Pith. sign in

REVIEW 60 references

Non-Fermi Liquids from Subsystem Symmetry Breaking in van der Waals Multilayers

T0 review · 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 Interlayer exciton condensation in multilayer van der Waals metals is predicted to create a three-dimensional marginal Fermi liquid with specific heat C ~ T(log(1/T))^2.

arxiv 2411.08091 v2 pith:I7RCHO6B submitted 2024-11-12 cond-mat.str-el cond-mat.mes-hall

Archisman Panigrahi , Ajesh Kumar This is my paper · ORCID
classification cond-mat.str-elcond-mat.mes-hall
keywords subsystemsymmetrybreakingfermifluctuationslayersliquidnumber
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

Metals are usually described by Landau's Fermi liquid theory, where low-energy electrons behave like long-lived quasiparticles. Some strongly interacting metals, called non-Fermi liquids, violate this picture. This paper proposes a new way to make a non-Fermi liquid using stacks of two-dimensional metallic layers, such as those found in van der Waals heterostructures.

In each layer, electron number is conserved separately since interlayer tunneling is strongly suppressed. When electrons in adjacent layers form excitons and condense, the relative electron number between layers is no longer conserved. This spontaneous symmetry breaking produces Goldstone modes, collective phase oscillations of the condensate. The authors show these modes couple to electrons with a strength that does not vanish at low momentum transfer, unlike the usual coupling of Goldstone modes to current. This strong coupling shortens the quasiparticle lifetime, turning the system into a marginal Fermi liquid when many layers are stacked.

Using a microscopic model with gallium arsenide parameters, they solve mean-field equations to find the exciton condensate. They then include fluctuations at the random phase approximation level and compute the electron self-energy and free energy. The result is a quasiparticle lifetime scaling as 1/(E log(1/E)) and a specific heat C ~ T(log(1/T))^2, the latter being a signature of the flat dispersion of the Goldstone mode along the stacking direction.

Extended reading notes

Core claim

The central claim is that a stack of two-dimensional Fermi liquid metals with interlayer exciton condensation and spontaneously broken subsystem number conservation forms a three-dimensional anisotropic marginal Fermi liquid. Concretely, the quasiparticle lifetime scales as tau(omega) ~ 1/(|omega| log(1/|omega|)) (Eq. 13), and the specific heat is C ~ T(log(1/T))^2 (Eq. 26). The abstract states: 'This coupling, which remains non-zero for small momentum transfers, leads to the emergence of a three-dimensional anisotropic marginal Fermi liquid state when the number of layers is sufficiently large.'

Load-bearing premise

The prediction depends on interlayer tunneling being negligible, so that each layer's particle number conservation is nearly exact. If tunneling is not exponentially small, the Goldstone modes acquire a gap m_e ~ t_e/c^2 (Appendix D), and the non-Fermi liquid behavior is confined to energies above that gap; below it the system returns to a Fermi liquid. The paper itself states that the discussion 'neglected interlayer tunneling, which explicitly breaks the subsystem symmetry' and that it 'can can be strongly suppressed in experiments'. The experimental realizability of the scenario rests on this suppression.

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.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the existence of an exact or exponentially suppressed subsystem symmetry, the flat Goldstone dispersion, and the mean-field/RPA approximations. The free parameters rho_s and c affect prefactors but not the predicted scaling forms. No new particles or entities are introduced.

free parameters (3)
  • rho_s
    Stiffness of the Goldstone mode action (Eq. 9). Not computed from the microscopic model; an input parameter in the low-energy theory.
  • c
    Velocity of the Goldstone mode (Eq. 9). Input parameter, not derived from the microscopic Hamiltonian.
  • UV cutoff Lambda
    Momentum cutoff in self-energy, free energy, and transport integrals (Eqs. 13, 26). Regulates logarithmic divergences; log(Lambda) pieces do not affect the specific heat scaling.
assumptions (6)
  • domain assumption Each layer has a conserved particle number (subsystem U(1) symmetry) and interlayer tunneling is negligible.
    Core premise stated in the introduction and used throughout. If tunneling is significant, the subsystem symmetry is explicitly broken and the NFL window closes below a scale set by the tunneling amplitude (Appendix D).
  • domain assumption The Goldstone mode action contains no z-derivative terms; the phase field has a flat dispersion along the stacking direction.
    Argued from subsystem symmetry after Eq. (9). This flat dispersion is responsible for the extra log in the specific heat. Assumes no higher-order allowed terms contribute at low energy.
  • domain assumption The mean-field approximation with only interlayer exciton order is valid; intralayer interactions, Hartree terms, and screening are neglected.
    Stated in the mean-field section. Neglect of screening is acknowledged in the Discussion as potentially suppressing Tc.
  • domain assumption The random phase approximation captures the dominant fluctuations.
    Used for the boson self-energy and free energy (Eqs. 12-14). The paper does not assess corrections beyond RPA.
  • ad hoc to paper A spherical Fermi surface is assumed for the low-energy scaling calculations.
    Stated before Section A: 'we will assume a spherical Fermi surface, and disregard the theta-dependence'. The actual band structure is warped cylindrical; this simplification may affect the anisotropy of the self-energy.
  • domain assumption Vortices in the phase field are neglected; the system is clean.
    Explicitly stated: 'we exclude the effect of vortices in phi which, in the presence of strong disorder, could become pinned and disrupt interlayer coherence'.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Non-Fermi Liquids from Subsystem Symmetry Breaking in van der Waals Multilayers." pith.science (2026). https://pith.science/paper/I7RCHO6B

@misc{pith2026241108091,
  author       = {Pith},
  title        = {Pith review of: Non-Fermi Liquids from Subsystem Symmetry Breaking in van der Waals Multilayers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I7RCHO6B}},
  note         = {Machine review of arXiv:2411.08091}
}
abstract

We investigate the spontaneous breaking of subsystem symmetry in a stack of two-dimensional Fermi liquid metals, each maintaining a subsystem number conservation symmetry, driven by interlayer exciton condensation. The resulting Goldstone modes in this broken symmetry phase couple to the quasiparticle current perpendicular to the layers. This coupling, which remains non-zero for small momentum transfers, leads to the emergence of a three-dimensional anisotropic marginal Fermi liquid state when the number of layers is sufficiently large. We propose a possible experimental realization of this phenomenon in two-dimensional multilayer van der Waals heterostructures. Using self-consistent mean-field calculations, we characterize the subsystem symmetry-broken metallic state and examine the effects of fluctuations on its physical properties within the random phase approximation. We find that these fluctuations produce additional logarithmic enhancements to the specific heat at low temperature, specifically $C\sim T (\log(1/T))^2$.

Figures

Figures reproduced from arXiv: 2411.08091 by the authors.

Figure 1
Figure 1. (a) Stack of two-dimensional Fermi liquid metals [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. (a) Dependence of the maximum value of |∆| (over all momenta), as a function of electron density at a fixed temperature (T = 0.05 meV/kB ≈ 0.58 K) for a system of 10 layers, with inter-layer distance az = 3 nm. (b) Dependence of the maximum value of |∆| as a function of temperature, at a fixed density, n = 55 × 1010/cm2 . For both the plots, we set m∗ = 0.07me and ϵr = 12.5. presence of such charge density wave orde… view at source ↗
Figure 3
Figure 3. Feynman diagrams at the level of RPA for (a) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: (a)We have to average the Boson self-energy contribution due to each Fermi surface patch (red patch) to obtain Π [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

60 extracted references · 45 canonical work pages

  1. [1]

    H. v. L¨ ohneysen, A. Rosch, M. Vojta, and P. W¨ olfle, Fermi-liquid instabilities at magnetic quantum phase transitions, Rev. Mod. Phys.79, 1015 (2007)

    2007

  2. [2]

    Lee, Recent Developments in Non-Fermi Liquid Theory, Annual Review of Condensed Matter Physics9, 227 (2018)

    S.-S. Lee, Recent Developments in Non-Fermi Liquid Theory, Annual Review of Condensed Matter Physics9, 227 (2018)

    work page 2018

  3. [3]

    A. V. Chubukov, A. Abanov, Y. Wang, and Y.-M. Wu, The interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal, Annals of Physics417, 168142 (2020)

    work page 2020

  4. [4]

    Nayak and F

    C. Nayak and F. Wilczek, Non-Fermi liquid fixed point in 2 + 1 dimensions, Nuclear Physics B417, 359 (1994)

    work page 1994

  5. [5]

    Lee, Low-energy effective theory of Fermi surface coupled with U(1) gauge field in 2 + 1 dimensions, Phys

    S.-S. Lee, Low-energy effective theory of Fermi surface coupled with U(1) gauge field in 2 + 1 dimensions, Phys. Rev. B80, 165102 (2009)

    work page 2009

  6. [6]

    M. A. Metlitski and S. Sachdev, Quantum phase transi- tions of metals in two spatial dimensions. I. Ising-nematic order, Phys. Rev. B82, 075127 (2010)

    work page 2010

  7. [7]

    M. A. Metlitski and S. Sachdev, Quantum phase transi- tions of metals in two spatial dimensions. II. Spin density wave order, Phys. Rev. B82, 075128 (2010)

    2010

  8. [8]

    Mandal and S.-S

    I. Mandal and S.-S. Lee, Ultraviolet/infrared mixing in non-Fermi liquids, Phys. Rev. B92, 035141 (2015)

    work page 2015

Show all 60 references
  1. [9]

    Holder and W

    T. Holder and W. Metzner, Anomalous dynamical scaling from nematic and U(1) gauge field fluctuations in two- dimensional metals, Phys. Rev. B92, 041112 (2015)

    2015

  2. [10]

    P. A. Lee, N. Nagaosa, and X.-G. Wen, Doping a Mott in- sulator: Physics of high-temperature superconductivity, Rev. Mod. Phys.78, 17 (2006)

    2006

  3. [11]

    Paschen and Q

    S. Paschen and Q. Si, Quantum phases driven by strong correlations, Nature Reviews Physics3, 9–26 (2021)

    2021

  4. [12]

    Taillefer, Scattering and Pairing in Cuprate Supercon- ductors, Annual Review of Condensed Matter Physics1, 51 (2010)

    L. Taillefer, Scattering and Pairing in Cuprate Supercon- ductors, Annual Review of Condensed Matter Physics1, 51 (2010)

    2010

  5. [13]

    E. Y. Andrei, D. K. Efetov, P. Jarillo-Herrero, A. H. MacDonald, K. F. Mak, T. Senthil, E. Tutuc, A. Yazdani, and A. F. Young, The marvels of moir´ e materials, Nature Reviews Materials6, 201–206 (2021)

    2021

  6. [14]

    K. P. Nuckolls and A. Yazdani, A microscopic perspective on moir´ e materials, Nature Reviews Materials9, 460–480 (2024)

    2024

  7. [15]

    K. F. Mak and J. Shan, Semiconductor moir´ e materials, Nature Nanotechnology17, 686–695 (2022)

    2022

  8. [16]

    Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional super- conductivity in magic-angle graphene superlattices, Na- ture556, 43–50 (2018)

    2018

  9. [17]

    H. Zhou, T. Xie, T. Taniguchi, K. Watanabe, and A. F. Young, Superconductivity in rhombohedral trilayer graphene, Nature598, 434–438 (2021)

    2021

  10. [18]

    D. M. Kennes, M. Claassen, L. Xian, A. Georges, A. J. Millis, J. Hone, C. R. Dean, D. N. Basov, A. N. Pa- supathy, and A. Rubio, Moir´ e heterostructures as a condensed-matter quantum simulator, Nature Physics 17, 155–163 (2021)

    2021

  11. [19]

    J. Cai, E. Anderson, C. Wang, X. Zhang, X. Liu, W. Holtzmann, Y. Zhang, F. Fan, T. Taniguchi, K. Watanabe, Y. Ran, T. Cao, L. Fu, D. Xiao, W. Yao, and X. Xu, Signatures of fractional quantum anomalous Hall states in twisted MoTe2, Nature622, 63–68 (2023)

    2023

  12. [20]

    Mandal and R

    I. Mandal and R. M. Fernandes, Valley-polarized nematic order in twisted moir´ e systems: In-plane orbital mag- netism and crossover from non-Fermi liquid to Fermi liq- uid, Phys. Rev. B107, 125142 (2023)

    2023

  13. [21]

    Y. Zeng, Z. Xia, K. Kang, J. Zhu, P. Kn¨ uppel, C. Vaswani, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Thermodynamic evidence of fractional Chern insulator in moir´ e MoTe2, Nature622, 69–73 (2023)

    2023

  14. [22]

    Z. Lu, T. Han, Y. Yao, A. P. Reddy, J. Yang, J. Seo, K. Watanabe, T. Taniguchi, L. Fu, and L. Ju, Fractional quantum anomalous Hall effect in multilayer graphene, Nature626, 759–764 (2024)

    2024

  15. [23]

    Z. Wang, D. A. Rhodes, K. Watanabe, T. Taniguchi, J. C. Hone, J. Shan, and K. F. Mak, Evidence of high- temperature exciton condensation in two-dimensional atomic double layers, Nature574, 76–80 (2019)

    2019

  16. [24]

    Shi, E.-M

    Q. Shi, E.-M. Shih, D. Rhodes, B. Kim, K. Barmak, K. Watanabe, T. Taniguchi, Z. Papi´ c, D. A. Abanin, J. Hone, and C. R. Dean, Bilayer WSe2 as a natural plat- form for interlayer exciton condensates in the strong cou- pling limit, Nature Nanotechnology17, 577–582 (2022)

    2022

  17. [25]

    Zhang, E

    Z. Zhang, E. C. Regan, D. Wang, W. Zhao, S. Wang, M. Sayyad, K. Yumigeta, K. Watanabe, T. Taniguchi, S. Tongay, M. Crommie, A. Zettl, M. P. Zaletel, and F. Wang, Correlated interlayer exciton insulator in het- erostructures of monolayer WSe2 and moir´ e WS2/WSe2, Nature Physic...

    2022

  18. [26]

    A. Y. Joe, A. M. Mier Valdivia, L. A. Jauregui, K. Pis- tunova, D. Ding, Y. Zhou, G. Scuri, K. De Greve, A. Sushko, B. Kim, T. Taniguchi, K. Watanabe, J. C. Hone, M. D. Lukin, H. Park, and P. Kim, Controlled interlayer exciton ionization in an electrostatic trap in atomically ...

    2024

  19. [27]

    X. Liu, N. Leisgang, P. E. Dolgirev, A. A. Zibrov, J. Sung, J. Wang, T. Taniguchi, K. Watanabe, V. Walther, H. Park, E. Demler, P. Kim, and M. D. Lukin, Optical signatures of interlayer electron coherence in a bilayer semiconductor (2024), arXiv:2409.08329 [cond-mat.str- el]

    2024 arXiv

  20. [28]

    P. X. Nguyen, R. Chaturvedi, B. Zou, K. Watanabe, T. Taniguchi, A. H. MacDonald, K. F. Mak, and J. Shan, Quantum oscillations in a dipolar excitonic insulator (2025), arXiv:2501.17829 [cond-mat.mes-hall]

    2025 arXiv

  21. [29]

    Oganesyan, S

    V. Oganesyan, S. A. Kivelson, and E. Fradkin, Quantum theory of a nematic Fermi fluid, Phys. Rev. B64, 195109 (2001)

    2001

  22. [30]

    Xu, Quantum critical points of helical Fermi liquids, Phys

    C. Xu, Quantum critical points of helical Fermi liquids, Phys. Rev. B81, 054403 (2010)

    2010

  23. [31]

    Watanabe and A

    H. Watanabe and A. Vishwanath, Criterion for stabil- ity of Goldstone modes and Fermi liquid behavior in a metal with broken symmetry, Proceedings of the National Academy of Sciences111, 16314–16318 (2014)

    2014

  24. [32]

    Bahri and A

    Y. Bahri and A. C. Potter, Stable non-Fermi-liquid phase of itinerant spin-orbit coupled ferromagnets, Phys. Rev. B92, 035131 (2015)

    2015

  25. [33]

    Kumar, Z

    A. Kumar, Z. Cheng, and A. C. Potter, Fractal non- Fermi liquids from moir´ e Hofstadter phonons, Phys. Rev. B102, 235120 (2020)

    2020

  26. [34]

    Lake and T

    E. Lake and T. Senthil, Non-Fermi Liquids from Kinetic Constraints in Tilted Optical Lattices, Phys. Rev. Lett. 131, 043403 (2023)

    2023

  27. [35]

    Anakru and Z

    A. Anakru and Z. Bi, Non-Fermi liquids from dipolar symmetry breaking, Phys. Rev. B108, 165112 (2023). 7

    2023

  28. [36]

    Ghorai, A

    U. Ghorai, A. Ghosh, S. Chakraborty, A. Das, and R. Sensarma, Excitonic metal and non-Fermi liquid be- havior in twisted double bilayer graphene near charge neutrality, Phys. Rev. B108, 045117 (2023)

    2023

  29. [37]

    C. D. Batista and Z. Nussinov, Generalized Elitzur’s theorem and dimensional reductions, Phys. Rev. B72, 045137 (2005)

    2005

  30. [38]

    R. M. Nandkishore and M. Hermele, Fractons, Annual Review of Condensed Matter Physics10, 295 (2019)

    2019

  31. [39]

    Pretko, X

    M. Pretko, X. Chen, and Y. You, Fracton phases of matter, International Journal of Modern Physics A35, 2030003 (2020)

    2020

  32. [40]

    Gromov and L

    A. Gromov and L. Radzihovsky, Colloquium: Fracton matter, Rev. Mod. Phys.96, 011001 (2024)

    2024

  33. [41]

    Seiberg and S.-H

    N. Seiberg and S.-H. Shao, Exotic symmetries, duality, and fractons in 2+1-dimensional quantum field theory, SciPost Phys.10, 027 (2021)

    2021

  34. [42]

    Distler, A

    J. Distler, A. Karch, and A. Raz, Spontaneously broken subsystem symmetries, Journal of High Energy Physics 2022(2022)

    2022

  35. [43]

    Han and Y

    S. Han and Y. B. Kim, Non-Fermi liquid induced by Bose metal with protected subsystem symmetries, Phys. Rev. B106, L081106 (2022)

    2022

  36. [44]

    J. P. Eisenstein and A. H. MacDonald, Bose–Einstein condensation of excitons in bilayer electron systems, Na- ture432, 691–694 (2004)

    2004

  37. [45]

    Eisenstein, Exciton Condensation in Bilayer Quan- tum Hall Systems, Annual Review of Condensed Matter Physics5, 159–181 (2014)

    J. Eisenstein, Exciton Condensation in Bilayer Quan- tum Hall Systems, Annual Review of Condensed Matter Physics5, 159–181 (2014)

    2014

  38. [46]

    K. Kim, N. Prasad, H. C. P. Movva, G. W. Burg, Y. Wang, S. Larentis, T. Taniguchi, K. Watanabe, L. F. Register, and E. Tutuc, Spin-Conserving Reso- nant Tunneling in Twist-Controlled WSe 2-hBN-WSe2 Heterostructures, Nano Letters18, 5967–5973 (2018)

    2018

  39. [47]

    S. M. Sze, Y. Li, and K. K. Ng, Physics of semiconductor devices (John wiley & sons, 2021)

    2021

  40. [48]

    Zheng, M

    L. Zheng, M. W. Ortalano, and S. Das Sarma, Exchange instabilities in semiconductor double-quantum-well sys- tems, Phys. Rev. B55, 4506 (1997)

    1997

  41. [49]

    F.-C. Wu, F. Xue, and A. H. MacDonald, Theory of two- dimensional spatially indirect equilibrium exciton con- densates, Phys. Rev. B92, 165121 (2015)

    2015

  42. [50]

    Zhu and S

    J. Zhu and S. Das Sarma, Interaction and coherence in two-dimensional bilayers, Phys. Rev. B109, 085129 (2024)

    2024

  43. [51]

    Panigrahi, Subsystem-symmetry-breaking- NFL-codes (2024), GitHub repository

    A. Panigrahi, Subsystem-symmetry-breaking- NFL-codes (2024), GitHub repository. URL: https://github.com/archisman-panigrahi/Subsystem- symmetry-breaking-NFL-codes

    2024

  44. [52]

    Sachdev, Quantum Phase Transitions, 2nd ed

    S. Sachdev, Quantum Phase Transitions, 2nd ed. (Cam- bridge University Press, Cambridge, England, 2011)

    2011

  45. [53]

    S. A. Hartnoll and A. P. Mackenzie, Colloquium: Planck- ian dissipation in metals, Rev. Mod. Phys.94, 041002 (2022)

    2022

  46. [54]

    Senthil, M

    T. Senthil, M. Vojta, and S. Sachdev, Weak magnetism and non-Fermi liquids near heavy-Fermion critical points, Phys. Rev. B69, 035111 (2004)

    2004

  47. [55]

    See Supplemental Material at [URL-will-be-inserted-by- publisher] for details of the calculation for self-energy, specific heat, and transport properties

  48. [56]

    Watanabe, S

    H. Watanabe, S. A. Parameswaran, S. Raghu, and A. Vishwanath, Anomalous Fermi-liquid phase in metal- lic skyrmion crystals, Phys. Rev. B90, 045145 (2014)

    2014

  49. [57]

    P. A. Lee and N. Nagaosa, Gauge theory of the normal state of high-T c superconductors, Phys. Rev. B46, 5621 (1992)

    1992

  50. [58]

    M. Y. Kharitonov and K. B. Efetov, Electron screening and excitonic condensation in double-layer graphene sys- tems, Phys. Rev. B78, 241401 (2008)

    2008

  51. [59]

    Bezanson, A

    J. Bezanson, A. Edelman, S. Karpinski, and V. B. Shah, Julia: A fresh approach to numerical computing, SIAM Review59, 65 (2017)

    2017

  52. [60]

    Peter, Numbat (2024), a statically typed programming language for scientific computations with first class sup- port for physical dimensions and units, version: 1.14.0

    D. Peter, Numbat (2024), a statically typed programming language for scientific computations with first class sup- port for physical dimensions and units, version: 1.14.0. URL:https://github.com/sharkdp/numbat. 8 Appendix A: Calculation of self-energy In this section, we provi...

    2024

Pith tools

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