Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Realization of tilted Dirac-like microwave cone in superconducting circuit lattices

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read The paper reports that adding a preferred-axis second-neighbor inductance to a 731-site honeycomb LC lattice tilts the microwave Dirac cone, with fitted tilts up to 59% group-velocity asymmetry.

desk verdict A genuinely new large-scale circuit platform with a credible 731-mode fit, but the headline tilt value is fitted, not directly measured, and the main text mislabels it as designed. read the letter →

arxiv 2501.10434 v1 pith:VOFIXBDJ submitted 2025-01-12 cond-mat.mes-hall cond-mat.othergr-qcquant-ph

Amir Youssefi , Ahmad Motavassal , Shingo Kono , Seyed Akbar Jafari , Tobias J. Kippenberg This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.othergr-qcquant-ph
keywords tiltedDiracconesuperconductingcircuitlatticelumped-elementLCresonatorhoneycombsecond-neighborcouplingdensityofstatesreconstructionemergentspacetimemicrowavephotonics
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

This paper reports an experimental platform in which a Dirac-like microwave cone is tilted by a designer amount, rather than by the fixed conditions of a particular material. Three superconducting honeycomb lattices made of 731 lumped LC resonators each show a cone whose tilt is set by the ratio of a first-neighbor inductance $L$ to a uniaxial second-neighbor inductance $L'$, with measured tilts reaching a 59% asymmetry between opposite-direction group velocities. The authors reconstruct the density of states from measured microwave transmission spectra and match it to a finite-lattice tight-binding model, extracting the tilt as an inductance ratio $\zeta = 2L/L'$. If correct, the result turns the tilt of a band crossing from a material property into a circuit-design parameter, which the authors argue is a step toward imprinting curved-spacetime metrics onto a chip.

What carries the argument

The load-bearing object is the honeycomb lattice as a circuit graph: every node is a parallel-plate capacitor $C$ to ground, connected to its three nearest neighbors by inductance $L$ and, along one preferred axis, to two of its second neighbors by inductance $L'$. Kirchhoff's laws reduce to the eigenvalue problem $DV = (\omega/\omega_0)^2 V$ with $\omega_0 = 1/\sqrt{LC}$, and the Bloch Hamiltonian acquires a $\mathbf{k}\cdot\zeta$ term proportional to the identity matrix, which tilts the cone; the identity $\zeta = 2L/L'$ is what makes the tilt a design knob. The measurement pipeline—peak detection in the transmission $S_{21}$ using phase gradients and amplitude, Lorentzian/Fano fits for linewidths, histogram construction of the density of states, and least-squares pairing of detected resonances to the finite-lattice model anchored at the Dirac frequency—is the machinery that turns raw microwave data into the quoted tilt values.

What would settle it

Take one of the tilted devices and redo the least-squares fit with the mode numbering shifted by one at the Dirac point: if the extracted $\zeta$ moves by more than the stated uncertainty, the tilt value is not robust to pairing ambiguity. Alternatively, measure a single-site local density of states at a corner and in the bulk: if the DOS dip at the Dirac frequency is absent where the model says it must be, the fit's starting point is wrong.

Watch

Extended reading notes

Core claim

The central claim is that uniaxial second-neighbor coupling in a honeycomb circuit lattice deterministically tilts the Dirac-like microwave cone, and that the tilt can be read out from the spectrum of a large finite lattice. Concretely, the paper shows that a honeycomb lattice of LC resonators with first-neighbor inductors $L$ and selective second-neighbor inductors $L'$ realizes a tight-binding model with tilt parameter $\zeta = 2L/L'$, giving opposite tilt at the $K$ and $K'$ valleys while leaving the crossing gapless. Three fabricated devices with designed $\zeta = 0$, $0.40$, and $0.52$ were measured at 15 mK; fitting the measured resonance frequencies to a 731-site model yields $\zeta \approx 0$, $0.43$, and $0.59$, i.e., up to 59% relative difference in opposite-direction group velocities. The paper presents this as the first deterministic, large-scale tuning of cone tilt in a superconducting circuit platform, and as a foundation for engineering an emergent spacetime metric through spatially varying $\zeta$.

Load-bearing premise

The central measurement depends on pairing every detected resonance with a specific eigenmode index relative to the Dirac frequency, and on assuming the fabricated 731-site chip matches the ideal uniform $L$, $C$, $L'$ model; if modes are missed or reordered near the Dirac point, or if disorder or parasitics distort the spectrum, the fitted tilt would be biased.

Editorial extensions

If this is right

  • Because the tilt is set by an inductance ratio, the same 731-site architecture can realize many $\zeta$ values without changing materials or atomic structure.
  • A spatially graded $L'$ would produce $\zeta(\mathbf{x})$, which the paper interprets as a moving-frame velocity that varies in space—equivalent to a curved Painlevé–Gullstrand spacetime metric.
  • Vortex-like tilt profiles would act as a synthetic gravitomagnetic field, with predicted cyclotron-like orbits and Landau quantization of microwaves.
  • Flux-tunable Josephson inductors would allow time-dependent $\zeta$, a route to generating synthetic gravitational waves in the lattice.
  • Coupling superconducting qubits into such tilted lattices offers a test bed for curved-spacetime-mediated entanglement.

Reading between the lines

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

  • One direct extension the authors do not test: push $\zeta$ toward 1 by choosing $L' \approx L/2$, which would bring one group velocity to zero—the type-I/type-II transition—and would test whether the cone remains gapless at the critical tilt.
  • A local probe that images constant-frequency contours, rather than a global DOS fit, could independently verify the tilt and would also reveal whether mode-pairing near the Dirac point is the fragile step in the extraction.
  • The uniaxial second-neighbor recipe is symmetry-based, so the same lumped-element circuits should be able to tilt cones in other Bravais lattices, not just honeycomb, whenever a $C_{2v}$-preserving sublattice-diagonal coupling can be wired in.
  • If the paper's 'time dilation' prediction is right, identical LC probe resonators placed in regions of different $\zeta$ should show frequency shifts scaling as $1/\sqrt{1-\zeta^2}$, a measurement within current cryogenic techniques.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper reports the realization of tilted Dirac-like microwave cones in three 731-site superconducting LC-resonator honeycomb lattices. The tilt is engineered by adding uniaxial second-neighbor inductances L′ to the honeycomb lattice, with designed tilt parameters ζ = 2L/L′ of 0, 0.40, and 0.52. The authors measure microwave transmission spectra at 15 mK, detect on the order of 720 of the 731 expected resonances, and fit the measured resonance frequencies to a finite-lattice tight-binding model with two free parameters, the frequency scale ω0 and the tilt parameter ζ. From the fit they report tilt values of 43% and 59% in the relative difference of opposite-direction group velocities, and they display the corresponding model band structures and DOS as evidence of tilted cones. The paper also interprets the tilted cone as an emergent spacetime metric and discusses possible gravity-emulation experiments.

Significance. If the central claim is established, this is a significant experimental advance: a compact lumped-element superconducting circuit architecture that can host hundreds of low-loss microwave modes, with a simple inductance-ratio knob that deterministically controls the tilt of a Dirac-like crossing. The two-parameter fit to roughly 730 spectral lines across three devices is a strength, and the qualitative trend of increasing fitted tilt with decreasing L′ is credible. The quantitative claim, however, is model-inferred rather than directly observed, and the current presentation overstates the agreement with design values. The platform could be of wide interest for circuit-QED lattices and analogue-gravity studies, but the quantitative tilt values need additional robustness evidence.

major comments (3)
  1. [SI Sec. 4C; Fig. S11] The tilt-extraction procedure anchors the mode numbering on the single resonance closest to the theoretical Dirac frequency and pairs every other measured resonance to a finite-lattice eigenmode by index relative to this anchor. The peak detector finds only 720 of 731 modes, and the SI explicitly lists missed modes in the noisy sub-1 GHz range, the crowded ~9 GHz range, and possibly near the Dirac point. If the missed modes are not index-symmetric around the anchor, the index offset accumulates for all subsequent modes and can be partly absorbed by the two free parameters f0 and ζ. The observed offset direction is consistent with this bias: the fitted ζ values of 0.434 and 0.590 exceed the designed values of 0.40 and 0.52 by about 8% and 13%, respectively. I therefore ask for a robustness analysis: repeat the fit under alternative worst-case pairings, for example by shifting the anchor by ±1 mode or by deleting the same number of low- and high-frequency modes as the experiment misses, and report how much the fitted ζ changes; alternatively, demonstrate that the missed-mode distribution is index symmetric around the Dirac point.
  2. [Abstract; Sec. 4; Figs. 3f-k] The headline value of a 59% tilt is a fitted parameter, not a directly measured tilt. The DOS bar plots in Figs. 3c-e are measured, but the band structures in Figs. 3f-k and the cone cross-sections in Figs. 3i-k are the infinite-lattice dispersion evaluated at the fitted f0 and ζ, so those plots do not independently confirm the tilt. The statement in Sec. 4 that the measured tilts match "the theoretical designed values of 59% and 43%" is also inaccurate: the designed ζ values stated in Sec. 3 are 0.40 and 0.52, so the fit overestimates the design by roughly 8% to 13%. The text should clearly distinguish extracted model parameters from directly observed quantities, and the design-versus-fit comparison should be given with consistent notation.
  3. [Sec. 3; SI Sec. 2] The extraction assumes that the fabricated lattice is exactly described by uniform L, C, and L′ and that parasitic couplings and fabrication disorder are negligible. This assumption is load-bearing because the two fitted parameters can absorb disorder-induced spectral shifts into a biased ζ, and a disorder-broadened or disorder-shifted spectrum near the Dirac point could mimic part of the DOS asymmetry attributed to tilt. The authors should provide an independent estimate of the disorder, for example from statistics of individually characterized resonators or from test-structure arrays, and show that the fitted ζ is stable when disorder of this magnitude is included in simulated spectra of the finite lattice.
minor comments (5)
  1. [Author line] The author name "Tobias J. Kippenebrg" appears to be a typo for "Tobias J. Kippenberg."
  2. [SI Sec. 4C] The sentence "for initially designed value of ζ = 2/5.02 ≈ 0.2" is internally inconsistent because 2/5.02 ≈ 0.398; the intended quantity is likely ζ/2 = L/L′ ≈ 0.2. Please correct the notation.
  3. [Sec. 4] The phrase "the theoretical designed values of 59% and 43%" should be corrected to the actual designed values of 52% and 40%; the current phrasing mixes fitted and design values.
  4. [Fig. S11] Fig. S11 reports fitted values of ζ/2 = 0.217 and 0.295, while the main text and Eq. (4) use ζ; the notation should be defined so that readers can compare these values with the designed ζ/2 = L/L′ = 0.20 and 0.26.
  5. [Data availability] The data-availability statement says the data and code "will be available on Zenodo" but gives no DOI or repository identifier; please provide a permanent link or DOI at the time of submission.

Circularity Check

1 steps flagged · score 4.0 of 10

The headline tilt values are least-squares fit outputs; the claim that they 'match' the designed values is made by quoting the fitted values (59%, 43%) as the theoretical designed values, while Eq. (4) and Section 3 give designed values of 52% and 40%.

  1. fitted input called prediction [Section 1 (Introduction), paragraph beginning 'In this paper, we overcome this challenge...']
    "In this work, we achieve a very strong tilting that matches the theoretical designed values of 59% and 43%."

    Section 3 defines the designed tilt from the circuit parameters via Eq. (4) as ζ = 2L/L' = 0, 0.40, 0.52 for L' = ∞, 1.9 nH, 1.4 nH. The SI (Fig. S11) reports the least-squares fitted values ζ/2 = 0.217 and 0.295, i.e. ζ = 0.434 and 0.590 (43.4% and 59.0%). The quoted 'theoretical designed values of 59% and 43%' are therefore not the designed values (40% and 52%) but the fitted values themselves. The claimed agreement between achieved and predicted tilt is manufactured by renaming the least-squares output as the theoretical prediction; with the actual designed values the match is only approximate (43% vs 40%, 59% vs 52%), so the exact 'match' is forced by construction.

full rationale

The experimental method is largely a legitimate parameter extraction: the authors measure the spectra of 731-site lattices, detect about 720 resonances, and fit a finite-lattice tight-binding model (parameters ω0 and ζ) to the measured frequencies (SI Sec. 4C). This tests the model against many independent data points, so the central demonstration of a tilted Dirac-like band structure is not circular in its entirety. The theoretical derivation of ζ = 2L/L' is repeated in the SI, so the self-citation [40] is not load-bearing despite author overlap. The main circularity is the specific claim that the achieved tilt 'matches the theoretical designed values of 59% and 43%': Section 3 and Eq. (4) give designed values ζ = 0.40 and 0.52, whereas 0.434 and 0.590 are the fitted outputs from Fig. S11. Quoting the fitted values as the 'theoretical designed values' makes the agreement exact by construction. This does not invalidate the qualitative observation, but it converts a fitted output into a seemingly predicted value. Separately, the one-to-one mode pairing relative to the Dirac frequency (SI Sec. 4C) is a possible source of bias if missed modes are asymmetrically distributed, but that is a robustness limitation, not a circularity.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central experimental claim rests on two fitted parameters (omega0 and zeta) and on the assumption that the ideal tight-binding model describes the fabricated lattice. No new physical entities are introduced; the spacetime metric is an interpretive mapping of the fitted dispersion.

free parameters (2)
  • omega0 (frequency scale) = f0 ~ 3.867, 3.843, 3.815 GHz for the three devices
    Overall resonance frequency scale, fitted by least squares to the measured spectrum in SI Sec. 4C; designed value was 2.91 GHz, but fitted values are consistently higher.
  • zeta (tilt parameter) = 0, 0.434 +/- 0.004, 0.590 +/- 0.004
    Tilt parameter of the tight-binding model, fitted to the full measured spectrum (SI Sec. 4C); the headline 'tilt value' is this fitted parameter.
assumptions (3)
  • domain assumption The fabricated device is exactly described by the uniform tight-binding model with constant on-site frequency, constant first-neighbor inductance L, and constant uniaxial second-neighbor inductance L', with no disorder or parasitic couplings beyond the designed layout.
    Invoked throughout the fitting in SI Sec. 4C; if disorder or parasitics are non-negligible, the extracted tilt would absorb them.
  • domain assumption The measured resonances can be unambiguously ordered and paired with model eigenmodes by counting mode number relative to the Dirac frequency, which is identified from the model with initial parameter guesses.
    Assumed in SI Sec. 4C; missed or spurious resonances could shift the pairing and bias the fit.
  • domain assumption A 731-site finite lattice with open boundaries is large enough that the mode density and the low-energy dispersion near the Dirac points are representative of the infinite-lattice band structure used to define the tilt.
    Supported by Fig. S3, but the tilt value is still assigned through the infinite-lattice parameter zeta; finite-size corrections are not included in the reported tilt.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Realization of tilted Dirac-like microwave cone in superconducting circuit lattices." pith.science (2026). https://pith.science/paper/VOFIXBDJ

@misc{pith2026250110434,
  author       = {Pith},
  title        = {Pith review of: Realization of tilted Dirac-like microwave cone in superconducting circuit lattices},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VOFIXBDJ}},
  note         = {Machine review of arXiv:2501.10434}
}
read the original abstract

Dirac-like band crossings are paradigms in condensed matter systems to emulate high-energy physics phenomena. They are associated with two aspects: gap and tilting. The ability to design sign-changing gap gives rise to band topology, whereas the tilting of band crossings which is a gateway for large gravity-like effects remains uncharted. In this work, we introduce an experimental platform to realize tilted Dirac-like microwave cone in large-scale superconducting circuit lattices. The direction and magnitude of the tilt can be controlled by engineering the axially preferred second neighbor coupling. We demonstrate three lattices with 731-site LC resonator featuring tilt values of up to 59% of relative difference in the opposite-direction group velocities. This is obtained by reconstructing the density of states (DOS) of measured microwave resonance frequencies. Harnessing the tilt of Dirac-like band crossings lays the foundation for weaving the fabric of an emergent solid-state spacetime.

Figures

Figures reproduced from arXiv: 2501.10434 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Emergent cavity-QED dynamics along the edge of a photonic lattice

    quant-ph 2025-07 accept novelty 7.0 of 10

    Emitters on a zigzag photonic-graphene edge realize a dissipative Jaynes-Cummings model whose emergent cavity mode localizes with a power law rather than exponentially.

Reference graph

Works this paper leans on

92 extracted references · 78 canonical work pages · cited by 1 Pith paper

  1. [40]

    Ma˜nes, Fernando de Juan, Mauricio Sturla, and Mar ´ ıa A

    Juan L. Ma˜nes, Fernando de Juan, Mauricio Sturla, and Mar ´ ıa A. H. Vozmediano. Generalized effective hamilto- nian for graphene under nonuniform strain. Physical Re- view B, 88(15), October 2013

    work page 2013

  2. [1]

    Introduction Propagation of photons in flat spacetime is character- ized by the light cones [44] that are associated with the energy-momentum or dispersion relation ε(p) = c|p| [26] where c is the speed of light. According to Einstein’s general relativity, in the presence of a gravity source, the light cones are tilted towards it [47], implying that the p...

    arXiv 2025

  3. [2]

    q2 j 2C + ϕ2 j 2Lr # − X j

    Theory First we discuss how to synthetically incorporate tilt- ing to the Dirac-like band crossing within our tight- binding model. The basic picture consists of adding anisotropic second neighbor hopping on a honeycomb lattice which can be conveniently realized by adding a second neighbor coupling only in one preferred direction denoted by red lines in t...

  4. [3]

    (3), we introduce a novel superconducting circuit lattice architecture based on the lumped element parallel- plate capacitors and planar meander inductors

    Fabrication of superconducting circuit lattice In order to experimentally implement the circuit model in Eq. (3), we introduce a novel superconducting circuit lattice architecture based on the lumped element parallel- plate capacitors and planar meander inductors. Figure 2a shows the circuit diagram of the lattice, where each node on the honeycomb structu...

  5. [4]

    Experimental Results In order to extract the spectrum of the device, we mea- sure the microwave transmission scattering parameter S21 through its two coupling ports. Figure 3a schemat- ically shows the measurement chain consisting of a mi- 5 0 2 4 6 8 0 0.1 0.2 0.3 0.4 0.5 0.6 0 2 4 6 8 0 0.1 0.2 0.3 0.4 0.5 0.6 0 2 4 6 8 0 0.1 0.2 0.3 0.4 0.5 0.6 1 2 3 4...

  6. [5]

    Harnessing the tilting of a microwave band structure is tantamount to engineering the fabric of the ensuing emergent space- time geometry

    Conclusion and outlook In this work, we introduced a novel experimental plat- form to demonstrate deterministic tilting of a Dirac-like microwave band crossing by desired amount. Harnessing the tilting of a microwave band structure is tantamount to engineering the fabric of the ensuing emergent space- time geometry. Spatial/temporal manipulation of circui...

  7. [6]

    Quantum simulators: Architectures and oppor- tunities

    Ehud Altman, Kenneth R Brown, Giuseppe Carleo, Lin- coln D Carr, Eugene Demler, Cheng Chin, Brian De- Marco, Sophia E Economou, Mark A Eriksson, Kai-Mei C Fu, et al. Quantum simulators: Architectures and oppor- tunities. PRX Quantum, 2(1):017003, 2021

    2021

  8. [7]

    Dresselhaus, editors

    Hideo Aoki and Mildred S. Dresselhaus, editors. Physics of Graphene. Springer International Publishing, 2014

    2014

Show all 92 references
  1. [8]

    N. P. Armitage, E. J. Mele, and Ashvin Vishwanath. Weyl and Dirac semimetals in three-dimensional solids. Reviews of Modern Physics, 90(1), January 2018

    2018

  2. [9]

    How to avoid the appearance of a classical world in gravity experiments, 2022

    Markus Aspelmeyer. How to avoid the appearance of a classical world in gravity experiments, 2022

    2022

  3. [10]

    Gravity mediated entanglement between oscillators as quantum superposition of geome- tries, 2023

    Ofek Bengyat, Andrea Di Biagio, Markus Aspelmeyer, and Marios Christodoulou. Gravity mediated entanglement between oscillators as quantum superposition of geome- tries, 2023

    2023

  4. [11]

    B. A. Bernevig and T. L. Hughes. Topological Insula- tors and Topological Superconductors. Princeton Univer- sity Press, 2013

    2013

  5. [12]

    N. D. Birrell and P. C. W. Davies. Quantum Fields in Curved Space. Cambridge University Press, February 1982

    1982

  6. [13]

    Quasiparticle dynamics in graphene

    Aaron Bostwick, Taisuke Ohta, Thomas Seyller, Karsten Horn, and Eli Rotenberg. Quasiparticle dynamics in graphene. Nature Physics, 3(1):36–40, December 2006

    2006

  7. [14]

    Sean M. Carroll. Spacetime and Geometry: An Introduc- tion to General Relativity. Cambridge University Press, Jul 2019

    2019

  8. [15]

    Photonic materials in circuit quantum electrodynamics

    Iacopo Carusotto, Andrew A Houck, Alicia J Koll´ ar, Pe- dram Roushan, David I Schuster, and Jonathan Simon. Photonic materials in circuit quantum electrodynamics. Nature Physics, 16(3):268–279, 2020

    2020

  9. [16]

    Locally mediated entanglement in linearized quan- tum gravity

    Marios Christodoulou, Andrea Di Biagio, Markus As- pelmeyer, ˇCaslav Brukner, Carlo Rovelli, and Richard Howl. Locally mediated entanglement in linearized quan- tum gravity. Physical Review Letters, 130(10), March 2023

    2023

  10. [17]

    Cooling of a levitated nanoparticle to the mo- tional quantum ground state

    Uroˇ s Deli´ c, Manuel Reisenbauer, Kahan Dare, David Grass, Vladan Vuleti´ c, Nikolai Kiesel, and Markus As- pelmeyer. Cooling of a levitated nanoparticle to the mo- tional quantum ground state. Science, 367(6480):892–895, February 2020

    2020

  11. [18]

    Farajollahpour, Z

    T. Farajollahpour, Z. Faraei, and S. A. Jafari. Solid- state platform for space-time engineering: The 8pmmn borophene sheet. Physical Review B, 99(23), June 2019

    2019

  12. [19]

    Farajollahpour and S

    T. Farajollahpour and S. A. Jafari. Synthetic non-abelian gauge fields and gravitomagnetic effects in tilted Dirac cone systems. Physical Review Research, 2(2), June 2020

    2020

  13. [20]

    Quantum phase transitions and vortex dynamics in superconducting net- works

    Rosario Fazio and Herre Van Der Zant. Quantum phase transitions and vortex dynamics in superconducting net- works. Physics Reports, 355(4):235–334, 2001

    2001

  14. [21]

    F. G. Friedlander. The Wave Equation on a Curved Space-time. Cambridge University Press, 1975

    1975

  15. [22]

    S. M. Girvin. Circuit QED: superconducting qubits cou- pled to microwave photons, page 113–256. Oxford Univer- sity Press, Oxford, June 2014

    2014

  16. [23]

    M. O. Goerbig, J.-N. Fuchs, G. Montambaux, and F. Pi´ echon. Tilted anisotropic Dirac cones in quinoid- type graphene and α−(BEDT-TTF)2i3. Phys. Rev. B, 78:045415, Jul 2008

    2008

  17. [24]

    Escape from black hole analogs in materials: Type-II weyl semimet- als and generic edge states

    Koji Hashimoto and Yoshinori Matsuo. Escape from black hole analogs in materials: Type-II weyl semimet- als and generic edge states. Physical Review B, 102(19), November 2020

    2020

  18. [25]

    Abolfath Hosseinzadeh and S.A. Jafari. Semiclassical transport in two-dimensional Dirac materials with spa- tially variable tilt. Annals of Physics, 471:169838, De- cember 2024

    2024

  19. [26]

    Black- hole horizon in the Dirac semimetal Zn 2In2S5

    Huaqing Huang, Kyung-Hwan Jin, and Feng Liu. Black- hole horizon in the Dirac semimetal Zn 2In2S5. Physical Review B, 98(12), September 2018

    2018

  20. [27]

    SK Firoz Islam and A. M. Jayannavar. Signature of tilted Dirac cones in weiss oscillations of 8pmmn borophene. Physical Review B, 96(23), December 2017

    2017

  21. [28]

    S. A. Jafari. Electric field assisted amplification of mag- netic fields in tilted Dirac cone systems. Physical Review B, 100(4), July 2019

    2019

  22. [29]

    S. A. Jafari. Moving frame theory of zero-bias photocur- 8 rent on the surface of topological insulators. Physical Re- view Research, 6(3), July 2024

    2024

  23. [30]

    Jalali-Mola and S

    Z. Jalali-Mola and S. A. Jafari. Polarization tensor for tilted Dirac fermion materials: Covariance in deformed Minkowski spacetime. Physical Review B, 100(7), August 2019

    2019

  24. [31]

    Photonic Crystals: Molding The Flow Of Light

    John D Joannopoulos, Steven G Johnson, Joshua N Winn, and Robert D Meade. Photonic Crystals: Molding The Flow Of Light. Princeton University Press, 2 edition, 2008

    2008

  25. [32]

    Molecular Dirac fermion systems — theoretical and experimental approaches —

    Koji Kajita, Yutaka Nishio, Naoya Tajima, Yoshikazu Suzumura, and Akito Kobayashi. Molecular Dirac fermion systems — theoretical and experimental approaches —. Journal of the Physical Society of Japan, 83(7):072002, July 2014

    2014

  26. [33]

    Katsnelson

    Mikhail I. Katsnelson. The Physics of Graphene. Cam- bridge University Press, March 2020

    2020

  27. [34]

    Quantum electrodynamics in a topological waveguide

    Eunjong Kim, Xueyue Zhang, Vinicius S Ferreira, Jash Banker, Joseph K Iverson, Alp Sipahigil, Miguel Bello, Alejandro Gonz´ alez-Tudela, Mohammad Mirhosseini, and Oskar Painter. Quantum electrodynamics in a topological waveguide. Physical Review X, 11(1):011015, 2021

    2021

  28. [35]

    Hyperbolic lattices in circuit quantum electrody- namics

    Alicia J Koll´ ar, Mattias Fitzpatrick, and Andrew A Houck. Hyperbolic lattices in circuit quantum electrody- namics. Nature, 571(7763):45–50, 2019

    2019

  29. [36]

    Magnetotransport of weyl semimetals with tilted Dirac cones

    Anirban Kundu, Zhuo Bin Siu, Hyunsoo Yang, and Man- soor B A Jalil. Magnetotransport of weyl semimetals with tilted Dirac cones. New Journal of Physics, 22(8):083081, August 2020

    2020

  30. [37]

    Littlewood

    Alejandro Lopez-Bezanilla and Peter B. Littlewood. Electronic properties of 8pmmn borophene. Physical Re- view B, 93(24), June 2016

    2016

  31. [38]

    Cuamba, Shih-Yang Lin, Lei Hao, Rui Wang, Hai Li, YuanYuan Zhao, and C

    Hong-Yan Lu, Armindo S. Cuamba, Shih-Yang Lin, Lei Hao, Rui Wang, Hai Li, YuanYuan Zhao, and C. S. Ting. Tilted anisotropic Dirac cones in partially hydrogenated graphene. Physical Review B, 94(19), November 2016

    2016

  32. [39]

    Regular coordinate sys- tems for schwarzschild and other spherical spacetimes

    Karl Martel and Eric Poisson. Regular coordinate sys- tems for schwarzschild and other spherical spacetimes. American Journal of Physics, 69(4):476–480, April 2001

    2001

  33. [41]

    Dirac-cone-like surface state in w(110): dispersion, spin texture and pho- toemission from first principles

    H Mirhosseini, M Flieger, and J Henk. Dirac-cone-like surface state in w(110): dispersion, spin texture and pho- toemission from first principles. New Journal of Physics, 15(3):033019, March 2013

    2013

  34. [42]

    Miyamoto, A

    K. Miyamoto, A. Kimura, K. Kuroda, T. Okuda, K. Shi- mada, H. Namatame, M. Taniguchi, and M. Donath. Spin- polarized Dirac-cone-like surface state with d character at w(110). Physical Review Letters, 108(6), February 2012

    2012

  35. [43]

    Moradpouri, S

    A. Moradpouri, S. A. Jafari, and Mahdi Torabian. Holo- graphic hydrodynamics of tilted Dirac materials. Journal of High Energy Physics, 2023(8), August 2023

    2023

  36. [44]

    Electron currents from gradual heating in tilted Dirac cone materials

    Ahmadreza Moradpouri, Mahdi Torabian, and Seyed Ak- bar Jafari. Electron currents from gradual heating in tilted Dirac cone materials. SciPost Physics Core, 6(1), Mar 2023

    2023

  37. [45]

    Ahmad Motavassal and S. A. Jafari. Circuit realization of a tilted Dirac cone: Platform for fabrication of curved spacetime geometry on a chip. Phys. Rev. B, 104:L241108, Dec 2021

    2021

  38. [46]

    Ogawa, R

    N. Ogawa, R. Yoshimi, K. Yasuda, A. Tsukazaki, M. Kawasaki, and Y. Tokura. Zero-bias photocurrent in ferromagnetic topological insulator. Nature Communica- tions, 7(1), July 2016

    2016

  39. [47]

    Microwave dielectric loss at single photon energies and millikelvin temperatures

    Aaron D O’Connell, M Ansmann, Radoslaw C Bialczak, Max Hofheinz, Nadav Katz, Erik Lucero, C McKenney, Matthew Neeley, Haohua Wang, Eva Maria Weig, et al. Microwave dielectric loss at single photon energies and millikelvin temperatures. Applied Physics Letters, 92(11), 2008

    2008

  40. [48]

    R. V. Pound and G. A. Rebka. Apparent weight of pho- tons. Physical Review Letters, 4(7):337–341, Apr 1960

    1960

  41. [49]

    Relativity: Special, General, and Cos- mological

    Wolfgang Rindler. Relativity: Special, General, and Cos- mological. Oxford University Press, 2 edition, 2006

    2006

  42. [50]

    Saber Rostamzadeh, Sevval Tasdemir, Mustafa Sarisaman, S. A. Jafari, and Mark-Oliver Goerbig. Tilt-induced vortical response and mixed anomaly in inhomogeneous weyl matter. Physical Review B, 107(7), February 2023

    2023

  43. [51]

    Study of gravita- tional deflection of light ray

    Saswati Roy and Asoke Kumar Sen. Study of gravita- tional deflection of light ray. Journal of Physics: Confer- ence Series, 1330(1):012002, October 2019

    2019

  44. [52]

    Introduction to General Relativity

    Lewis Ryder. Introduction to General Relativity. Cam- bridge University Press, jun 2009

    2009

  45. [53]

    Circuit qed lattices: Towards quantum simulation with superconducting cir- cuits

    Sebastian Schmidt and Jens Koch. Circuit qed lattices: Towards quantum simulation with superconducting cir- cuits. Annalen der Physik, 525(6):395–412, 2013

    2013

  46. [54]

    Controlling atom-photon bound states in an array of josephson-junction resonators

    Marco Scigliuzzo, Giuseppe Calaj` o, Francesco Ciccarello, Daniel Perez Lozano, Andreas Bengtsson, Pasquale Scar- lino, Andreas Wallraff, Darrick Chang, Per Delsing, and Simone Gasparinetti. Controlling atom-photon bound states in an array of josephson-junction resonators. Phy...

    2022

  47. [55]

    Anomalous heat flow in 8pmmn borophene with tilted Dirac cones

    Parijat Sengupta, Yaohua Tan, Enrico Bellotti, and Junxia Shi. Anomalous heat flow in 8pmmn borophene with tilted Dirac cones. Journal of Physics: Condensed Matter, 30(43):435701, October 2018

    2018

  48. [56]

    Waveguide quantum electrodynamics: collective radiance and photon-photon correlations

    Alexandra S Sheremet, Mihail I Petrov, Ivan V Iorsh, Alexander V Poshakinskiy, and Alexander N Poddubny. Waveguide quantum electrodynamics: collective radiance and photon-photon correlations. Reviews of Modern Physics, 95(1):015002, 2023

    2023

  49. [57]

    Reflectance of Dirac electrons in organic conductor

    Yoshikazu Suzumura, Igor Proskurin, and Masao Ogata. Reflectance of Dirac electrons in organic conductor. Jour- nal of Physics: Conference Series, 603:012011, April 2015

    2015

  50. [58]

    L. L. Tao and Evgeny Y. Tsymbal. Two-dimensional type-II Dirac fermions in a LaAlO 3/LaNiO3/LaAlO3 quantum well. Physical Review B, 98(12), September 2018

    2018

  51. [59]

    Brouwer, and Emil J

    Maximilian Trescher, Bj¨ orn Sbierski, Piet W. Brouwer, and Emil J. Bergholtz. Quantum transport in Dirac mate- rials: Signatures of tilted and anisotropic Dirac and Weyl cones. Physical Review B, 91(11), March 2015

    2015

  52. [60]

    Low-disorder microwave cavity lattices for quantum simulation with photons

    Devin L Underwood, Will E Shanks, Jens Koch, and An- drew A Houck. Low-disorder microwave cavity lattices for quantum simulation with photons. Physical Review A, 86(2):023837, 2012

    2012

  53. [61]

    Imaging pho- ton lattice states by scanning defect microscopy

    DL Underwood, WE Shanks, Andy CY Li, Lamia Ateshian, Jens Koch, and Andrew A Houck. Imaging pho- ton lattice states by scanning defect microscopy. Physical Review X, 6(2):021044, 2016

    2016

  54. [62]

    Varykhalov, D

    A. Varykhalov, D. Marchenko, J. S´ anchez-Barriga, E. Golias, O. Rader, and G. Bihlmayer. Tilted Dirac cone on W(110) protected by mirror symmetry. Physical Re- view B, 95(24), June 2017

    2017

  55. [63]

    G. E. Volovik. Black hole and hawking radiation by type- II weyl fermions. JETP Letters, 104(9):645–648, Novem- 9 ber 2016

    2016

  56. [64]

    G. E. Volovik. Type-II weyl semimetal versus gravastar. JETP Letters, 114(4):236–242, August 2021

    2021

  57. [65]

    G. E. Volovik and K. Zhang. Lifshitz transitions, type-II Dirac and Weyl fermions, event horizon and all that.Jour- nal of Low Temperature Physics, 189(5-6):276–299, Octo- ber 2017

    2017

  58. [66]

    Andrew Wild, Eros Mariani, and Mikhail E. Portnoi. Op- tical absorption in two-dimensional materials with tilted Dirac cones. Physical Review B, 105(20), May 2022

    2022

  59. [67]

    Topological materials: Weyl semimetals

    Binghai Yan and Claudia Felser. Topological materials: Weyl semimetals. Annual Review of Condensed Matter Physics, 8(1):337–354, mar 2017

    2017

  60. [68]

    Baskaran

    Jiayue Yang, Niayesh Afshordi, Mahdi Torabian, Seyed Akbar Jafari, and G. Baskaran. Smart holes: Ana- logue black holes with the right temperature and entropy, 2024

    2024

  61. [69]

    Effects of Dirac cone tilt in a two-dimensional Dirac semimetal

    Zhao-Kun Yang, Jing-Rong Wang, and Guo-Zhu Liu. Effects of Dirac cone tilt in a two-dimensional Dirac semimetal. Physical Review B, 98(19), November 2018

    2018

  62. [70]

    Tunning the tilt of the Dirac cone by atomic manipu- lations in 8pmmn borophene

    Yasin Yekta, Hanif Hadipour, and Seyed Akbar Jafari. Tunning the tilt of the Dirac cone by atomic manipu- lations in 8pmmn borophene. Communications Physics, 6(1), March 2023

    2023

  63. [71]

    Topological lattices realized in superconducting circuit optomechanics

    Amir Youssefi, Shingo Kono, Andrea Bancora, Mahdi Chegnizadeh, Jiahe Pan, Tatiana Vovk, and Tobias J Kip- penberg. Topological lattices realized in superconducting circuit optomechanics. Nature, 612(7941):666–672, 2022

    2022

  64. [72]

    Oganov, Qiang Zhu, Yongjun Tian, and Hui-Tian Wang

    Xiang-Feng Zhou, Xiao Dong, Artem R. Oganov, Qiang Zhu, Yongjun Tian, and Hui-Tian Wang. Semimetal- lic two-dimensional boron allotrope with massless Dirac fermions. Physical Review Letters, 112(8), February 2014

    2014

  65. [73]

    Analogies between the black hole inte- rior and the type II weyl semimetals

    Mikhail Zubkov. Analogies between the black hole inte- rior and the type II weyl semimetals. Universe, 4(12):135, November 2018. Supplementary Information for: Realization of tilted Dirac-like microwave cone in superconducting circuit lattices Contents

    2018

  66. [74]

    Fabrication of superconducting circuit lattice 4

  67. [75]

    Experimental Results 4

  68. [76]

    Conclusion and outlook 6 References 7

  69. [77]

    From dispersion relation to spacetime metric 10

  70. [78]

    Fourier analysis for infinite lattice 12 B

    Theory of tilted microwave cone in circuit resonator graphs 11 A. Fourier analysis for infinite lattice 12 B. Coupling finite lattice to input and output ports 14

  71. [79]

    Designing the value of lattice capacitor and inductance values 15 B

    Design and simulation 15 A. Designing the value of lattice capacitor and inductance values 15 B. Finite lattice mode shapes 15 C. Coupling Capacitor Optimum Value 16

  72. [80]

    Peak Detection Algorithm 17 B

    Data processing 17 A. Peak Detection Algorithm 17 B. Determination of the bandwidth of resonances 18 C. Fitting the Model to Detected Peaks 21

  73. [81]

    Supplementary References 25 References 25 10 In this supplement, in addition to providing pedagogical introduction to the concepts from special/general relativity that can be followed with basic solid-state physics background, we offer details of the computations to enable a s...

  74. [82]

    It is important to make a connection between the dispersion relation of excitations and the geometry of the spacetime

    From dispersion relation to spacetime metric In this paper we draw implications for the structure of underlying ”spacetime” by looking into the dispersion relation that gives energy of excitations as a function of their wave-vector k. It is important to make a connection betwe...

  75. [83]

    Theory of tilted microwave cone in circuit resonator graphs The structure of the circuit lattice is shown in Fig. S1. Left and right parts indicate top and side view. Each node or site is connected to its first three neighbors via the base inductance L and to the common ground...

  76. [84]

    Designing the value of lattice capacitor and inductance values B

    Design and simulation A. Designing the value of lattice capacitor and inductance values B. Finite lattice mode shapes To approach the frequency spectrum of a very large (effectively infinite) network and examine any distortions within it, we need to increase the network size. ...

  77. [85]

    Peak Detection Algorithm In this section, we explain how to find resonances from the measured data of scattering matrix S21

    Data processing A. Peak Detection Algorithm In this section, we explain how to find resonances from the measured data of scattering matrix S21. Normally, at each resonance, the magnitude ( |S21|) and phase gradient (PhG) of S21 indicates a peak. Generally, we can look at PhG a...

  78. [86]

    Supplementary References

  79. [87]

    Fano resonances in photonics

    Mikhail F Limonov, Mikhail V Rybin, Alexander N Poddubny, and Yuri S Kivshar. Fano resonances in photonics. Nature Photonics, 11(9):543–554, September 2017

    2017

  80. [88]

    Zheludev, Stefan A

    Boris Luk’yanchuk, Nikolay I. Zheludev, Stefan A. Maier, Naomi J. Halas, Peter Nordlander, Harald Giessen, and Chong Tow Chong. The fano resonance in plasmonic nanostructures and metamaterials. Nature Materials, 9(9):707–715, Sep 2010

    2010

  81. [89]

    Ahmad Motavassal and S. A. Jafari. Circuit realization of a tilted dirac cone: Platform for fabrication of curved spacetime geometry on a chip. Phys. Rev. B, 104:L241108, Dec 2021

    2021

  82. [90]

    D.M. Pozar. Microwave Engineering. Wiley, 2011

    2011

  83. [91]

    Introduction to General Relativity

    Lewis Ryder. Introduction to General Relativity. Cambridge University Press, jun 2009

    2009

  84. [92]

    Savitzky and M

    Abraham. Savitzky and M. J. E. Golay. Smoothing and differentiation of data by simplified least squares procedures. Analytical Chemistry, 36(8):1627–1639, 1964

    1964

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.