Pith. sign in

REVIEW 3 major objections 6 minor 35 references

Spin-phase transition in an array of quantum rings controlled by cavity photons

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Cavity photons can switch the spin order of a quantum ring array from fully polarized to single unpaired spins, with strong coupling suppressing the switch.

desk verdict New model prediction of cavity-controlled spin order in ring arrays, but the spin-phase transition hinges on an unbenchmarked LSDA exchange term. read the letter →

arxiv 2411.13176 v1 pith:23SWWR7P submitted 2024-11-20 cond-mat.mes-hall

Vidar Gudmundsson , Vram Mughnetsyan , Hsi-Sheng Goan , Jeng-Da Chai , Nzar Rauf Abdullah , Chi-Shung Tang , Valeriu Moldoveanu , Andrei Manolescu This is my paper · ORCID
classification cond-mat.mes-hall
keywords quantumringscavityphotonsspin-phasetransitionorbitalmagnetizationspindensityfunctionaltheoryelectron-photoncouplingtwo-dimensionalelectrongaslateralsuperlattice
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 predicts a spin-phase transition in a square array of quantum rings driven by the cavity photon field rather than by an external pulse. For three electrons per ring at two magnetic flux quanta per unit cell, the static ground state is fully spin-polarized at weak electron-photon coupling and low photon energy, and switches to a state with a single unpaired spin per ring when either the coupling strength or the photon energy is increased. The same transition is visible in the orbital magnetization, and strong electron-photon coupling suppresses it. If correct, this means the magnetic ordering of an extended two-dimensional electron gas can be controlled contact-free by tuning a cavity mode.

What carries the argument

The load-bearing object is the electron-photon interaction Hamiltonian for the cavity mode, whose paramagnetic part is $g_\gamma\hbar\omega_c(lI_x+lI_y)(a^\dagger_\gamma+a_\gamma)$ and whose diamagnetic part is $g_\gamma^2\hbar\omega_c N\big((a^\dagger_\gamma a_\gamma+\tfrac12)+\tfrac12(a^\dagger_\gamma a^\dagger_\gamma+a_\gamma a_\gamma)\big)$, with $I_x$, $I_y$, and $N$ functionals of the electron charge and current densities that are updated self-consistently. The Coulomb interaction is treated by a spin-density-functional approximation with an exact direct term, while the electron-photon interaction is treated by configuration interaction in a truncated photon Fock space built on tensor-product states of electron and photon states. The cavity vector potential has the same spatial form as the vector potential of the external homogeneous magnetic field, so the mode couples naturally to persistent ring currents; the spin configuration is read from the spin magnetization $M_s$, and its transition is mirrored in the orbital magnetization $M_o$.

What would settle it

Recompute the static ground state of the three-electron ring cell at two flux quanta with a method that treats exchange exactly, such as exact diagonalization of the few-electron cell or a many-body wavefunction approach, scanning the same photon-energy and coupling range. If the transition from fully polarized to single-unpaired-spin disappears when the local spin-density exchange-correlation functional is replaced by exact exchange, the predicted transition is an artifact of the approximation rather than a property of the physical system.

Watch

Extended reading notes

Core claim

The central claim is that the spin ordering of the two-dimensional electron gas in each ring can be controlled by the dimensionless electron-photon coupling $g_\gamma$ and the photon energy $E_\gamma$ of a single circularly symmetric cavity mode. For three electrons per ring and two flux quanta per unit cell, the system is fully spin polarized in the static ground state for small $g_\gamma$ and small $E_\gamma$; increasing either quantity drives it into a phase with one unpaired spin per ring. The transition shows up in the orbital magnetization as well as the spin magnetization. Strong coupling suppresses the transition, and dynamical calculations show spin fluctuations near the transition point even though the excitation pulse cannot exert a torque on the spins. The authors attribute the effect to inter-ring Coulomb exchange, which is stronger in ring arrays than in dot arrays and is weakened by the electron-photon interaction.

Load-bearing premise

The prediction rests on the local spin-density approximation faithfully capturing the inter-ring exchange interaction, since that exchange is the mechanism the paper says drives the transition.

Editorial extensions

If this is right

  • Cavity photons can serve as a contact-free control parameter for the magnetic state of an extended two-dimensional electron gas, not just as a probe of it.
  • Because the transition is mirrored in the orbital magnetization, the spin-phase change can be read out magnetically without measuring spins directly.
  • Strong electron-photon coupling suppresses the transition, so tuning the coupling strength can select between the fully polarized and single-unpaired-spin phases.
  • Spin fluctuations appear near the transition in dynamical calculations, offering a signature of critical behavior even though the excitation exerts no torque on the spins.
  • The stronger inter-ring exchange in ring arrays compared with dot arrays suggests ring superlattices are a more favorable platform for cavity-controlled exchange magnetism.

Reading between the lines

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

  • If the mechanism is robust, analogous photon-controlled spin-order transitions could appear in other lattice geometries, such as antidot lattices or superlattices with different electron fillings, wherever inter-cell exchange is the ordering agent.
  • The prediction could be tested in a GaAs ring superlattice inside a far-infrared or terahertz cavity by measuring orbital magnetization or magnetotransport while tuning photon frequency; a sharp jump in $M_s/M_0$ at fixed magnetic field would be the experimental signature.
  • Because the central mechanism is carried by the approximate local spin-density exchange-correlation functional, exact few-cell calculations that treat inter-ring exchange without approximation would clarify whether the transition survives beyond the functional.
  • The balance between the paramagnetic and diamagnetic electron-photon coupling terms may determine whether the transition can be driven resonantly at fixed coupling by photon energy alone, which would make the effect dynamically addressable.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper models a two-dimensional electron gas (2DEG) arranged in a square array of quantum rings, placed in a perpendicular magnetic field and coupled to a single circularly symmetric FIR cavity photon mode. The Coulomb interaction is treated with spin-density functional theory (exact direct term, LSDA exchange-correlation), while the para- and diamagnetic electron-photon couplings are treated by configuration interaction in a truncated photon Fock space, updated self-consistently. For two electrons per ring the system stays in a triplet spin configuration. For three electrons per ring at two flux quanta per cell, the static calculations show a change in the spin magnetization from a fully spin-polarized state to a state with a single unpaired spin per ring as either the photon energy Eγ or the coupling gγ is increased, and strong coupling suppresses this change; the orbital magnetization mirrors the transition. Time-dependent simulations after a pulse show spin fluctuations near the transition. The authors conclude that the inter-ring exchange interaction drives the transition and that cavity photons provide a control knob for spin order in the ring array.

Significance. If the result holds, the paper demonstrates a non-contact, cavity-based control of spin ordering in an extended ring-array 2DEG, with a concrete observable (orbital magnetization) and a predicted phase boundary as a function of photon energy and coupling. The work is an interesting extension of the authors' earlier QED-DFT and QED-DFT-TP studies from dot arrays to ring arrays, and it makes a specific, falsifiable prediction. The methods are not fitted to the target data, so there is no circularity in the central numerical result. The main significance is conditional on two numerical/modeling issues: the convergence of the truncated photon space and the reliability of the LSDA exchange-correlation functional for the very spin-multiplicity change that defines the transition.

major comments (3)
  1. [Appendix A / Sec. III.B] The central spin-phase boundary in Fig. 6(d) is presented without any convergence tests for the two numerical truncations introduced in Appendix A: the 16-photon Fock-space truncation and the 32×32 Brillouin-zone grid. Appendix A states that these choices 'guarantee the accuracy' for gγ > 0.10, but no supporting data are shown. Because the transition is identified as a jump in Ms between discrete values, a small error in the total energy near the level crossing could shift or eliminate the boundary. Please provide convergence scans of Ms and Etot with respect to the photon-number cutoff and the BZ grid at representative (gγ, Eγ) points on both sides of the transition.
  2. [Sec. II / Sec. III.B / Conclusions] The transition is attributed in the Conclusions to 'the inter-ring exchange interaction is at work', but in the model the entire exchange-correlation contribution is represented by the Tanatar-Ceperley LSDA functional, introduced via Ref. [18] and described in Sec. II. The transition is a change in ground-state spin multiplicity, which is governed by the small energy difference between spin configurations—precisely the quantity LSDA is least reliable for, particularly in strongly inhomogeneous few-electron ring cells. Without a benchmark against exact diagonalization, quantum Monte Carlo, or an exact-exchange calculation for the ring array or a representative cluster, the phase boundary in Fig. 6(d) could be an artifact of the approximate functional rather than a property of the physical system. Please provide such a benchmark and show that the boundary is stable with respect to the choice of exchange-correlation approximation.
  3. [Sec. III.B / Fig. 6] The manuscript labels the change as a 'spin-phase transition' without a quantitative criterion. The data in Fig. 6(d) show a change in Ms between two plateaus, but no discontinuity, order-parameter analysis, or dependence on system size is presented, and the calculations are at T = 1 K. Please clarify whether this is a ground-state level crossing in the infinite superlattice, a first-order transition in the self-consistent solution, or a smooth crossover, and define the location of the transition point (for example, the midpoint of the Ms jump) so that the reader can compare different coupling and energy values.
minor comments (6)
  1. [Eq. (14) and figure captions] The notation µ∗_B is used in Eq. (14) and in the captions of Figs. 2 and 6, but the text elsewhere uses the Bohr magneton; please define µ∗_B explicitly and state how it differs from the free-electron Bohr magneton.
  2. [Sec. III.A] The phrase 'Fig. 2 (in the present paper)' is confusing because the preceding sentence also refers to a figure in Ref. [20]; please rephrase to avoid ambiguity.
  3. [Eq. (10) / Sec. III] The parameter Vt appears in Eq. (10) but is only defined later as Vt/ℏωc = 0.8; please introduce it in Sec. II or immediately before Eq. (10).
  4. [Sec. II] The notation QJ is mentioned as a previous name for the orbital magnetization but is never defined in this paper; either define it or remove the reference.
  5. [Appendix A] The phrase '16 lowest eigenstates of the photon number operator' should specify whether this is n = 0,1,...,15 or n = 1,...,16, and the '32×32 nonequispaced grid ... built on a repeated 4-point Gaussian quadrature' needs a brief explanation or reference.
  6. [Fig. 5 caption] The notation 'nel2' and '∆ nel2' mixes a variable name with the product ne l^2; please make the notation consistent with the text.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the spin-phase transition is a computed numerical output, not a fitted or definitionally forced prediction.

full rationale

The central claim, a photon-controlled spin-phase transition for Ne=3 rings, is a numerical result of a self-consistent QED-DFT-TP calculation, not a quantity fitted to data or defined in terms of the claimed outcome. The electron-photon interaction is expressed via density and current functionals, and the spin magnetization is evaluated from self-consistent spin densities; no input parameter is relabeled as a prediction. The paper's heavy reliance on Refs. [18], [20], and [22] is method reuse: the vector potential, exchange-correlation approximation, and numerical basis are inherited from prior work by the same group, but the new physical result is computed from the model rather than imported by citation. The acknowledged use of the Tanatar-Ceperley local spin-density approximation for exchange-correlation is a genuine correctness risk, since the transition is attributed to inter-ring exchange, and LSDA may misplace spin-stability energies in few-electron inhomogeneous rings; however, this is an approximation-error concern, not circularity, because the functional is an independent external input fitted to the homogeneous 2DEG rather than to the present target. No self-definitional step, fitted-input-called-prediction step, imported uniqueness theorem, or renaming of a known result appears. The score of 1 reflects only that the paper leans on a chain of the authors' own method papers, which is normal and does not make the derivation circular.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central prediction rests on the LSDA exchange-correlation functional, a single-mode long-wavelength cavity model, and numerical truncations; none of these are benchmarked against independent calculations or experiments in this paper.

free parameters (3)
  • V0 = 64 meV
    Depth of the periodic ring potential in Eq. (1), chosen by hand to define the ring array; it sets the confinement strength and influences the transition's location in parameter space.
  • photon Fock-space truncation N_ph = 16
    Number of photon number states retained in the truncated many-body basis (Appendix A); the paper asserts this guarantees accuracy for gγ > 0.10 but provides no convergence scan.
  • pulse parameters = Vt/ℏωc = 0.8, ℏωext = 3.5 meV, ℏΓ = 0.5 meV
    Chosen parameters for the time-dependent excitation in Eq. (10); these choices shape the reported dynamic spin fluctuations and are not derived from experiment.
assumptions (5)
  • domain assumption The local spin-density approximation (LSDA) with Tanatar-Ceperley correlation accurately describes exchange-correlation effects in the ring array, including the inter-ring exchange that drives the spin transition.
    Invoked in Sec. II via Ref. [18]; the paper attributes the transition to inter-ring exchange, so the result depends on this approximate functional's fidelity.
  • domain assumption The electron-photon interaction is dominated by a single circularly symmetric TE011 cavity mode in the long-wavelength approximation, giving the vector potential of Eq. (2).
    The model keeps only one photon mode and uses a specific spatial form for its vector potential; real cavities have additional modes and spatial variations that are neglected.
  • domain assumption The superlattice is periodic and the θ points in the Brillouin zone decouple, so the dynamics can be solved independently for each θ point with the Liouville-von Neumann equation.
    Used in Sec. II, Eq. (11); it is an exact symmetry of the model but assumes perfect translational invariance and ignores edge or disorder effects.
  • domain assumption GaAs effective mass, dielectric constant, and effective g-factor (m*=0.067me, κ=12.4, g*=-0.44) properly describe electrons in the ring array.
    Standard material parameters taken from the 2DEG literature; they set the energy scales and the quantitative position of the transition.
  • ad hoc to paper The 16-photon and 32x32 Brillouin-zone grid truncations are converged for the coupling range studied.
    Appendix A states these choices 'guarantee the accuracy' for gγ > 0.10, but no convergence data are shown; this is a practical numerical assumption introduced for this paper.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Spin-phase transition in an array of quantum rings controlled by cavity photons." pith.science (2026). https://pith.science/paper/23SWWR7P

@misc{pith2026241113176,
  author       = {Pith},
  title        = {Pith review of: Spin-phase transition in an array of quantum rings controlled by cavity photons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/23SWWR7P}},
  note         = {Machine review of arXiv:2411.13176}
}
read the original abstract

We model a spin-phase transition in a two-dimensional square array, or a lateral superlattice, of quantum rings in an external perpendicular homogeneous magnetic field. The electron system is placed in a circular cylindrical far-infrared photon cavity with a single circularly symmetric photon mode. Our numerical results reveal that the spin ordering of the two-dimensional electron gas in each quantum ring can be influenced or controlled by the electron-photon coupling strength and the energy of the photons. The Coulomb interaction between the electrons is described by a spin-density functional approach, but the para- and the diamagnetic electron-photon interactions are modeled via a configuration interaction formalism in a truncated many-body Fock-space, which is updated in each iteration step of the density functional approach. In the absence of external electromagnetic pulses this spin-phase transition is replicated in the orbital magnetization of the rings. The spin-phase transition can be suppressed by a strong electron-photon interaction. In addition, fluctuations in the spin configuration are found in dynamical calculations, where the system is excited by a time-dependent scheme specially fit for emphasizing the diamagnetic electron-photon interaction.

Figures

Figures reproduced from arXiv: 2411.13176 by the authors.

Figure 1
Figure 1. FIG. 1. Four unit cells of the potentials defining the two [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The total energy [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The dynamic mean photon number [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (5 more)
Figure 5
Figure 5. Figure 5: FIG. 5. The electron density [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The total energy [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. The total energy [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. The total energy [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. The total energy [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

35 extracted references · 32 canonical work pages

  1. [18]

    Gudmundsson, V

    V. Gudmundsson, V. Mughnetsyan, N. R. Abdullah, C.- S. Tang, V. Moldoveanu, and A. Manolescu, Effects of a far-infrared photon cavity field on the magnetization of a square quantum dot array, Phys. Rev. B 106, 115308 (2022)

    work page 2022

  2. [1]

    Flick, H

    J. Flick, H. Appel, M. Ruggenthaler, and A. Rubio, Cav- ity Born–Oppenheimer Approximation for Correlated Electron–Nuclear-Photon Systems, Journal of Chemical Theory and Computation 13, 1616–1625 (2017)

    work page 2017

  3. [2]

    Flick, N

    J. Flick, N. Rivera, and P. Narang, Strong light-matter coupling in quantum chemistry and quantum photonics, Nanophotonics 7, 1479–1501 (2018)

    work page 2018

  4. [3]

    Tancogne-Dejean, M

    N. Tancogne-Dejean, M. J. T. Oliveira, X. Andrade, H. Appel, C. H. Borca, G. Le Breton, F. Buchholz, A. Castro, S. Corni, A. A. Correa, U. De Giovannini, A. Delgado, F. G. Eich, J. Flick, G. Gil, A. Gomez, N. Helbig, H. H¨ ubener, R. Jest¨ adt, J. Jornet-Somoza, A. H. Larsen, I. V. Lebedeva, M. L¨ uders, M. A. L. Mar- ques, S. T. Ohlmann, S. Pipolo, M. Ra...

    work page 2020

  5. [4]

    Buchholz, I

    F. Buchholz, I. Theophilou, S. E. B. Nielsen, M. Ruggen- thaler, and A. Rubio, Reduced Density-Matrix Approach to Strong Matter-Photon Interaction, ACS Photonics 6, 2694–2711 (2019)

    work page 2019

  6. [5]

    J. A. Hutchison, T. Schwartz, C. Genet, E. Devaux, and T. W. Ebbesen, Modifying Chemical Landscapes by Cou- pling to Vacuum Fields, Angewandte Chemie Interna- 9 -37.3 -37.2 -37.1 -37.0 -36.9 -36.8 -36.7 -36.6 0 5 10 15 20 25 30 (a) Eγ = 0.7 meV Eγ = 1.4 meV Etot (meV) t (ps) 0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0 5 10 15 20 25 30 (b) Eγ = 0...

    work page 2012

  7. [6]

    Schafer, J

    C. Schafer, J. Flick, E. Ronca, P. Narang, and ´Angel Ru- bio, Shining Light on the Microscopic Resonant Mech- anism Responsible for Cavity-Mediated Chemical Reac- tivity (2021)

    work page 2021

  8. [7]

    Keller, G

    J. Keller, G. Scalari, F. Appugliese, S. Rajabali, M. Beck, J. Haase, C. A. Lehner, W. Wegscheider, M. Failla, M. Myronov, D. R. Leadley, J. Lloyd-Hughes, P. Nataf, and J. Faist, Landau polaritons in highly nonparabolic two-dimensional gases in the ultrastrong coupling regime, Phys. Rev. B 101, 075301 (2020)

    work page 2020

Show all 35 references
  1. [8]

    J. Li, D. Golez, G. Mazza, A. J. Millis, A. Georges, and M. Eckstein, Electromagnetic coupling in tight-binding models for strongly correlated light and matter, Phys. Rev. B 101, 205140 (2020)

    2020

  2. [9]

    Flick, C

    J. Flick, C. Sch¨ afer, M. Ruggenthaler, H. Appel, and A. Rubio, Ab Initio Optimized Effective Poten- tials for Real Molecules in Optical Cavities: Pho- ton Contributions to the Molecular Ground State, ACS Photonics 5, 992–1005 (2018), pMID: 29594185, https://doi.org/10.1021/a...

    2018 doi

  3. [10]

    Flick, Simple Exchange-Correlation Energy Function- als for Strongly Coupled Light-Matter Systems Based on the Fluctuation-Dissipation Theorem, Phys

    J. Flick, Simple Exchange-Correlation Energy Function- als for Strongly Coupled Light-Matter Systems Based on the Fluctuation-Dissipation Theorem, Phys. Rev. Lett. 129, 143201 (2022)

    2022

  4. [11]

    Malave, A

    J. Malave, A. Ahrens, D. Pitagora, C. Covington, and K. Varga, Real-space, real-time approach to quantum- electrodynamical time-dependent density functional the- ory, The Journal of Chemical Physics157 (2022), 194106

    2022

  5. [12]

    D. B. Dar, A. Baranova, and N. T. Maitra, Reformula- tion of Time-Dependent Density Functional Theory for Nonperturbative Dynamics: The Rabi Oscillation Prob- lem Resolved, Phys. Rev. Lett. 133, 096401 (2024)

    2024

  6. [13]

    Zhang, M

    Q. Zhang, M. Lou, X. Li, J. L. Reno, W. Pan, J. D. Watson, M. J. Manfra, and J. Kono, Collective non- perturbative coupling of 2D electrons with high-quality- factor terahertz cavity photons, Nature Physics 12, 1005 (2016)

    2016

  7. [14]

    Scalari, C

    G. Scalari, C. Maissen, D. Turˇ cinkov´ a, D. Hagenm¨ uller, S. D. Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, Ultrastrong Cou- pling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial, Science 335, 1323–1326 (2012)

    2012

  8. [15]

    Rokaj, M

    V. Rokaj, M. Ruggenthaler, F. G. Eich, and A. Ru- bio, Free electron gas in cavity quantum electrodynamics, Phys. Rev. Res. 4, 013012 (2022)

    2022

  9. [16]

    Rokaj, M

    V. Rokaj, M. Penz, M. A. Sentef, M. Ruggenthaler, and A. Rubio, Quantum Electrodynamical Bloch Theory with Homogeneous Magnetic Fields, Phys. Rev. Lett. 123, 10 -37 -36.9 -36.8 -36.7 -36.6 -36.5 -36.4 -36.3 -36.2 0 5 10 15 20 25 30 (a) Eγ = 0.7 meV Eγ = 1.4 meV Etot (meV) t (p...

    2019

  10. [17]

    Rokaj, M

    V. Rokaj, M. Penz, M. A. Sentef, M. Ruggenthaler, and A. Rubio, Polaritonic Hofstadter butterfly and cavity control of the quantized Hall conductance, Phys. Rev. B 105, 205424 (2022)

    2022

  11. [19]

    Mughnetsyan, V

    V. Mughnetsyan, V. Gudmundsson, N. R. Abdullah, C.-S. Tang, V. Moldoveanu, and A. Manolescu, Mag- netic Properties of A Cavity-Embedded Square Lattice of Quantum Dots or Antidots, Annalen der Physik 536, 2300274 (2024)

    2024

  12. [20]

    Gudmundsson, V

    V. Gudmundsson, V. Mughnetsyan, H.-S. Goan, J.-D. Chai, N. R. Abdullah, C.-S. Tang, V. Moldoveanu, and A. Manolescu, Magneto-optical properties of a quantum dot array interacting with a far-infrared photon mode of a cylindrical cavity, Phys. Rev. B 109, 235306 (2024)

    2024

  13. [21]

    Gudmundsson, V

    V. Gudmundsson, V. Mughnetsyan, N. R. Abdullah, C.- S. Tang, V. Moldoveanu, and A. Manolescu, Controlling the excitation spectrum of a quantum dot array with a photon cavity, Phys. Rev. B 108, 115306 (2023)

    2023

  14. [22]

    Gudmundsson, V

    V. Gudmundsson, V. Mughnetsyan, H.-S. Goan, J.-D. Chai, N. R. Abdullah, C.-S. Tang, V. Moldoveanu, and A. Manolescu, Tuning of paramagnetic and diamagnetic cavity photon excitations in a square array of quan- tum dots in a magnetic field, Phys. Rev. B 110, 205301 (2024)

    2024

  15. [23]

    M. I. Lubin, O. Heinonen, and M. D. Johnson, Spin- ensemble density-functional theory for inhomogeneous quantum Hall systems, Phys. Rev. B 56, 10373–10382 (1997)

    1997

  16. [24]

    Koskinen, M

    M. Koskinen, M. Manninen, and S. M. Reimann, Hund’s Rules and Spin Density Waves in Quantum Dots, Phys. Rev. Lett. 79, 1389–1392 (1997)

    1997

  17. [25]

    von Barth and L

    U. von Barth and L. Hedin, A local exchange-correlation potential for the spin polarized case. i, Journal of Physics C: Solid State Physics 5, 1629–1642 (1972)

    1972

  18. [26]

    Tanatar and D

    B. Tanatar and D. M. Ceperley, Ground state of the two- dimensional electron gas, Phys. Rev. B 39, 5005–5016 (1989)

    1989

  19. [27]

    R. D. Hofstadter, Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields, Phys. Rev. B 14, 2239 (1976)

    1976

  20. [28]

    Ferrari, Two-dimensional electrons in a strong mag- netic field: A basis for single-particle states, Phys

    R. Ferrari, Two-dimensional electrons in a strong mag- netic field: A basis for single-particle states, Phys. Rev. B 42, 4598 (1990)

    1990

  21. [29]

    H. Silberbauer, Magnetic minibands in lateral semicon- 11 -38.0 -37.8 -37.6 -37.4 -37.2 -37.0 -36.8 -36.6 -36.4 -36.2 0 5 10 15 20 25 30 (a) gγ = 0.06 gγ = 0.08 gγ = 0.10 Etot (meV) t (ps) -37.8 -37.6 -37.4 -37.2 -37.0 -36.8 -36.6 -36.4 -36.2 0 5 10 15 20 25 30 (b) gγ = 0.05 g...

    1992

  22. [30]

    Gudmundsson and R

    V. Gudmundsson and R. R. Gerhardts, Effects of screen- ing on the Hofstadter butterfly, Phys. Rev. B 52, 16744 (1995)

    1995

  23. [31]

    Pfannkuche, V

    D. Pfannkuche, V. Gudmundsson, and P. Maksym, Com- parison of a Hartree, a Hartree-Fock, and an Exact Treat- ment of Quantum Dot Helium, Phys. Rev. B 47, 2244 (1993)

    1993

  24. [32]

    Stockklauser, P

    A. Stockklauser, P. Scarlino, J. V. Koski, S. Gasparinetti, C. K. Andersen, C. Reichl, W. Wegscheider, T. Ihn, K. Ensslin, and A. Wallraff, Strong Coupling Cavity QED with Gate-Defined Double Quantum Dots Enabled by a High Impedance Resonator, Phys. Rev. X 7, 011030 (2017)

    2017

  25. [33]

    Scarlino, J

    P. Scarlino, J. H. Ungerer, D. J. van Woerkom, M. Mancini, P. Stano, C. M¨ uller, A. J. Landig, J. V. Koski, C. Reichl, W. Wegscheider, T. Ihn, K. Ensslin, and A. Wallraff, In situ Tuning of the Electric-Dipole Strength of a Double-Dot Charge Qubit: Charge-Noise Protection and...

    2022

  26. [34]

    F. Fung, E. Rosenfeld, J. D. Schaefer, A. Kabcenell, J. Gieseler, T. X. Zhou, T. Madhavan, N. Aslam, A. Ya- coby, and M. D. Lukin, Toward Programmable Quantum Processors Based on Spin Qubits with Mechanically Me- diated Interactions and Transport, Phys. Rev. Lett. 132, 263602 (2024)

    2024

  27. [35]

    C. E. Bradley, J. Randall, M. H. Abobeih, R. C. Berrevoets, M. J. Degen, M. A. Bakker, M. Markham, D. J. Twitchen, and T. H. Taminiau, A Ten-Qubit Solid- State Spin Register with Quantum Memory up to One Minute, Phys. Rev. X 9, 031045 (2019)

    2019

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.