

    2025

  48. [56]

    Jayachandran, B

    A. Jayachandran, B. Patrahau, J. G. Ricca, M. Mahato, Y. Pang, K. Nagarajan, A. Thomas, C. Genet, and T. W. Ebbesen, A phenomenological symmetry rule for chem- ical reactivity under vibrational strong coupling, Ange- wandte Chemie , e202503915 (2025)

    2025

  49. [57]

    Lin, H.-C

    Z. Lin, H.-C. Chan, W. Yang, Y. Sha, C. Xiao, S. Zhang, and W. Yao, Spontaneous Symmetry Breaking of Cavity Vacuum and Emergent Gyrotropic Effects in Embedded Moir´ e Superlattices, Phys. Rev. Lett.136, 046903 (2026)

    2026

  50. [58]

    Flick, H

    J. Flick, H. Appel, M. Ruggenthaler, and A. Rubio, Cavity Born–Oppenheimer approximation for correlated electron–nuclear-photon systems, Journal of chemical theory and computation13, 1616 (2017)

    2017

  51. [59]

    M. R. Fiechter and J. O. Richardson, Understanding the cavity Born–Oppenheimer approximation, The Journal of Chemical Physics160(2024)

    2024

  52. [60]

    Latini, D

    S. Latini, D. Shin, S. A. Sato, C. Sch¨ afer, U. De Giovan- nini, H. H¨ ubener, and A. Rubio, The ferroelectric photo ground state of SrTiO 3: Cavity materials engineering, Proceedings of the National Academy of Sciences118, e2105618118 (2021)

    2021

  53. [61]

    H. Liu, F. Troisi, H. H¨ ubener, S. Latini, and A. Rubio, Cavity-mediated electron-electron interactions: Renor- malizing Dirac states in graphene, Science Advances11, eadz1855 (2025)

    2025

  54. [62]

    M.-L. M. Tchenkoue, M. Penz, I. Theophilou, M. Ruggenthaler, and A. Rubio, Force balance approach for advanced approximations in density functional theo- ries, The Journal of Chemical Physics151(2019)

    2019

  55. [63]

    Tancogne-Dejean, M

    N. Tancogne-Dejean, M. Penz, A. Laestadius, M. A. Csirik, M. Ruggenthaler, and A. Rubio, Exchange ener- gies with forces in density-functional theory, The Journal of Chemical Physics160(2024)

    2024

  56. [64]

    Rokaj, M

    V. Rokaj, M. Ruggenthaler, F. G. Eich, and A. Ru- bio, Free electron gas in cavity quantum electrodynamics, Physical Review Research4, 013012 (2022)

    2022

  57. [65]

    D. M. Welakuh, V. Rokaj, M. Ruggenthaler, and A. Ru- bio, Nonperturbative mass renormalization effects in nonrelativistic quantum electrodynamics, Physical Re- view Research7, 013093 (2025)

    2025

  58. [66]

    Chirolli, M

    L. Chirolli, M. Polini, V. Giovannetti, and A. H. Mac- Donald, Drude weight, cyclotron resonance, and the Dicke model of graphene cavity QED, Physical review letters109, 267404 (2012)

    2012

  59. [67]

    Gruner and D.-G

    T. Gruner and D.-G. Welsch, Green-function approach to the radiation-field quantization for homogeneous and inhomogeneous Kramers-Kronig dielectrics, Physical Re- view A53, 1818 (1996)

    1996

  60. [68]

    Lindel, R

    F. Lindel, R. Bennett, and S. Y. Buhmann, Macroscopic quantum electrodynamics approach to nonlinear optics and application to polaritonic quantum-vacuum detec- tion, Physical Review A103, 033705 (2021)

    2021

  61. [69]

    M. K. Svendsen, Y. Kurman, P. Schmidt, F. Koppens, I. Kaminer, and K. S. Thygesen, Combining density func- tional theory with macroscopic QED for quantum light- matter interactions in 2D materials, Nature Communica- tions12, 2778 (2021)

    2021

  62. [70]

    Pantazopoulos, J

    P.-A. Pantazopoulos, J. Feist, A. Kamra, and F. J. Garc ´ ıa-Vidal, Electrostatic nature of cavity-mediated in- teractions between low-energy matter excitations, Phys- ical Review B109, L201408 (2024)

    2024

  63. [71]

    Carlsson, S

    O. Carlsson, S. Chattopadhyay, J. B. Curtis, F. Lin- del, L. Graziotto, J. Faist, and E. Demler, Casimir sta- bilization of fluctuating electronic nematic order, arXiv preprint arXiv:2510.05088 (2025)

    2025

  64. [72]

    M. K. Svendsen, M. Ruggenthaler, H. H¨ ubener, C. Sch¨ afer, M. Eckstein, A. Rubio, and S. Latini, Ef- fective equilibrium theory of quantum light-matter in- teraction in cavities for extended systems and the long 14 wavelength approximation, Communications Physics8, 425 (2025)

    2025

  65. [73]

    Vi˜ nas Bostr¨ om, M

    E. Vi˜ nas Bostr¨ om, M. H. Michael, C. Eckhardt, and A. Rubio, Equilibrium nonlinear phononics by electric field fluctuations of terahertz cavities, Physical Review Research7, 033163 (2025)

    2025

  66. [74]

    C. Fan, E. Vi˜ nas Bostr¨ om, X. Cheng, L. Grunwald, Z. Zhang, D. M. Kennes, D. N. Basov, and A. Rubio, Cavity control of multiferroic order in single-layer NiI 2, npj Computational Materials12, 205 (2026)

    2026

  67. [75]

    Acosta, N

    M. Acosta, N. Novak, V. Rojas, S. Patel, R. Vaish, J. Ko- ruza, G. Rossetti, and J. R¨ odel, BaTiO 3-based piezo- electrics: Fundamentals, current status, and perspec- tives, Applied Physics Reviews4(2017)

    2017

  68. [76]

    M. A. Pe˜ na and J. L. G. Fierro, Chemical structures and performance of perovskite oxides, Chemical reviews101, 1981 (2001)

    1981

  69. [77]

    Humayun, Z

    M. Humayun, Z. Li, M. Israr, A. Khan, W. Luo, C. Wang, and Z. Shao, Perovskite type ABO3 oxides in photocatal- ysis, electrocatalysis, and solid oxide fuel cells: state of the art and future prospects, Chemical Reviews125, 3165 (2025)

    2025

  70. [78]

    S. Saha, T. Sinha, and A. Mookerjee, Electronic struc- ture, chemical bonding, and optical properties of para- electric BaTiO3, Physical Review B62, 8828 (2000)

    2000

  71. [79]

    ˇSmejkal, J

    L. ˇSmejkal, J. Sinova, and T. Jungwirth, Beyond conven- tional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry, Physical Review X12, 031042 (2022)

    2022

  72. [80]

    J. Quan, C. Fan, B. Fan, I.-T. Lu, D. M. Kennes, and A. Rubio, Macroscopic polarization and magneti- zation from cavity vacuum fluctuations, arXiv preprint arXiv:2607.19612 (2026)

    2026 arXiv

  73. [81]

    But one can always analyze the symmetry reduction induced on the mate- rial’s electron density

    Actually, it is not always possible to assign cavity modes an irrep of the material’s point group if the material or the cavity is allowed to rotate in 3D. But one can always analyze the symmetry reduction induced on the mate- rial’s electron density

  74. [82]

    Troisi, H

    F. Troisi, H. H¨ ubener, A. Rubio, and S. Latini, Cavity- QED-controlled two-dimensional Moir´ e excitons without twisting, Nature Communications (2025)

    2025

  75. [83]

    H¨ ubener, U

    H. H¨ ubener, U. De Giovannini, C. Sch¨ afer, J. Andberger, M. Ruggenthaler, J. Faist, and A. Rubio, Engineering quantum materials with chiral optical cavities, Nature Materials20, 438 (2021)

    2021

  76. [84]

    J. C. Owens, M. G. Panetta, B. Saxberg, G. Roberts, S. Chakram, R. Ma, A. Vrajitoarea, J. Simon, and D. I. Schuster, Chiral cavity quantum electrodynamics, Nature Physics18, 1048 (2022)

    2022

  77. [85]

    K. M. Kulkarni, H. Xu, F. Tay, G. M. Rodriguez-Barrios, D. Kim, A. Alabastri, V. Rokaj, C. B. Dag, A. Baydin, and J. Kono, Realization of a chiral photonic-crystal cav- ity with broken time-reversal symmetry, arXiv preprint arXiv:2509.14366 (2025)

    2025

  78. [86]

    M. I. Aroyo, J. M. Perez-Mato, D. Orobengoa, E. Tasci, G. de la Flor, and A. Kirov, Crystallography online: Bil- bao crystallographic server, Bulg. Chem. Commun43, 183 (2011)

    2011

  79. [87]

    S. V. Gallego, J. Etxebarria, L. Elcoro, E. S. Tasci, and J. M. Perez-Mato, Automatic calculation of symmetry- adapted tensors in magnetic and non-magnetic materials: a new tool of the Bilbao Crystallographic Server, Foun- dations of Crystallography75, 438 (2019)

    2019

  80. [88]

    Giannozzi, O

    P. Giannozzi, O. Baseggio, P. Bonf` a, D. Brunato, R. Car, I. Carnimeo, C. Cavazzoni, S. De Gironcoli, P. Delugas, F. Ferrari Ruffino,et al., Quantum ESPRESSO toward the exascale, The Journal of chemical physics152(2020)

    2020

  81. [89]

    Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Physical Review B—Condensed Mat- ter and Materials Physics88, 085117 (2013)

    D. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Physical Review B—Condensed Mat- ter and Materials Physics88, 085117 (2013)

    2013

  82. [90]

    M. J. Van Setten, M. Giantomassi, E. Bousquet, M. J. Verstraete, D. R. Hamann, X. Gonze, and G.-M. Rig- nanese, The PseudoDojo: Training and grading a 85 ele- ment optimized norm-conserving pseudopotential table, Computer Physics Communications226, 39 (2018)

    2018

  83. [91]

    Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Physical review B41, 7892 (1990)

    D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Physical review B41, 7892 (1990)

    1990

  84. [92]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Physical review let- ters77, 3865 (1996)

    1996

  85. [93]

    J. P. Perdew and Y. Wang, Accurate and simple ana- lytic representation of the electron-gas correlation energy, Physical review B45, 13244 (1992)

    1992

  86. [94]

    C. Lin, S. Ponc´ e, and N. Marzari, General invariance and equilibrium conditions for lattice dynamics in 1D, 2D, and 3D materials, npj Computational Materials8, 236 (2022)

    2022

  87. [95]

    Lazzeri and F

    M. Lazzeri and F. Mauri, First-Principles Calculation of Vibrational Raman Spectra in Large Systems: Signature of Small Rings in Crystalline SiO 2, Phys. Rev. Lett.90, 036401 (2003)

    2003

  88. [96]

    Choi, S.-H

    S.-M. Choi, S.-H. Jhi, and Y.-W. Son, Effects of strain on electronic properties of graphene, Physical Review B—Condensed Matter and Materials Physics81, 081407 (2010)

    2010

  89. [97]

    J. L. Ma˜ nes, F. Guinea, and M. A. Vozmediano, Exis- tence and topological stability of Fermi points in multi- layered graphene, Physical Review B—Condensed Mat- ter and Materials Physics75, 155424 (2007)

    2007

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.