Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators

Abstract

Recent experiments reported evidence of superconductivity and re-entrant integer quantum anomalous Hall (RIQAH) insulator upon doping the ${\nu }_e=2/3$ fractional quantum anomalous Hall states (FQAH) in twisted MoTe${}_2$, separated by narrow resistive regions. Anyons of a FQAH generally have a finite effective mass, and when described by anyon-flux composite fermions (CF), experience statistical magnetic fields with a commensurate filling. Here, we show that most of the experimental observations can be explained by invoking the effects of disorder on the Landau-Hofstadter bands of CFs. In particular, by making minimal assumptions about the anyon energetics and dispersion, we show that doping anyons drives plateau transitions of CFs into integer quantum Hall states, which physically corresponds to either to a superconductor or to a RIQAH phase. We develop a dictionary that allows us to infer the response in these phases and the critical regions from the knowledge of the response functions of the plateau transitions. In particular, this allows us to relate the superfluid stiffness of the superconductor to the polarizability of CFs. As a first step towards a quantitative understanding, we borrow results from the celebrated integer quantum Hall plateau transitions to make quantitative prediction for the critical behavior of the superfluid stiffness, longitudinal and Hall conductivity, and response to out-of-plane magnetic field, all of which agree reasonably well with the experimental observations. Our results provide strong support for anyon superconductivity being the mechanism for the observed superconductor in the vicinity of the ${\nu }_e=2/3$ FQAH insulator.

v2, 5 pages, 3 figures

References in corpus (16)

• Anderson Transitions
• Fractional quantum Hall states at zero magnetic field
• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Observation of Fractionally Quantized Anomalous Hall Effect
• Fractional quantum Hall effect in the absence of Landau levels
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Engineering geometrically flat Chern bands with Fubini-Study Kähler structure
• Wave function multifractality and dephasing at metal-insulator and quantum Hall transitions
• Microscopic Mechanism of Anyon Superconductivity Emerging from Fractional Chern Insulators
• Molecular anyons in fractional quantum Hall effect
• Electromagnetic response and emergent topological orders in transition metal dichalcogenide MoTe${}_2$ bilayers
• Apparent inconsistency between Streda formula and Hall conductivity in reentrant integer quantum anomalous Hall effect in twisted MoTe${}_2$

Cited by in corpus (3)

• Spinless and spinful charge excitations in moiré Fractional Chern Insulators
• Anyon Dispersion in Aharonov-Casher Bands and Implications for Twisted MoTe${}_2$
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor