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Holon metal, charge-density-wave and chiral superconductor from doping fractional Chern insulator and SU(3)$_1$ chiral spin liquid

Ya-Hui Zhang

TL;DR

The paper addresses the nature of compressible phases near doping of the ν$=-\tfrac{2}{3}$ FCI, proposing a dual description with doping a gapped SU(3)$_1$ chiral spin liquid. It derives a holon-metal state with three small Fermi pockets (charge $-e$ in the CSL case and $-e/3$ in the FCI case) and analyzes its instabilities toward a CDW metal; it further shows that an external magnetic field can stabilize the holon metal and induce quantum oscillations with frequency $f=\tfrac{3\hbar A_{\rm FS}}{e}$. The work also outlines two distinct routes to superconductivity: (i) conventional $p\pm ip$ pairing within a CDW metal, and (ii) intra-flavor pairing in the holon metal leading to a topologically enriched superconducting state. It connects these theoretical constructions to experiments in twisted MoTe$_2$, offering testable signatures such as the three-pocket Fermi surface, Hall responses, and magnetic-field-dependent oscillations. Overall, it provides a unified framework for understanding the interplay of holon metals, CDW order, and possible superconductivity near fractional Chern insulator doping.

Abstract

Recent experiments have observed superconductivity proximate to the nu = -2/3 fractional quantum anomalous Hall (FQAH) insulator in twisted MoTe2. A critical open question is whether the underlying normal state is a Fermi liquid with a large Fermi surface or a strongly correlated metal with low carrier density. In this work, we develop a theory of the phases emerging from doping the $ν= -2/3$ fractional Chern insulator (FCI). We establish a duality between this problem and doping a gapped SU(3)$_1$ chiral spin liquid (CSL).

Holon metal, charge-density-wave and chiral superconductor from doping fractional Chern insulator and SU(3)$_1$ chiral spin liquid

TL;DR

The paper addresses the nature of compressible phases near doping of the ν FCI, proposing a dual description with doping a gapped SU(3) chiral spin liquid. It derives a holon-metal state with three small Fermi pockets (charge in the CSL case and in the FCI case) and analyzes its instabilities toward a CDW metal; it further shows that an external magnetic field can stabilize the holon metal and induce quantum oscillations with frequency . The work also outlines two distinct routes to superconductivity: (i) conventional pairing within a CDW metal, and (ii) intra-flavor pairing in the holon metal leading to a topologically enriched superconducting state. It connects these theoretical constructions to experiments in twisted MoTe, offering testable signatures such as the three-pocket Fermi surface, Hall responses, and magnetic-field-dependent oscillations. Overall, it provides a unified framework for understanding the interplay of holon metals, CDW order, and possible superconductivity near fractional Chern insulator doping.

Abstract

Recent experiments have observed superconductivity proximate to the nu = -2/3 fractional quantum anomalous Hall (FQAH) insulator in twisted MoTe2. A critical open question is whether the underlying normal state is a Fermi liquid with a large Fermi surface or a strongly correlated metal with low carrier density. In this work, we develop a theory of the phases emerging from doping the fractional Chern insulator (FCI). We establish a duality between this problem and doping a gapped SU(3) chiral spin liquid (CSL).

Paper Structure

This paper contains 21 sections, 40 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Doping SU(2)$_1$ CSL and bosonic Laughlin state: anyon superfluid
  3. Doped SU(2)$_1$ CSL
  4. Doped bosonic Laughlin state
  5. Holon metal from doped SU(3)$_1$ CSL
  6. Property of the holon metal
  7. Alternative derivation and wavefunction
  8. Pairing instability and charge-density-wave trion Fermi liquid
  9. Dope FCI:holon metal and CDW metal
  10. Transport property
  11. Instability to CDW metal
  12. Stabilization of the holon metal and quantum oscillations under magnetic field
  13. Discussion on the experiment in twisted MoTe$_2$
  14. Conclusion
  15. Transport property for holon metal from doping the FCI
  16. ...and 6 more sections

Figures (1)

  • Figure 1: (a) Illustration of phase diagram with temperature and doping $n_e=\frac{1}{3}-x$ at small $x$. 'SC' indicates superconductor and 'CDW' indicates the CDW metal. Anyon gas can just crossover to the holon metal without any sharp phase transition. The holon metal is unstable to the CDW metal. A superconductor, if exists, may likely emerge within the CDW metal phase, but the microscopic pairing mechanism is unclear. (b) At a fixed $x$, an illustrated phase diagram with the temperature $T$ and the magnetic field $B$. In the holon metal phase, each pocket from $\psi_I$ feels an effective magnetic field of $-\frac{1}{3}B$, which can suppress the pairing and the instability into the CDW phase.