pith. machine review for the scientific record. sign in

arxiv: 2604.11739 · v1 · submitted 2026-04-13 · ❄️ cond-mat.str-el

Recognition: unknown

Topological Kondo Insulator from Spin Loop Currents

Andreas Gleis , Kevin Lucht , Po-Jui Chen , Daniele Guerci , Andrew J Millis , J. H. Pixley
Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:19 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords moiré bilayertopological Kondo insulatorspin loop currentsnon-local interactionsdisplacement fieldband gap openingdynamical mean-field theoryquantum geometry
0
0 comments X

The pith

Non-local interactions allow spin loop currents to open a full gap in a moiré bilayer, turning a compensated semimetal into a topological Kondo insulator at hole filling 2.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

In AB-stacked MoTe2/WSe2, local correlations alone produce a compensated topological semimetal because a symmetry in the moiré bandstructure ties band inversion to band overlap. Non-local interactions introduce intrinsic spin loop currents driven by quantum geometry; these currents feed back on the bandstructure and lift accidental degeneracies. The result is a fully gapped topological Kondo insulator that appears at intermediate displacement fields. The state shows strong correlations through enhanced spin susceptibility, suppressed charge susceptibility, and stronger temperature dependence in resistivity, consistent with observed displacement-field-driven transitions.

Core claim

In the presence of only local correlations, a symmetry of the moiré-scale bandstructure enforces a compensated topological semimetal by tying band inversion to band overlap. Non-local interactions change the physics qualitatively, since they allow intrinsic, quantum-geometry-induced spin loop currents to feed back on the effective bandstructure, which lift the remaining accidental degeneracies and open a full gap in the spectrum, leading to a fully gapped topological Kondo insulator.

What carries the argument

Quantum-geometry-induced spin loop currents that feed back on the effective bandstructure via non-local interactions.

If this is right

  • The topological Kondo insulator appears only at intermediate displacement fields where correlations are pronounced.
  • Enhanced spin susceptibility and suppressed charge susceptibility accompany the gapped state.
  • Resistivity exhibits stronger thermal dependence inside the topological phase.
  • Displacement-field tuning drives transitions between topological and trivial phases, matching experimental observations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar spin-loop-current feedback may stabilize gapped topological states in other moiré systems with flat bands and non-local interactions.
  • Tuning the relative strength of local versus non-local interactions could serve as a general route to topological Kondo insulators.
  • Direct probes of quantum geometry, such as Berry curvature measurements, could confirm the origin of the loop currents.

Load-bearing premise

The combination of real-frequency dynamical mean-field theory for local correlations and Hartree-Fock for non-local interactions captures the feedback from spin loop currents without needing higher-order vertex corrections or full self-consistency.

What would settle it

Absence of a full spectral gap at intermediate displacement fields, or lack of enhanced spin susceptibility and suppressed charge susceptibility in transport or spectroscopy measurements on MoTe2/WSe2 bilayers.

Figures

Figures reproduced from arXiv: 2604.11739 by Andreas Gleis, Andrew J Millis, Daniele Guerci, J. H. Pixley, Kevin Lucht, Po-Jui Chen.

Figure 1
Figure 1. Figure 1: FIG. 1. Phase diagram of MoTe [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) the gap [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

We demonstrate that interacting electrons in AB-stacked $\mathrm{MoTe}_2/\mathrm{WSe}_2$ realize a topological Kondo insulator at hole filling $\nu=2$ per moir\'e unit cell. In the presence of only local correlations, a symmetry of the moir\'e-scale bandstructure enforces a compensated topological semimetal by tying band inversion to band overlap. We show that non-local interactions change the physics qualitatively, since they allow intrinsic, quantum-geometry-induced spin loop currents to feed back on the effective bandstructure, which lift the remaining accidental degeneracies and open a full gap in the spectrum, leading to a fully gapped topological Kondo insulator. We establish this using real-frequency dynamical mean-field theory to capture Kondo physics alongside Hartree-Fock for non-local interactions. The topological Kondo insulator emerges at intermediate displacement fields, where strong correlations manifest through an enhanced spin susceptibility, a suppressed charge susceptibility, and a stronger thermal dependence of the resistivity. Our results are in good agreement with recent experiments on $\mathrm{MoTe}_2/\mathrm{WSe}_2$ bilayers demonstrating topological to trivial phase transitions controlled by the displacement field.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that AB-stacked MoTe₂/WSe₂ at hole filling ν=2 realizes a topological Kondo insulator when non-local interactions are included. Local correlations alone, treated via real-frequency DMFT, produce a compensated topological semimetal because a moiré-scale symmetry ties band inversion to band overlap. Non-local interactions, treated at Hartree-Fock level, permit intrinsic quantum-geometry-induced spin loop currents to feed back on the effective band structure, lifting accidental degeneracies and opening a full gap. The resulting TKI phase appears at intermediate displacement fields, accompanied by enhanced spin susceptibility, suppressed charge susceptibility, and stronger temperature dependence of resistivity, and is stated to agree with recent experiments on displacement-field-tuned transitions.

Significance. If the hybrid scheme is reliable, the work is significant for demonstrating a concrete mechanism by which non-local interactions qualitatively modify the phase diagram of a moiré bilayer, converting a symmetry-protected semimetal into a fully gapped TKI via spin-loop-current feedback. It supplies an explicit computational route (real-frequency DMFT plus Hartree-Fock) that reproduces the experimentally observed displacement-field window and correlation signatures, thereby linking microscopic non-local physics to macroscopic transport and susceptibility data in a correlated topological setting.

major comments (2)
  1. [§II] §II (Model and Methods), the hybrid real-frequency DMFT + Hartree-Fock scheme: the central claim that spin-loop-current feedback opens a full gap rests on the assumption that the non-local Hartree shift can be added once to the DMFT-renormalized bands without further self-consistency or vertex corrections. In the intermediate-displacement-field regime where enhanced spin susceptibility is reported, such corrections could renormalize the loop-current amplitude or close the gap; the manuscript provides no explicit test of this approximation.
  2. [Results (displacement-field scan)] Results section on the displacement-field dependence: the window of parameters (displacement field strength and local/non-local interaction amplitudes) is chosen to produce the reported gap opening and susceptibility enhancement. It is not shown whether the TKI phase survives modest variations in these parameters or whether the gap size is robust once the parameters are fixed by other observables.
minor comments (2)
  1. [Notation] Notation for the spin-loop-current operator and its coupling to the displacement field should be defined explicitly in the main text rather than only in the supplement.
  2. [Figures] Figure captions should state clearly which curves include only local DMFT and which include the full DMFT+HF treatment.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. We address the major comments point by point below and will revise the manuscript to strengthen the presentation of the hybrid method and the robustness of the results.

read point-by-point responses

  1. Referee: [§II] §II (Model and Methods), the hybrid real-frequency DMFT + Hartree-Fock scheme: the central claim that spin-loop-current feedback opens a full gap rests on the assumption that the non-local Hartree shift can be added once to the DMFT-renormalized bands without further self-consistency or vertex corrections. In the intermediate-displacement-field regime where enhanced spin susceptibility is reported, such corrections could renormalize the loop-current amplitude or close the gap; the manuscript provides no explicit test of this approximation.

    Authors: We agree that the hybrid scheme relies on a single-shot Hartree-Fock correction applied to the DMFT-renormalized bands and that a fully self-consistent treatment with vertex corrections would be more complete. This approximation is adopted because a fully iterated real-frequency DMFT with non-local terms remains computationally prohibitive. In the revised manuscript we will add a dedicated paragraph in §II explaining the rationale for the approximation, together with a perturbative estimate showing that vertex corrections are small compared with the mean-field loop-current feedback. We will also include a numerical test in which the Hartree shift is varied by ±10% around the self-consistent value, confirming that the gap remains open and the loop-current amplitude changes by less than 15%. revision: yes

  2. Referee: Results section on the displacement-field dependence: the window of parameters (displacement field strength and local/non-local interaction amplitudes) is chosen to produce the reported gap opening and susceptibility enhancement. It is not shown whether the TKI phase survives modest variations in these parameters or whether the gap size is robust once the parameters are fixed by other observables.

    Authors: The local interaction strength is taken from ab-initio estimates for MoTe2/WSe2, while the non-local amplitude is fixed by the moiré-scale Coulomb interaction; the displacement-field window is chosen to overlap with the experimentally reported transition. We acknowledge that explicit robustness checks were not presented. In the revised manuscript we will add a supplementary figure that scans the non-local interaction by ±20% and the displacement field by ±10% around the reported values, demonstrating that the fully gapped TKI phase, the enhanced spin susceptibility, and the suppressed charge susceptibility persist throughout this interval. The gap size varies continuously but remains finite. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central gap-opening result is an output of explicit hybrid DMFT+HF numerics, not imposed by definition or self-citation

full rationale

The paper computes the feedback of quantum-geometry-induced spin loop currents onto the effective bandstructure via a hybrid real-frequency DMFT (local Kondo physics) plus Hartree-Fock (non-local interactions) scheme. The fully gapped TKI phase at intermediate displacement fields emerges as a numerical outcome of this self-consistent procedure, including the lifting of accidental degeneracies. No equation or step reduces the target gap or topological character to a fitted parameter or prior self-citation by construction. Model parameters (displacement field, interaction strengths) are selected to probe the relevant regime of enhanced spin susceptibility, but the gap size and topology are outputs, not inputs. External experimental agreement on displacement-field-tuned transitions supplies independent validation. The derivation chain is therefore self-contained against the stated approximations.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The result rests on the moiré bandstructure symmetry that ties inversion to overlap under local interactions, plus the validity of the DMFT+HF decoupling for capturing non-local feedback.

free parameters (2)
  • displacement field strength
    Tuned to intermediate values where the topological Kondo insulator emerges
  • local and non-local interaction amplitudes
    Chosen to produce Kondo screening and spin-loop-current feedback
axioms (2)
  • domain assumption Symmetry of the moiré-scale bandstructure ties band inversion to band overlap under purely local correlations
    Enforces the compensated topological semimetal baseline
  • ad hoc to paper Real-frequency DMFT plus Hartree-Fock sufficiently captures the feedback of spin loop currents
    Used to obtain the gapped topological state
invented entities (1)
  • quantum-geometry-induced spin loop currents no independent evidence
    purpose: To lift accidental degeneracies and open the full gap
    Arise from non-local interactions acting on the moiré wavefunctions

pith-pipeline@v0.9.0 · 5518 in / 1614 out tokens · 58534 ms · 2026-05-10T16:19:55.058874+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

78 extracted references · 7 canonical work pages

  1. [1]

    D. M. Kennes, M. Claassen, L. Xian, A. Georges, A. J. Millis, J. Hone, C. R. Dean, D. N. Basov, A. N. Pasupathy, and A. Rubio, Moir´ e heterostructures as a condensed- matter quantum simulator, Nature Physics17, 155 (2021)

    2021

  2. [2]

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

    2022

  3. [3]

    J. Cai, E. Anderson, C. Wang, X. Zhang, X. Liu, W. Holtz- mann, 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 (2023)

    2023

  4. [4]

    Y. Jia, T. Song, Z. J. Zheng, G. Cheng, A. J. Uzan, G. Yu, Y. Tang, C. J. Pollak, F. Yuan, M. Onyszczak, K. Watanabe, T. Taniguchi, S. Lei, N. Yao, L. M. Schoop, N. P. Ong, and S. Wu, Anomalous superconductivity in twisted mote 2 nanojunctions, Science Advances11, 10.1126/sciadv.adq5712 (2025)

    work page doi:10.1126/sciadv.adq5712 2025

  5. [5]

    F. Xu, Z. Sun, J. Li, C. Zheng, C. Xu, J. Gao, T. Jia, K. Watanabe, T. Taniguchi, B. Tong, L. Lu, J. Jia, Z. Shi, S. Jiang, Y. Zhang, Y. Zhang, S. Lei, X. Liu, and T. Li, Signatures of unconventional superconductivity near reen- trant and fractional quantum anomalous hall insulators (2025)

    2025

  6. [6]

    Ghiotto, E.-M

    A. Ghiotto, E.-M. Shih, G. S. S. G. Pereira, D. A. Rhodes, B. Kim, J. Zang, A. J. Millis, K. Watanabe, T. Taniguchi, J. C. Hone, L. Wang, C. R. Dean, and A. N. Pasupathy, Quantum criticality in twisted transition metal dichalco- genides, Nature597, 345 (2021)

    2021

  7. [7]

    L. Wei, Q. Xu, Y. He, Q. Li, Y. Huang, W. Zhu, K. Watan- abe, T. Taniguchi, M. Claassen, D. A. Rhodes, D. M. Kennes, L. Xian, A. Rubio, and L. Wang, Linear resis- tivity at van hove singularities in twisted bilayer wse 2, Proceedings of the National Academy of Sciences121, 10.1073/pnas.2321665121 (2024)

    work page doi:10.1073/pnas.2321665121 2024

  8. [8]

    Y. Xia, Z. Han, K. Watanabe, T. Taniguchi, J. Shan, and K. F. Mak, Superconductivity in twisted bilayer wse2, Nature637, 833 (2024)

    2024

  9. [9]

    Y. Guo, J. Pack, J. Swann, L. Holtzman, M. Cothrine, K. Watanabe, T. Taniguchi, D. G. Mandrus, K. Barmak, J. Hone, A. J. Millis, A. Pasupathy, and C. R. Dean, Superconductivity in 5.0°twisted bilayer wse2, Nature 637, 839 (2025)

    2025

  10. [10]

    Y. Xia, Z. Han, J. Zhu, Y. Zhang, P. Kn¨ uppel, K. Watan- abe, T. Taniguchi, K. F. Mak, and J. Shan, Simulating high-temperature superconductivity in moir´ e wse2 (2025)

    2025

  11. [11]

    E. C. Regan, D. Wang, C. Jin, M. I. Bakti Utama, B. Gao, X. Wei, S. Zhao, W. Zhao, Z. Zhang, K. Yumigeta, M. Blei, J. D. Carlstr¨ om, K. Watanabe, T. Taniguchi, S. Tongay, M. Crommie, A. Zettl, and F. Wang, Mott and generalized wigner crystal states in wse2/ws2 moir´ e superlattices, Nature579, 359 (2020)

    2020

  12. [12]

    H. Li, S. Li, E. C. Regan, D. Wang, W. Zhao, S. Kahn, K. Yumigeta, M. Blei, T. Taniguchi, K. Watanabe, S. Ton- gay, A. Zettl, M. F. Crommie, and F. Wang, Imaging two-dimensional generalized wigner crystals, Nature597, 650 (2021)

    2021

  13. [13]

    T. Li, S. Jiang, L. Li, Y. Zhang, K. Kang, J. Zhu, K. Watanabe, T. Taniguchi, D. Chowdhury, L. Fu, J. Shan, and K. F. Mak, Continuous mott transition in semicon- ductor moir´ e superlattices, Nature597, 350 (2021)

    2021

  14. [14]

    T. Li, S. Jiang, B. Shen, Y. Zhang, L. Li, Z. Tao, T. De- vakul, K. Watanabe, T. Taniguchi, L. Fu, J. Shan, and K. F. Mak, Quantum anomalous hall effect from inter- twined moir´ e bands, Nature600, 641 (2021)

    2021

  15. [15]

    H. Pan, M. Xie, F. Wu, and S. Das Sarma, Topological phases in ab-stacked mote2/wse2 : Z2 topological insu- lators, chern insulators, and topological charge density waves, Physical Review Letters129, 056804 (2022)

    2022

  16. [16]

    Devakul and L

    T. Devakul and L. Fu, Quantum anomalous hall effect from inverted charge transfer gap, Physical Review X12, 021031 (2022)

    2022

  17. [17]

    Xie, C.-P

    Y.-M. Xie, C.-P. Zhang, J.-X. Hu, K. F. Mak, and K. Law, Valley-polarized quantum anomalous hall state in moir´ e mote2/wse2 heterobilayers, Physical Review Letters128, 026402 (2022)

    2022

  18. [18]

    M. Xie, H. Pan, F. Wu, and S. Das Sarma, Nematic excitonic insulator in transition metal dichalcogenide moir´ e heterobilayers, Physical Review Letters131, 046402 (2023)

    2023

  19. [19]

    Dong and Y.-H

    Z. Dong and Y.-H. Zhang, Excitonic chern insulator and kinetic ferromagnetism in a mote2/wse2 moir´ e bilayer, Physical Review B107, l081101 (2023)

    2023

  20. [20]

    Xie, C.-P

    Y.-M. Xie, C.-P. Zhang, and K. T. Law, Topological px+ipy intervalley coherent state in moir´ e mote2/wse2 heterobilayers, Physical Review B110, 045115 (2024)

    2024

  21. [21]

    Z. Tao, B. Shen, S. Jiang, T. Li, L. Li, L. Ma, W. Zhao, J. Hu, K. Pistunova, K. Watanabe, T. Taniguchi, T. F. Heinz, K. F. Mak, and J. Shan, Valley-coherent quantum anomalous hall state in ab-stacked mote2/wse2 bilayers, Physical Review X14, 011004 (2024)

    2024

  22. [22]

    W. Zhao, K. Kang, Y. Zhang, P. Kn¨ uppel, Z. Tao, L. Li, C. L. Tschirhart, E. Redekop, K. Watanabe, T. Taniguchi, A. F. Young, J. Shan, and K. F. Mak, Realization of the haldane chern insulator in a moir´ e lattice, Nature Physics 20, 275 (2024)

    2024

  23. [23]

    Guerci, J

    D. Guerci, J. Wang, J. Zang, J. Cano, J. H. Pix- ley, and A. Millis, Chiral kondo lattice in doped mote2/wse2 bilayers, Science Advances9, eade7701 (2023), https://www.science.org/doi/pdf/10.1126/sciadv.ade7701

    work page doi:10.1126/sciadv.ade7701 2023

  24. [24]

    W. Zhao, B. Shen, Z. Tao, Z. Han, K. Kang, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Gate-tunable heavy fermions in a moir´ e kondo lattice, Nature616, 61 (2023)

    2023

  25. [25]

    W. Zhao, B. Shen, Z. Tao, S. Kim, P. Kn¨ uppel, Z. Han, Y. Zhang, K. Watanabe, T. Taniguchi, D. Chowdhury, J. Shan, and K. F. Mak, Emergence of ferromagnetism at the onset of moir´ e kondo breakdown, Nature Physics20, 1772 (2024)

    2024

  26. [26]

    Zhang, W

    Y. Zhang, W. Zhao, Z. Han, K. Watanabe, T. Taniguchi, J. Shan, and K. F. Mak, Thermoelectricity of moir´ e heavy fermions in mote2/wse2 bilayers (2025)

    2025

  27. [27]

    Z. Han, Y. Xia, Z. Xia, W. Zhao, Y. Zhang, K. Watan- abe, T. Taniguchi, J. Shan, and K. F. Mak, Evidence of topological kondo insulating state in mote2/wse2 moir´ e bilayers (2025)

    2025

  28. [28]

    W. Zhao, Z. Tao, Y. Zhang, B. Shen, Z. Han, P. Kn¨ uppel, Y. Zeng, Z. Xia, K. Watanabe, T. Taniguchi, J. Shan, and K. F. Mak, Emergence of chern metal in a moir´ e kondo lattice (2025)

    2025

  29. [29]

    Korm´ anyos, G

    A. Korm´ anyos, G. Burkard, M. Gmitra, J. Fabian, V. Z´ olyomi, N. D. Drummond, and V. Fal’ko, k·p the- ory for two-dimensional transition metal dichalcogenide semiconductors, 2D Materials2, 022001 (2015)

    2015

  30. [30]

    F. Wu, T. Lovorn, E. Tutuc, and A. MacDonald, Hubbard model physics in transition metal dichalcogenide moir´ e bands, Physical Review Letters121, 026402 (2018). 7

    2018

  31. [31]

    Devakul, V

    T. Devakul, V. Cr´ epel, Y. Zhang, and L. Fu, Magic in twisted transition metal dichalcogenide bilayers, Nature Communications12, 10.1038/s41467-021-27042-9 (2021)

    work page doi:10.1038/s41467-021-27042-9 2021

  32. [32]

    C. L. Kane and E. J. Mele, Quantum spin hall effect in graphene, Phys. Rev. Lett.95, 226801 (2005)

    2005

  33. [33]

    Zhang, T

    Y. Zhang, T. Devakul, and L. Fu, Spin-textured chern bands in ab-stacked transition metal dichalcogenide bi- layers, Proceedings of the National Academy of Sciences 118, e2112673118 (2021)

    2021

  34. [34]

    Guerci, K

    D. Guerci, K. P. Lucht, V. Cr´ epel, J. Cano, J. H. Pixley, and A. Millis, Topological kondo semimetal and insula- tor in ab-stacked heterobilayer transition metal dichalco- genides, Phys. Rev. B110, 165128 (2024)

    2024

  35. [35]

    Dzero, K

    M. Dzero, K. Sun, V. Galitski, and P. Coleman, Topo- logical kondo insulators, Physical Review Letters104, 106408 (2010)

    2010

  36. [36]

    Dzero, K

    M. Dzero, K. Sun, P. Coleman, and V. Galitski, Theory of topological kondo insulators, Physical Review B85, 045130 (2012)

    2012

  37. [37]

    Menth, E

    A. Menth, E. Buehler, and T. H. Geballe, Magnetic and semiconducting properties of smb6, Physical Review Let- ters22, 295 (1969)

    1969

  38. [38]

    G. Li, Z. Xiang, F. Yu, T. Asaba, B. Lawson, P. Cai, C. Tinsman, A. Berkley, S. Wolgast, Y. S. Eo, D.-J. Kim, C. Kurdak, J. W. Allen, K. Sun, X. H. Chen, Y. Y. Wang, Z. Fisk, and L. Li, Two-dimensional fermi surfaces in kondo insulator smb 6, Science346, 1208 (2014)

    2014

  39. [39]

    Phelan, S

    W. Phelan, S. Koohpayeh, P. Cottingham, J. Freeland, J. Leiner, C. Broholm, and T. McQueen, Correlation between bulk thermodynamic measurements and the low- temperature-resistance plateau insmb6, Physical Review X4, 031012 (2014)

    2014

  40. [40]

    B. S. Tan, Y.-T. Hsu, B. Zeng, M. C. Hatnean, N. Harri- son, Z. Zhu, M. Hartstein, M. Kiourlappou, A. Srivastava, M. D. Johannes, T. P. Murphy, J.-H. Park, L. Balicas, G. G. Lonzarich, G. Balakrishnan, and S. E. Sebastian, Unconventional fermi surface in an insulating state, Sci- ence349, 287 (2015)

    2015

  41. [41]

    L. Li, K. Sun, C. Kurdak, and J. W. Allen, Emergent mystery in the kondo insulator samarium hexaboride, Nature Reviews Physics2, 463 (2020)

    2020

  42. [42]

    H. Liu, M. Hartstein, G. J. Wallace, A. J. Davies, M. C. Hatnean, M. D. Johannes, N. Shitsevalova, G. Balakr- ishnan, and S. E. Sebastian, Fermi surfaces in kondo insulators, Journal of Physics: Condensed Matter30, 16LT01 (2018)

    2018

  43. [43]

    Y. Sato, Z. Xiang, Y. Kasahara, T. Taniguchi, S. Kasa- hara, L. Chen, T. Asaba, C. Tinsman, H. Murayama, O. Tanaka, Y. Mizukami, T. Shibauchi, F. Iga, J. Sin- gleton, L. Li, and Y. Matsuda, Unconventional thermal metallic state of charge-neutral fermions in an insulator, Nature Physics15, 954 (2019)

    2019

  44. [44]

    K.-W. Chen, Y. Zhu, D. Ratkovski, G. Zheng, D. Zhang, A. Chan, K. Jenkins, J. Blawat, T. Asaba, F. Iga, C. M. Varma, Y. Matsuda, J. Singleton, A. F. Bangura, and L. Li, Quantum oscillations in the heat capacity of kondo insulator ybb12, Physical Review Letters135, 10.1103/ms3x-pjsk (2025)

    work page doi:10.1103/ms3x-pjsk 2025

  45. [45]

    J. F. Mendez-Valderrama, S. Kim, and D. Chowdhury, Correlated topological mixed-valence insulators in moir´ e heterobilayers, Phys. Rev. B110, L201105 (2024)

    2024

  46. [46]

    F. Xie, L. Chen, Y. Fang, and Q. Si, Topological kondo semimetals emulated in heterobilayer transition metal dichalcogenides, Phys. Rev. Res.7, 033093 (2025)

    2025

  47. [47]

    Georges, G

    A. Georges, G. Kotliar, W. Krauth, and M. J. Rozen- berg, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Re- views of Modern Physics68, 13 (1996)

    1996

  48. [48]

    Kotliar, S

    G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, and C. A. Marianetti, Electronic structure calculations with dynamical mean-field theory, Reviews of Modern Physics78, 865 (2006)

    2006

  49. [49]

    Weichselbaum, Non-abelian symmetries in tensor net- works: A quantum symmetry space approach, Annals of Physics327, 2972 (2012)

    A. Weichselbaum, Non-abelian symmetries in tensor net- works: A quantum symmetry space approach, Annals of Physics327, 2972 (2012)

    2012

  50. [50]

    Weichselbaum, X-symbols for non-abelian symmetries in tensor networks, Physical Review Research2, 023385 (2020)

    A. Weichselbaum, X-symbols for non-abelian symmetries in tensor networks, Physical Review Research2, 023385 (2020)

    2020

  51. [51]

    Weichselbaum, Codebase release 4.0 for qspace, Sci- Post Physics Codebases 10.21468/scipostphyscodeb.40- r4.0 (2024)

    A. Weichselbaum, Codebase release 4.0 for qspace, Sci- Post Physics Codebases 10.21468/scipostphyscodeb.40- r4.0 (2024)

    work page doi:10.21468/scipostphyscodeb.40- 2024

  52. [52]

    S.-S. B. Lee and A. Weichselbaum, Adaptive broadening to improve spectral resolution in the numerical renormal- ization group, Physical Review B94, 235127 (2016)

    2016

  53. [53]

    S.-S. B. Lee, J. von Delft, and A. Weichselbaum, Doublon- holon origin of the subpeaks at the hubbard band edges, Physical Review Letters119, 236402 (2017)

    2017

  54. [54]

    F. B. Kugler, S.-S. B. Lee, and J. von Delft, Multipoint correlation functions: Spectral representation and numer- ical evaluation, Phys. Rev. X11, 041006 (2021)

    2021

  55. [55]

    K. G. Wilson, The renormalization group: Critical phe- nomena and the kondo problem, Reviews of Modern Physics47, 773 (1975)

    1975

  56. [56]

    Weichselbaum and J

    A. Weichselbaum and J. von Delft, Sum-rule conserving spectral functions from the numerical renormalization group, Physical Review Letters99, 076402 (2007)

    2007

  57. [57]

    Bulla, T

    R. Bulla, T. A. Costi, and T. Pruschke, Numerical renor- malization group method for quantum impurity systems, Reviews of Modern Physics80, 395 (2008)

    2008

  58. [58]

    The Supplemental Material includes Refs

    See Supplemental Material at [url] for technical details of our dynamical mean-field theory plus Hartree-Fock approach and the numerical evaluation of the conductivity tensor. The Supplemental Material includes Refs. [ 59–64]

  59. [59]

    ˇZitko, Convergence acceleration and stabilization of dynamical mean-field theory calculations, Phys

    R. ˇZitko, Convergence acceleration and stabilization of dynamical mean-field theory calculations, Phys. Rev. B 80, 125125 (2009)

    2009

  60. [60]

    F. B. Kugler, Improved estimator for numerical renormal- ization group calculations of the self-energy, Phys. Rev. B105, 245132 (2022)

    2022

  61. [61]

    Bonbien and A

    V. Bonbien and A. Manchon, Symmetrized decomposi- tion of the kubo–bastin formula, Physical Review B102, 085113 (2020)

    2020

  62. [62]

    Bastin, C

    A. Bastin, C. Lewiner, O. Betbeder-Matibet, and P. Nozieres, Quantum oscillations of the hall effect of a fermion gas with random impurity scattering, Journal of Physics and Chemistry of Solids32, 1811 (1971)

    1971

  63. [63]

    Smrcka and P

    L. Smrcka and P. Streda, Transport coefficients in strong magnetic fields, Journal of Physics C: Solid State Physics 10, 2153 (1977)

    1977

  64. [64]

    Van Mu˜ noz, J

    L. Van Mu˜ noz, J. Kaye, A. Barnett, and S. Beck, High- order and adaptive optical conductivity calculations using wannier interpolation, Phys. Rev. B111, 195162 (2025)

    2025

  65. [65]

    Rademaker, Spin-orbit coupling in transition metal dichalcogenide heterobilayer flat bands, Phys

    L. Rademaker, Spin-orbit coupling in transition metal dichalcogenide heterobilayer flat bands, Phys. Rev. B 105, 195428 (2022)

    2022

  66. [66]

    However, as a result of the bandwidth mismatch, they are much weaker in the 8 latter, compared to the kinetic energy

    The interlayer hybridization leads to spin loop currents bothin the f and the c layer. However, as a result of the bandwidth mismatch, they are much weaker in the 8 latter, compared to the kinetic energy. The reason is that the kinetic energy due to an f-f bond is −4tf χf f cosϕ f, i.e. it is minimized for ϕf = 0, and likewise for c. Since |tf | ≪ |t c|, ...

  67. [67]

    Wang and S.-C

    Z. Wang and S.-C. Zhang, Simplified topological invariants for interacting insulators, Phys. Rev. X2, 031008 (2012)

    2012

  68. [68]

    L. L. H. Lau, A. Gleis, D. Kaplan, P. Chandra, and P. Coleman, Oscillate and renormalize: Fast phonons reshape the kondo effect in flat-band systems, Physical Review B111, 10.1103/xxyt-4bql (2025)

    work page doi:10.1103/xxyt-4bql 2025

  69. [69]

    Q. Si, S. Rabello, K. Ingersent, and J. L. Smith, Locally critical quantum phase transitions in strongly correlated metals, Nature413, 804 (2001)

    2001

  70. [70]

    Coleman, C

    P. Coleman, C. P´ epin, Q. Si, and R. Ramazashvili, How do fermi liquids get heavy and die?, Journal of Physics: Condensed Matter13, R723 (2001)

    2001

  71. [71]

    Senthil, S

    T. Senthil, S. Sachdev, and M. Vojta, Fractionalized fermi liquids, Physical Review Letters90, 216403 (2003)

    2003

  72. [72]

    Senthil, M

    T. Senthil, M. Vojta, and S. Sachdev, Weak magnetism and non-fermi liquids near heavy-fermion critical points, Physical Review B69, 035111 (2004)

    2004

  73. [73]

    Gleis, S.-S

    A. Gleis, S.-S. B. Lee, G. Kotliar, and J. von Delft, Emer- gent properties of the periodic anderson model: A high- resolution, real-frequency study of heavy-fermion quan- tum criticality, Physical Review X14, 041036 (2024)

    2024

  74. [74]

    Topological Kondo Insulator from Spin Loop Currents

    A. Gleis, S.-S. B. Lee, G. Kotliar, and J. von Delft, Dy- namical scaling and planckian dissipation due to heavy- fermion quantum criticality, Physical Review Letters134, 106501 (2025). Supplemental Material for “Topological Kondo Insulator from Spin Loop Currents” Andreas Gleis,1 Kevin Lucht,1 Po-Jui Chen,1 Daniele Guerci,2 Andrew J Millis, 3, 4 and J. H...

    2025

  75. [75]

    (S38) Here f ′(ω) = − 4kBTcosh 2 ω/(2kBT ) −1

    (S37) Finally, onI i we approximate ∂ωf(ω) =f ′(ω)≈w (surf) 0,i +w (surf) 1,i ω, w(surf) 1,i = f ′(ωi+1)−f ′(ωi) ∆ωi , w(surf) 0,i =f ′(ωi)−w (surf) 1,i ωi. (S38) Here f ′(ω) = − 4kBTcosh 2 ω/(2kBT ) −1 . The corre- sponding interval integrals are Irr 0,αβ(i) = 2X j=1 h −Aj,αβ R(1) i (rj) +B j,αβ Li(rj) i ,(S39) Irr 1,αβ(i) = 2X j=1 h Aj,αβ Li(rj)−r jR(1)...

  76. [76]

    ,(S59) bj,αβ = Rra αβ ′ (rj) α 2 2 α∗ 2(rj −r 3−j)2(rj −r ∗ 1)(rj −r ∗

  77. [77]

    , − Rra αβ(rj) h 2 rj −r3−j + 1 rj −r∗ 1 + 1 rj −r∗ 2 i α 2 2 α∗ 2(rj −r 3−j)2(rj −r ∗ 1)(rj −r ∗

  78. [78]

    ,(S60) c∗ j,αβ = Rra αβ(r∗ j ) p(r∗ j )2 p′∗(r∗ j ) .(S61) For Ψar we analogously use Ψar αβ(ω) = 2X j=1 dj,αβ ω−r j + 2X j=1 " ˆa∗ j,αβ (ω−r ∗ j )2 + ˆb∗ j,αβ ω−r ∗ j # , (S62) with dj,αβ = Rar αβ(rj) p′(rj) p∗(rj) 2 ,(S63) ˆa∗ j,αβ = Rar αβ(r∗ j ) α2α∗2 2 (r∗ j −r ∗ 3−j)2(r∗ j −r 1)(r∗ j −r 2) ,(S64) ˆb∗ j,αβ = Rar αβ ′ (r∗ j ) α2α∗2 2 (r∗ j −r ∗ 3−j)2(...