Pith. sign in

REVIEW 4 major objections 3 minor 58 references

Continuous transition from Fermi liquid to A fractional Chern insulator

T0 review · 4 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read The paper proposes a continuous quantum phase transition at fixed ν=2/3 between a Fermi liquid and a fractional Chern insulator (FCI*), and predicts that the Fermi-liquid side mimics an anyon gas at high temperature with ρxy close to…

desk verdict A clearly written composite-boson proposal for a FL-FCI* transition whose finite-T transport prediction is suggestive but rests on uncontrolled approximations. read the letter →

arxiv 2507.22130 v1 pith:PQEB2G4L submitted 2025-07-29 cond-mat.str-el

Ya-Hui Zhang This is my paper
classification cond-mat.str-el
keywords fractionalCherninsulatorcompositeFermiliquidbosonquantumphasetransitiontwistedMoTe2Hallresistivityanyongaspartonconstruction
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 proposes a theory in which a Fermi liquid (FL) and a fractional Chern insulator can be connected by a continuous quantum phase transition at the fixed filling $\nu = 2/3$. In the composite-boson language, the FL is a composite Fermi liquid of the boson $b$ and the transition is induced by condensing $b$; the resulting insulator is an FCI* phase carrying an extra neutral sector, with the same charge transport as an ordinary FCI. On the FL side the wavefunction acquires an extra factor $\prod_{i

What carries the argument

The central object is the composite-boson parton construction $c(r) = b(r) f(r)$, with $f$ held in the $\nu = 1/m$ Laughlin state; this converts the FL-FCI question into a composite-Fermi-liquid to superfluid* transition of $b$. The argument is carried by a critical Lagrangian (Eq.~15) in which a complex boson field $\varphi$ (the condensate field for $b$) couples to the internal gauge field $a$, together with a composite fermion $\psi$, a Chern-Simons term $-\frac{1}{4\pi m} \alpha\, d\alpha$, and a monopole coupling $\lambda(\varphi^\dagger \psi M^m_\alpha + \text{h.c.})$. The finite-temperature prediction follows from the self-consistent compressibility equation $\kappa_{M\alpha}(\Delta - s) = n_\varphi$, the free-boson density $n_\varphi = -\frac{2\pi T}{W_\varphi} \log\left(1 - e^{-\Delta/T}\right)$, and the Ioffe-Larkin composition rule that converts the boson and fermion resistivities into the electron resistivity tensor.

What would settle it

Measure $\rho_{xy}(T)$ and $\rho_{xx}(T)$ at fixed $\nu = 2/3$ in twisted MoTe$_2$ while tuning the bandwidth (by twist angle, pressure, or displacement field). The scenario predicts a smooth crossover from $\rho_{xy} \approx 0$ at low $T$ to $\rho_{xy} \approx (3/2)\,h/e^2$ with small $\rho_{xx}$ once $T$ exceeds the composite-boson gap; a first-order jump, a different high-temperature plateau, or the absence of a low-temperature FL-like regime would contradict the claim.

Watch

Extended reading notes

Core claim

The paper's central claim is that at $\nu = 2/3$ the FL-to-FCI transition can be continuous, provided the FCI side is the FCI* phase rather than the minimal FCI. Starting from the parton factorization $c = b f$ with $f$ in the $\nu = 1/3$ Laughlin state, the electron FL corresponds to the composite boson $b$ forming a composite Fermi liquid; condensing $b$ gives a superfluid* of $b$ that translates, for the electron, into an FCI* insulator. Close to the transition the FL wavefunction contains the extra Jastrow factor $\prod_{i<j} |z_i - z_j|^6$. The paper further claims that on the FL side the finite-temperature transport crosses over from ordinary Fermi-liquid behavior at $T \ll s$ to an 'anyon gas' regime at higher $T$, with $\rho_{xy}$ close to $(3/2)\,h/e^2$ and small $\rho_{xx}$, and that this crossover follows from thermally excited composite bosons depleting the Fermi surface. This offers a conventional alternative to anyonic-superconductivity explanations of the twisted MoTe$_2$ experiments.

Load-bearing premise

The finite-temperature transport prediction rests on treating the thermally excited composite bosons as a free, dilute Bose gas whose relaxation time is temperature-independent and set by disorder, and on the self-consistent compressibility equation $\kappa_{M\alpha}(\Delta - s) = n_\varphi$; the interaction term $g$ and umklapp scattering are dropped, so if those corrections matter the $\rho_{xy} \approx 3/2$ plateau is not protected.

Editorial extensions

If this is right

  • Decreasing the bandwidth at $\nu = 2/3$ should drive a continuous progression FL $\to$ FCI* $\to$ FCI, with the FCI* region differing from the FCI only by an extra neutral sector visible in specific heat and thermal transport.
  • The FL near the transition is strongly correlated, with the $\prod_{i<j} |z_i-z_j|^6$ factor in its wavefunction; the paper argues this should enhance pairing and can lead to a chiral superconductor as a descendant state.
  • At temperatures above the composite-boson gap $s$, the FL side should show $\rho_{xy} \approx (3/2)\,h/e^2$ with small $\rho_{xx}$, crossing over to $\rho_{xy} \approx 0$ only below $T \ll s$.
  • These finite-temperature signatures do not require the FCI* phase or the critical point itself to exist; a correlated FL with a cheap composite-boson excitation would show the same crossover.
  • At the critical point $s=0$, $\rho_{xx}$ grows linearly in temperature at low $T$, with the slope set by the boson relaxation time.

Reading between the lines

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

  • If the free-boson self-consistency holds, the optical conductivity on the FL side should exhibit a Drude weight growing as $T \log T$ at low temperature; this is derived for the bosonic sector and should carry over to the electron response, but the paper does not spell it out.
  • Since FCI*'s neutral sector carries no charge, a thermal Hall measurement at $\nu = 2/3$ should show an excess $\kappa_{xy}/T$ relative to the pure FCI even while $\rho_{xy}$ is unchanged; that would be a clean way to distinguish FCI* from FCI.
  • The crossover temperature where $\rho_{xy}$ approaches $3/2$ should track the composite-boson gap $s$; varying the bandwidth in twisted MoTe$_2$ should therefore move the crossover, a direct experimental check that the paper leaves implicit.
  • Exact-diagonalization or overlap calculations with the proposed $\prod_{i<j}|z_i-z_j|^6$ Jastrow FL wavefunction on small moiré-system clusters could test whether the proximate FL really carries this correlation factor.
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

4 major / 3 minor

Summary. The paper proposes a composite-boson field theory for a continuous quantum phase transition between a Fermi liquid (FL) and an FCI* phase—an FCI with an additional neutral sector—at filling ν=2/3. The construction writes the electron as c=bf, puts f in a Laughlin state, and describes the transition as a CFL-to-superfluid* transition of the composite boson b, captured by a φ^4 theory (Eq. 11). The paper further predicts that on the FL side, thermally excited composite bosons deplete the Fermi surface, producing a finite-temperature regime with ρxy close to 3/2 h/e² and small ρxx, with FL behavior recovered only at low temperature. The transport calculation uses a self-consistent dilute-boson approximation with disorder-dominated relaxation times. The paper connects this scenario to the high-temperature Hall anomaly and possible superconductivity in twisted MoTe2.

Significance. If the scenario is correct, it offers a conventional, non-anyon alternative to exotic explanations of the high-temperature transport in twisted MoTe2 and gives a concrete falsifiable prediction: a crossover from ρxy≈0 to ρxy≈3/2 h/e² on the metallic side as temperature increases. Strengths of the paper include a transparent parton construction, a self-contained transport calculation with no parameter fitted to the target Hall value, and unusually explicit disclosure of the approximations made (g=0, temperature-independent τ, omitted umklapp). The paper is honest that the transition is to an intermediate FCI* phase rather than a conventional FCI. However, the central continuous-transition claim is a modeled scenario rather than a derived result, and the headline transport signature is not protected by symmetry or topology, so the significance hinges on whether the approximations can be justified or at least robustly tested.

major comments (4)
  1. [Sec. I, Sec. III, Eq. (11)] The paper's central claim is a continuous transition, but the construction is explicitly a compromise: the transition is from the FL to an intermediate FCI* phase, and Sec. I states that the FCI* phase 'may depend on model details' and 'occupy at most a very narrow region,' and that no direct FL-to-conventional-FCI transition was found. Eq. (11) is a φ^4 theory for condensing the composite boson b, but no argument is given that the CFL-to-SF* transition is continuous at fixed density or that the FCI* phase is stable over a finite parameter range. The title and abstract should either be softened to 'candidate continuous transition' or supported by an explicit consistency check, such as a duality, large-N limit, or numerical benchmark.
  2. [Sec. IV, Eq. (18), Appendix B2, Eq. (B8)] The finite-temperature transport prediction is the main falsifiable contact with experiment, but it rests on uncontrolled approximations. Eq. (18) sets g=0 ('we ignore the interaction term g for simplicity'), and Appendix B2 assumes temperature-independent τφ and τψ and omits umklapp scattering, which the paper itself notes would add a T² contribution to ρxx. Fig. 2 shows nφ≈0.1 at T=0.04Wφ, about 30% of the ν=1/3 density, so the dilute-gas approximation is already marginal in the plotted crossover regime. Because σφ domination is what forces ρxy toward 3/2, a Hartree-level inclusion of g or a scan over τφ and τψ would be needed to show the plateau is robust; otherwise this prediction should be presented as an estimate rather than a signature.
  3. [Sec. IV, Eqs. (19)-(20)] The high-temperature ρxy≈3/2 is not a topologically protected value; it follows from the specific combination of a C=-1 Chern insulator at ν=1 and a hole sector at ν=1/3, together with the assumption that σφ is the only sizable longitudinal channel. If the ψ sector contributes a comparable longitudinal or Hall conductivity, or if the background Chern number or hole density is different, the plateau value shifts. This model dependence should be stated explicitly and distinguished from a quantized Hall response.
  4. [Sec. IV, first paragraph; Eq. (17)] The description of the s=0 point is internally problematic: the paper says that at T=0 the φ density is zero and the system 'behaves as if φ is gapped and indistinguishable from a FL phase.' A gapless φ at a genuine quantum critical point should produce T=0 signatures, such as a condensate at fixed density or singular corrections to observables. Moreover, Eq. (17) makes κMα vanish as T→0 for ∆>0, and the self-consistent equation (B5) has a singular limit at s=0 and ∆=0, where the 2D Bose-gas density formula diverges. The authors should clarify whether the 'critical regime' is really a finite-temperature crossover with a small gap rather than an actual continuous quantum phase transition.
minor comments (3)
  1. [Title and Abstract] The title says 'Fermi liquid to A fractional Chern insulator,' while the abstract and Sec. I specify the transition is to FCI*, not the conventional FCI; the title should be revised to match the actual claim.
  2. [Throughout] There are several typographical errors: 'intermeidate' in Sec. I, 'langauge' in Sec. II, 'compresibility' in Appendix A1, 'sub' instead of 'sum' in Appendix A2, and 'moederate' in the Fig. 2 caption.
  3. [Sec. IV, Fig. 1] The physical scales of Wφ, Wψ, s, τφ, and τψ are not tied to twisted MoTe2 parameters; a rough estimate of the crossover temperature in kelvin would make the experimental connection more concrete.

Circularity Check

0 steps flagged · score 2.0 of 10

No load-bearing circularity: the central FL-to-FCI* construction and finite-temperature transport follow from explicitly stated parton and self-consistency assumptions; self-citations are background only.

full rationale

The derivation chain is self-contained in the sense relevant to circularity. The FL state with the |zi-zj|^6 Jastrow factor is obtained by explicit algebra from the stated parton construction c=bf with f in a Laughlin state (Eq. 1) and b in a CFL state (Eq. 4), not by fitting or by importing the conclusion. The FCI* phase is defined as a superfluid* of b with a decoupled neutral sector, and its charge response is read off from the standard Chern-Simons term (Eq. 14); this is a construction, not a hidden input. The finite-temperature transport prediction is the least secure part of the paper, but it is not circular: the thermally-excited boson density n_phi is determined self-consistently from Eq. B5, and the Hall value rho_xy about (3/2)h/e^2 at nu=2/3 follows from the Ioffe-Larkin composition rule (Eq. B6) plus the stated nu=1 Chern background and hole sector. No parameter is fitted to the target observable; W_phi, W_psi, and tau are chosen for illustration and are acknowledged as model parameters. The approximations (g=0, temperature-independent tau, omission of umklapp) are stated openly and introduce accuracy risk, but they do not reduce the claims to their inputs by definition. The only self-citations (Refs. [28] and [37]) appear in a background sentence about previously studied bosonic Laughlin and CFL transitions; they are not load-bearing for the present critical theory or transport calculation. Accordingly, no circular step is identified; the score reflects only the presence of minor background self-citations.

Assumptions & free parameters 5 free parameters · 5 assumptions · 2 invented entities

The central claims rest on a chain of assumptions from the parton construction to the FCI* stability and the dilute-boson transport calculation. The only hand-set numbers are the bandwidths and relaxation times used for illustration; no experimental data are fitted, but no external benchmark is used either.

free parameters (5)
  • Wφ = 1 (arbitrary units in figures)
    Bandwidth of φ; controls nφ(T) via Eq. A2/B5; the plots set Wφ=1, so quantitative predictions are illustrative.
  • Wψ = 1 (equal to Wφ in figures)
    Bandwidth of ψ; enters κMα and ρψ;xx; chosen equal to Wφ.
  • τφ = h/τφ = 0.1 Wφ
    Relaxation time for φ; assumed temperature independent; sets σφ and the crossover scale.
  • τψ = h/τψ = 0.1 Wφ
    Relaxation time for ψ; assumed temperature independent; sets ρψ;xx.
  • s = varied (0, small positive)
    Tuning parameter, the zero-temperature gap of φ; values chosen to show crossover, not fixed by experiment.
assumptions (5)
  • domain assumption Parton decomposition c=b f with f in a Laughlin state at ν=1/m is a valid description of the zero-field FCI.
    Introduced in Sec. II, Eq. 1-3; this is the standard composite boson construction, assumed rather than derived.
  • domain assumption Composite boson b at effective filling -1/m forms a Halperin-Lee-Read CFL when not condensed.
    Used in Eq. 6 and Sec. II A; the CFL phase is taken as the starting point for the FL side.
  • ad hoc to paper The FL-FCI* transition is controlled by condensing b, described by a φ^4 theory with a continuous transition tuned by s.
    Eq. 11/15; the paper calls this a compromise (Sec. III) and does not prove continuity; this is the main unproven step.
  • ad hoc to paper The FCI* phase is a stable intermediate phase with a neutral sector described by Eq. 12-14.
    Sec. III A; the paper admits its existence may depend on model details.
  • ad hoc to paper At finite T, thermally excited φ can be modeled as a free dilute Bose gas with a temperature-independent relaxation time.
    Appendix B, Eq. B5-B8; interactions (g), umklapp, and T-dependent scattering are ignored.
invented entities (2)
  • FCI* phase, a fractional Chern insulator with an additional neutral sector
    purpose: Intermediate phase that allows a continuous FL to FCI description via composite boson condensation; has the same charge transport as FCI but with hidden neutral degrees of freedom.
    Proposed in Sec. III A; the paper states its existence depends on model details, and it is invisible to charge transport, so there is no independent falsifiable handle yet.
  • Gapped composite boson φ as a 6π vortex of the electron
    purpose: Thermally excited density nφ depletes the Fermi surface and produces the anyon-gas-like high-temperature transport on the FL side.
    Introduced in Sec. IV-V; the only predicted consequence is the high-T ρxy crossover, which is not independent of the model used to compute it.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Continuous transition from Fermi liquid to A fractional Chern insulator." pith.science (2026). https://pith.science/paper/PQEB2G4L

@misc{pith2026250722130,
  author       = {Pith},
  title        = {Pith review of: Continuous transition from Fermi liquid to A fractional Chern insulator},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PQEB2G4L}},
  note         = {Machine review of arXiv:2507.22130}
}
abstract

Recent experiments in moir\'e materials have observed fractional Chern insulators (FCI) at zero magnetic field, providing an opportunity to study the transition from FCI to the more conventional phases such as Fermi liquid (FL) and superconductor (SC) by tuning the interaction strength or bandwidth. In this work, we formulate a critical theory for a continuous transition at the filling $\nu=\frac{2}{3}$ between the FL and a FCI* phase that hosts an additional neutral sector, but has the same transport signatures as the usual FCI. In our framework, this corresponds to a transition from a composite Fermi liquid (CFL) to a superfluid* phase of the composite bosons. The Fermi liquid close to the transition has an additional factor $|z_i-z_j|^6$ in its wavefunction. Also, the transport behavior at high temperature on the FL side is actually like an `anyon gas' phase on top of the FCI, with $\rho_{xy}$ close to $\frac{3}{2}\frac{h}{e^2}$. FL behavior with $\rho_{xy} \approx 0$ is recovered only at very low temperature. We also briefly discuss the possibility of a chiral superconductor as the descendant of this strongly correlated FL and the potential relevance to the twisted MoTe$_2$ system.

Figures

Figures reproduced from arXiv: 2507.22130 by the authors.

Figure 1
Figure 1. FIG. 1. Resistivity [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The dependence of ∆ = [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. For the filling ν = 2 3 , we should add an additional integer quantum Hall part to the conductivity, which is shown in the main text. One finds that at small T, ρxx ∼ σxx ∼ AkBT (AkBT) 2+( 1 m ) 2 , where A ∼ 2πτφ h . Interestingly there is a linear T resistivity at low temperature, whose coefficient actually scales with the relaxation time of the critical boson φ. Here we assume τφ is mainly decided by the disorder… view at source ↗

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

58 extracted references · 40 canonical work pages

  1. [1]

    K. Sun, Z. Gu, H. Katsura, and S. D. Sarma, Nearly flatbands with nontrivial topology, Physical review let- ters 106, 236803 (2011)

    work page 2011

  2. [2]

    Sheng, Z.-C

    D. Sheng, Z.-C. Gu, K. Sun, and L. Sheng, Fractional quantum hall effect in the absence of landau levels, Na- ture communications 2, 389 (2011)

    work page 2011

  3. [3]

    Neupert, L

    T. Neupert, L. Santos, C. Chamon, and C. Mudry, Frac- tional quantum hall states at zero magnetic field, Physi- cal review letters 106, 236804 (2011)

    work page 2011

  4. [4]

    Wang, Z.-C

    Y.-F. Wang, Z.-C. Gu, C.-D. Gong, and D. Sheng, Frac- tional quantum hall effect of hard-core bosons in topo- logical flat bands, Physical review letters 107, 146803 (2011)

    work page 2011

  5. [5]

    Tang, J.-W

    E. Tang, J.-W. Mei, and X.-G. Wen, High-temperature fractional quantum hall states, Physical review letters 106, 236802 (2011)

    work page 2011

  6. [6]

    Regnault and B

    N. Regnault and B. A. Bernevig, Fractional chern insu- lator, Physical Review X 1, 021014 (2011)

    work page 2011

  7. [7]

    E. J. Bergholtz and Z. Liu, Topological flat band models and fractional chern insulators, International Journal of Modern Physics B 27, 1330017 (2013)

    work page 2013

  8. [8]

    S. A. Parameswaran, R. Roy, and S. L. Sondhi, Fractional quantum hall physics in topological flat bands, Comptes Rendus Physique 14, 816 (2013)

    work page 2013

Show all 58 references
  1. [9]

    Neupert, L

    T. Neupert, L. Santos, S. Ryu, C. Chamon, and C. Mudry, Fractional topological liquids with time- reversal symmetry and their lattice realization, Phys. Rev. B 84, 165107 (2011)

    2011

  2. [10]

    Zhang, D

    Y.-H. Zhang, D. Mao, Y. Cao, P. Jarillo-Herrero, and T. Senthil, Nearly flat chern bands in moir´ e superlattices, Physical Review B 99, 075127 (2019)

    2019

  3. [11]

    F. Wu, T. Lovorn, E. Tutuc, I. Martin, and A. MacDon- ald, Topological insulators in twisted transition metal dichalcogenide homobilayers, Physical review letters122, 086402 (2019)

    2019

  4. [12]

    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, Nature 10.1038/s41586-023- 06289-w (2023)

    2023 doi

  5. [13]

    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´ emote2, Nature 10.1038/s41586- 023-06452-3 (2023)

    2023 doi

  6. [14]

    H. Park, J. Cai, E. Anderson, Y. Zhang, J. Zhu, X. Liu, C. Wang, W. Holtzmann, C. Hu, Z. Liu, T. Taniguchi, K. Watanabe, J.-h. Chu, T. Cao, L. Fu, W. Yao, C.- Z. Chang, D. Cobden, D. Xiao, and X. Xu, Observation of fractionally quantized anomalous hall effect, Nature 10.1038/s...

    2023 doi

  7. [15]

    F. Xu, Z. Sun, T. Jia, C. Liu, C. Xu, C. Li, Y. Gu, K. Watanabe, T. Taniguchi, B. Tong, J. Jia, Z. Shi, S. Jiang, Y. Zhang, X. Liu, and T. Li, Observation of integer and fractional quantum anomalous hall effects in twisted bilayer mote2, Phys. Rev. X 13, 031037 (2023)

    2023

  8. [16]

    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, Nature 626, 759 (2024)

    2024

  9. [17]

    H. Yu, M. Chen, and W. Yao, Giant magnetic field from moir´ e induced berry phase in homobilayer semiconduc- tors, National Science Review 7, 12 (2020)

    2020

  10. [18]

    Devakul, V

    T. Devakul, V. Cr´ epel, Y. Zhang, and L. Fu, Magic in twisted transition metal dichalcogenide bilayers, Nature communications 12, 6730 (2021)

    2021

  11. [19]

    H. Li, U. Kumar, K. Sun, and S.-Z. Lin, Spontaneous fractional chern insulators in transition metal dichalco- genide moir´ e superlattices, Physical Review Research3, L032070 (2021)

    2021

  12. [20]

    Cr´ epel and L

    V. Cr´ epel and L. Fu, Anomalous hall metal and fractional chern insulator in twisted transition metal dichalco- genides, Phys. Rev. B 107, L201109 (2023)

    2023

  13. [21]

    Wang, X.-W

    C. Wang, X.-W. Zhang, X. Liu, Y. He, X. Xu, Y. Ran, T. Cao, and D. Xiao, Fractional chern insulator in twisted bilayer mote 2, arXiv preprint arXiv:2304.11864 (2023)

    2023 arXiv

  14. [22]

    A. P. Reddy, F. F. Alsallom, Y. Zhang, T. Devakul, and L. Fu, Fractional quantum anomalous hall states in twisted bilayer mote 2 and wse 2, arXiv preprint arXiv:2304.12261 (2023). 7

    2023 arXiv

  15. [23]

    C. Xu, J. Li, Y. Xu, Z. Bi, and Y. Zhang, Maximally Lo- calized Wannier Orbitals, Interaction Models and Frac- tional Quantum Anomalous Hall Effect in Twisted Bi- layer MoTe2, arXiv e-prints , arXiv:2308.09697 (2023), arXiv:2308.09697 [cond-mat.str-el]

    2023 arXiv

  16. [24]

    J. Yu, J. Herzog-Arbeitman, M. Wang, O. Vafek, B. A. Bernevig, and N. Regnault, Fractional Chern Insulators vs. Non-Magnetic States in Twisted Bi- layer MoTe2, arXiv e-prints , arXiv:2309.14429 (2023), arXiv:2309.14429 [cond-mat.mes-hall]

    2023 arXiv

  17. [25]

    Goldman, A

    H. Goldman, A. P. Reddy, N. Paul, and L. Fu, Zero-field composite fermi liquid in twisted semiconductor bilayers, Phys. Rev. Lett. 131, 136501 (2023)

    2023

  18. [26]

    J. Dong, J. Wang, P. J. Ledwith, A. Vishwanath, and D. E. Parker, Composite fermi liquid at zero magnetic field in twisted mote 2, Phys. Rev. Lett. 131, 136502 (2023)

    2023

  19. [27]

    Morales-Dur´ an, N

    N. Morales-Dur´ an, N. Wei, and A. H. MacDonald, Magic angles and fractional chern insulators in twisted homobi- layer tmds, arXiv preprint arXiv:2308.03143 (2023)

    2023 arXiv

  20. [28]

    Song, Y.-H

    X.-Y. Song, Y.-H. Zhang, and T. Senthil, Phase tran- sitions out of quantum hall states in moir´ e materials, Physical Review B 109, 085143 (2024)

    2024

  21. [29]

    Z. Dong, A. S. Patri, and T. Senthil, Theory of fractional quantum anomalous hall phases in pentalayer rhombohe- dral graphene moir´ e structures (2023), arXiv:2311.03445 [cond-mat.str-el]

    2023 arXiv

  22. [30]

    B. Zhou, H. Yang, and Y.-H. Zhang, Fractional quan- tum anomalous hall effects in rhombohedral multilayer graphene in the moir \’eless limit and in coulomb im- printed superlattice, arXiv preprint arXiv:2311.04217 (2023)

    2023 arXiv

  23. [31]

    J. Dong, T. Wang, T. Wang, T. Soejima, M. P. Zaletel, A. Vishwanath, and D. E. Parker, Anomalous hall crys- tals in rhombohedral multilayer graphene i: Interaction- driven chern bands and fractional quantum hall states at zero magnetic field (2023), arXiv:2311.05568 [cond- mat.str-el]

    2023 arXiv

  24. [32]

    Z. Guo, X. Lu, B. Xie, and J. Liu, Theory of fractional chern insulator states in pentalayer graphene moir\’e su- perlattice, arXiv preprint arXiv:2311.14368 (2023)

    2023 arXiv

  25. [33]

    Y. H. Kwan, J. Yu, J. Herzog-Arbeitman, D. K. Efe- tov, N. Regnault, and B. A. Bernevig, Moir \’e fractional chern insulators iii: Hartree-fock phase diagram, magic angle regime for chern insulator states, the role of the moir\’e potential and goldstone gaps in rhombohedral gr...

    2023

  26. [34]

    H. L. Stormer, D. C. Tsui, and A. C. Gossard, The frac- tional quantum hall effect, Reviews of Modern Physics 71, S298 (1999)

    1999

  27. [35]

    H. L. Stormer, Nobel lecture: the fractional quantum hall effect, Reviews of Modern Physics 71, 875 (1999)

    1999

  28. [36]

    Barkeshli and J

    M. Barkeshli and J. McGreevy, Continuous transition between fractional quantum hall and superfluid states, Physical Review B 89, 235116 (2014)

    2014

  29. [37]

    Song and Y.-H

    X.-Y. Song and Y.-H. Zhang, Deconfined criticalities and dualities between chiral spin liquid, topological supercon- ductor and charge density wave chern insulator, SciPost Physics 15, 215 (2023)

    2023

  30. [38]

    Lu, H.-Q

    H. Lu, H.-Q. Wu, B.-B. Chen, and Z. Y. Meng, Contin- uous transition between bosonic fractional chern insula- tor and superfluid, Physical Review Letters 134, 076601 (2025)

    2025

  31. [39]

    Wang, X.-Y

    T. Wang, X.-Y. Song, M. P. Zaletel, and T. Senthil, Emergent qed 3 at the bosonic laughlin state to super- fluid transition, arXiv preprint arXiv:2507.07611 (2025)

    2025

  32. [40]

    Lotriˇ c and S

    T. Lotriˇ c and S. H. Simon, Paired parton trial states for the superfluid-fractional chern insulator transition, arXiv preprint arXiv:2504.20139 (2025)

    2025

  33. [41]

    Barkeshli and J

    M. Barkeshli and J. McGreevy, Continuous transitions between composite fermi liquid and landau fermi liquid: A route to fractionalized mott insulators, Physical Re- view B 86, 075136 (2012)

    2012

  34. [42]

    B. I. Halperin, P. A. Lee, and N. Read, Theory of the half- filled landau level, Physical Review B 47, 7312 (1993)

    1993

  35. [43]

    Senthil, Theory of a continuous mott transition in two dimensions, Physical Review B 78, 045109 (2008)

    T. Senthil, Theory of a continuous mott transition in two dimensions, Physical Review B 78, 045109 (2008)

    2008

  36. [44]

    Wang and M

    T. Wang and M. P. Zaletel, Chiral superconductiv- ity near a fractional chern insulator, arXiv preprint arXiv:2507.07921 (2025)

    2025 arXiv

  37. [45]

    F. Xu, Z. Sun, J. Li, C. Zheng, C. Xu, J. Gao, T. Jia, K. Watanabe, T. Taniguchi, B. Tong, et al., Signa- tures of unconventional superconductivity near reentrant and fractional quantum anomalous hall insulators, arXiv preprint arXiv:2504.06972 (2025)

    2025 arXiv

  38. [46]

    R. B. Laughlin, Superconducting ground state of nonin- teracting particles obeying fractional statistics, Physical Review Letters 60, 2677 (1988)

    1988

  39. [47]

    R. B. Laughlin, The relationship between high- temperature superconductivity and the fractional quan- tum hall effect, Science 242, 525 (1988)

    1988

  40. [48]

    B. I. Halperin, Anyon superconductivity, Helv. Phys. Acta 65, 80 (1990)

    1990

  41. [49]

    M. P. A. Fisher and D.-H. Lee, Correspondence be- tween two-dimensional anyons and superconductivity, Phys. Rev. B 43, 130 (1991)

    1991

  42. [50]

    Tang and X.-G

    E. Tang and X.-G. Wen, Superconductivity with intrinsic topological order induced by pure coulomb interaction and time-reversal symmetry breaking, Physical Review B—Condensed Matter and Materials Physics 88, 195117 (2013)

    2013

  43. [51]

    M. Kim, A. Timmel, L. Ju, and X.-G. Wen, Topological chiral superconductivity beyond pairing in a fermi liquid, Physical Review B 111, 014508 (2025)

    2025

  44. [52]

    Z. D. Shi and T. Senthil, Doping a fractional quantum anomalous hall insulator, arXiv preprint arXiv:2409.20567 (2024)

    2024

  45. [53]

    Darius Shi, C

    Z. Darius Shi, C. Zhang, and T. Senthil, Doping lattice non-abelian quantum hall states, arXiv e-prints , arXiv (2025)

    2025

  46. [54]

    Ioffe and A

    L. Ioffe and A. Larkin, Gapless fermions and gauge fields in dielectrics, Physical Review B 39, 8988 (1989). 8 Appendix A: Superfluid transition from a bosonic composite F ermi liquid We consider a model with physical boson b at density ν = 1 m with odd m. We will discuss a CF...

    1989

  47. [55]

    However, at finite T , there are thermally excited bosons and the system is again described by a two fluid picture such that the CFL part is depleted by a finite nφ

    Dilute boson gas at finite temperature in the CFL side Let us focus on the CFL phase in the side of s > 0, where nφ = 0 , ⟨dα⟩ 2π = 0 at T = 0. However, at finite T , there are thermally excited bosons and the system is again described by a two fluid picture such that the CFL ...

  48. [56]

    At T = 0, it is in the familiar CFL phase

    T ransport property In the following we discuss the transport property of this bosonic phase in the s >0 side. At T = 0, it is in the familiar CFL phase. At finite T , we have contributions from both the doped CFL part and φ. The conductivity of the physical boson is the sub o...

  49. [57]

    But we need to fix nψ + nφ = 1 m through a chemical potential term: δL = +δµ( 1 2πm dα + φ†φ) (B1) Note that the variation of α0 leads to 1 2πm dα = nψ

    Density of φ at finite temperature At finite T , there may be finite density of thermally excited φ bosons. But we need to fix nψ + nφ = 1 m through a chemical potential term: δL = +δµ( 1 2πm dα + φ†φ) (B1) Note that the variation of α0 leads to 1 2πm dα = nψ. Now the dispersi...

  50. [58]

    We will see that the resistivity behaves like an FL only when T < sand becomes more like an anyon gas at a higher temperature

    T ransport in the critical regime We now move to calculate the resistivity tensor, especially in the regime T > son the side of s >0. We will see that the resistivity behaves like an FL only when T < sand becomes more like an anyon gas at a higher temperature. We still use the...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.