The Conjugate Composite Fermi Liquid
Abstract: Recent experimental observations of the fractional quantum anomalous Hall effect in spin/valley polarized moir\'{e} systems call for a more expansive theoretical exploration of strongly correlated physics in partially filled topological bands. In this work we study a state that we refer to as the conjugate-composite Fermi liquid (cCFL), which arises when a pair of Chern bands with opposite Chern numbers are both half-filled. We demonstrate that the cCFL is the parent state of various interesting phenomena. As an example, we demonstrate that with the existence of an inplane spin order, the cCFL could be driven into a quantum bad metal phase, in the sense that it is a metallic phase whose zero temperature longitudinal resistivity is finite, but far greater than the Mott-Ioffe-Regal limit, i.e. $\rhoe_{xx} \gg h/e2$. The bad metal phase is also accompanied with a new Wiedemann-Franz law, meaning the thermal conductivity is proportional to the electrical resistivity rather than conductivity. Other proximate phases of the cCFL such as superconductivity and a chiral spin liquid phase can occur when the composite fermions (CF) form the inter-valley CF-exciton condensate.
- Z. Dong, A. S. Patri, and T. Senthil, Theory of fractional quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures, arXiv e-prints , arXiv:2311.03445 (2023), arXiv:2311.03445 [cond-mat.str-el] .
- B. Zhou, H. Yang, and Y.-H. Zhang, Fractional quantum anomalous Hall effects in rhombohedral multilayer graphene in the moiréless limit and in Coulomb imprinted superlattice, arXiv e-prints , arXiv:2311.04217 (2023), arXiv:2311.04217 [cond-mat.str-el] .
- X.-Y. Song, Y.-H. Zhang, and T. Senthil, Phase transitions out of quantum hall states in moiré tmd bilayers (2023), arXiv:2308.10903 [cond-mat.str-el] .
- C. L. Kane and E. J. Mele, Quantum spin hall effect in graphene, Phys. Rev. Lett. 95, 226801 (2005a).
- C. L. Kane and E. J. Mele, Z2subscript𝑍2{Z}_{2}italic_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT topological order and the quantum spin hall effect, Phys. Rev. Lett. 95, 146802 (2005b).
- M. Barkeshli, C.-M. Jian, and X.-L. Qi, Theory of defects in abelian topological states, Physical Review B 88, 10.1103/physrevb.88.235103 (2013).
- M. Cheng, Superconducting proximity effect on the edge of fractional topological insulators, Phys. Rev. B 86, 195126 (2012).
- B. I. Halperin, P. A. Lee, and N. Read, Theory of the half-filled landau level, Phys. Rev. B 47, 7312 (1993).
- D. T. Son, Is the composite fermion a dirac particle?, Phys. Rev. X 5, 031027 (2015).
- N. Morales-Durán, N. Wei, and A. H. MacDonald, Magic angles and fractional chern insulators in twisted homobilayer tmds (2023), arXiv:2308.03143 [cond-mat.str-el] .
- N. Paul, Y. Zhang, and L. Fu, Giant proximity exchange and flat chern band in 2d magnet-semiconductor heterostructures, Science Advances 9, 10.1126/sciadv.abn1401 (2023).
- C. Wang and T. Senthil, Composite fermi liquids in the lowest landau level, Phys. Rev. B 94, 245107 (2016a).
- M. P. A. Fisher, G. Grinstein, and S. M. Girvin, Presence of quantum diffusion in two dimensions: Universal resistance at the superconductor-insulator transition, Phys. Rev. Lett. 64, 587 (1990).
- S. Giombi, G. Tarnopolsky, and I. R. Klebanov, On c j and c t in conformal qed, Journal of High Energy Physics 2016, 10.1007/jhep08(2016)156 (2016).
- Y. Huh, P. Strack, and S. Sachdev, Conserved current correlators of conformal field theories in 2+1 dimensions, Phys. Rev. B 88, 155109 (2013).
- F. Evers and A. D. Mirlin, Anderson transitions, Rev. Mod. Phys. 80, 1355 (2008).
- V. J. Emery and S. A. Kivelson, Superconductivity in bad metals, Phys. Rev. Lett. 74, 3253 (1995).
- S. Kim, T. Senthil, and D. Chowdhury, Continuous mott transition in moiré semiconductors: role of long-wavelength inhomogeneities (2022).
- S.-S. Lee, Stability of the u(1) spin liquid with a spinon fermi surface in 2+1212+12 + 1 dimensions, Phys. Rev. B 78, 085129 (2008).
- P. A. Lee and N. Nagaosa, Gauge theory of the normal state of high-tcsubscript𝑡𝑐{\mathit{t}}_{\mathit{c}}italic_t start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT superconductors, Phys. Rev. B 46, 5621 (1992).
- M. E. Peskin, Mandelstam-’t hooft duality in abelian lattice models, Annals of Physics 113, 122 (1978).
- C. Dasgupta and B. I. Halperin, Phase transition in a lattice model of superconductivity, Phys. Rev. Lett. 47, 1556 (1981).
- M. P. A. Fisher and D. H. Lee, Correspondence between two-dimensional bosons and a bulk superconductor in a magnetic field, Phys. Rev. B 39, 2756 (1989).
- L. Zou and D. Chowdhury, Deconfined metallic quantum criticality: A u(2)𝑢2u(2)italic_u ( 2 ) gauge-theoretic approach, Phys. Rev. Res. 2, 023344 (2020).
- I. Mandal, Critical fermi surfaces in generic dimensions arising from transverse gauge field interactions, Phys. Rev. Res. 2, 043277 (2020).
- V. Kalmeyer and R. B. Laughlin, Equivalence of the resonating-valence-bond and fractional quantum hall states, Phys. Rev. Lett. 59, 2095 (1987).
- C.-J. Lee and M. Mulligan, Universal conductivity at a 2d superconductor-insulator transition: the effects of quenched disorder and coulomb interaction (2023), arXiv:2308.05155 [cond-mat.str-el] .
- J. Wu and P. Phillips, Vortex glass is a metal: Unified theory of the magnetic-field and disorder-tuned bose metals, Phys. Rev. B 73, 214507 (2006).
- N. Myerson-Jain, C.-M. Jian, and C. Xu, Vortex fermi liquid and strongly correlated quantum bad metal (2022), arXiv:2209.04472 [cond-mat.str-el] .
- Y.-H. Zhang, Composite fermion insulator in opposite-fields quantum hall bilayers (2018), arXiv:1810.03600 [cond-mat.str-el] .
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