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 $ν_e = 2/3$ 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 $ν_e = 2/3$ FQAH insulator.

Figures (3)

• Figure 1: a) Cartoon of the finite temperature phase diagram in the vicinity of the $\nu_e=2/3$ FQAH state, as a function of doping $\nu_e$ and displacement field $D$ (after MoTe2SC). The red dotted line separates regions where we assume that $2/3$- and $1/3$-anyons are energetically more favorable. b) $2/3$-anyon dispersion with three minima in a Brillouin zone without disorder. Red solid lines denote filled LLs that appear due to statistical flux. Introduction of smooth potential disorder approximately preserves valley symmetry, but broadens levels within each valley. c) The density of states (with and without disorder) for the $2/3$-anyons.
• Figure 2: a) Schematic behavior of the superfluid stiffness $\kappa$ at $T=0$ and $D=0$ as a function of $\nu_e$. b,c) Schematic behavior of the (b) longitudinal resistivity $\rho_{xx}$ and (c) Hall resistivity $\rho_{xy}$ as a function of doping, at several different temperatures. The temperature dependence of $\rho_{xx}, \rho_{xy}$ is more pronounced in the SC and RIQAH states as compared to the $2/3$ plateau itself because their characteristic energy scales are governed by the doped anyon density and, thus, are much smaller than the parent FQAH gap. On the SC side, this asymmetry is further amplified by small superfluid stiffness at small doping.
• Figure 3: The boundary of the phases of interest, which are shaded in the plot. $\phi/\phi_0$ is the flux per unit cell. (Left) the boundaries of anyon superconductor resulting from doped $2/3$ anyons. (Right) the boundaries of RIQH state resulting from doped $1/3$ anyons. The green line is defined by $\delta \nu = \frac{2}{3}\delta\nu_B$ which represents the center of FQAH state. The parameters used in these plots are $\frac{\pi \tau}{m} = 10$ for $1/3$ anyons and $\frac{\pi \tau}{m} = 40$ for $2/3$ anyons, so chosen such that the results agree reasonably with Ref. MoTe2SC. Note that, in principle, the masses of an anyon on the electron- or hole-doping sides may differ, but here we neglect this fact for simplicity.