Orbitally tuned composite-fermion metal-to-superfluid transitions

Abstract

The effective interaction between composite fermions, set entirely by the Coulomb potential and the underlying electronic Landau level orbitals, can stabilize exotic fractional quantum Hall states. In particular, half-filled Landau levels with different orbital character can host either metallic or paired phases of composite fermions. Here, we leverage experimental control over the orbital composition to realize a composite-fermion pairing transition in the first excited Landau level of bilayer graphene. Transport measurements at filling factors v = 9/2 and 11/2 reveal conductive states giving way to well-developed plateaus with increasing displacement fields. These states are insensitive to an in-plane magnetic field, indicating single-component ground states and thus pointing at non-Abelian orders. Our numerical study, based on displacement-field-dependent Landau-level wavefunctions, supports the orbital origin of the pairing transition and suggests Moore-Read or anti-Pfaffian ground states.

Figures (12)

• Figure 1: FQH states in the first excited LL of BLG. (a)$R_{xx}$ as a function of $\nu$ and $D$, taken at $T = 10~\mathrm{mK}$ and $B = 12~\mathrm{T}$. The insets illustrate how the displacement field tunes the single-electron wavefunction composition across the BLG sites. At increasing negative $D$, the weight shifts to the $A$ sites, which are occupied by $N=2$ orbitals for $4\leq\nu\leq 6$, and by $N=0$ orbitals for $6\leq\nu\leq8$. Half-filled FQH states emerge below $-540~\mathrm{mV/nm}$ at $\nu=\frac{9}{2}$ and $\frac{11}{2}$, but not at $\nu=\frac{13}{2},\frac{15}{2}$. (b) Longitudinal $R_{xx}$ and transverse $R_{xy}$ resistances as a function of $\nu$, taken at $D= -975~\mathrm{mV/nm}$, indicated by the dashed white line in panel (a). The $R_{xx}$ dips at $\nu=\frac{9}{2}$ and $\frac{11}{2}$ are accompanied by $R_{xy}$ plateaus, shown in the insets.
• Figure 2: Strength of paired and Jain FQH states as a function of $D$.(a) The activation gaps $\Delta$ at $\nu=\frac{9}{2}$ and $\frac{11}{2}$ increase with negative $D$. The insets above illustrate the orbital composition of the LL wavefunctions for low and high displacement fields. (b) The gaps of Jain states at $\nu=\frac{22}{5}$ and $\frac{27}{5}$ decrease over the displacement-field range where half-filled gaps increase. (c) The strengths of the resistance minima $\delta R_{xx}$ follow the same trend as the gaps in (a). $\delta R_{xx}$ was determined as illustrated in the inset for $|D|=975~\mathrm{mV/nm}$.
• Figure 3: Spin polarization of half-filled states. $R_{xx}$ measurements around $\nu=\frac{9}{2}$ at $T=10~\mathrm{mK}$ and $B_\perp=9~\mathrm{T}$ for different in-plane magnetic fields $B_\parallel$. The inset shows $\delta R_{xx}$ at $\nu=\frac{9}{2}$ as a function of $B_\parallel$.
• Figure 4: Orbital composition and many-body ground states in the first excited LL of BLG.(a) The single-electron states in BLG's first excited LL are composed of $N=0,1,2$ orbital wavefunctions. At $\nu=\frac{9}{2}$, a negative $D$ enhances the $N=2$ component at the expense of $N=0$, and vice versa at $\frac{15}{2}$. (b) The overlap between the Coulomb ground state and trial wavefunctions. The ground state changes from a CFL to a Moore--Read state as $|D|$ increases at $\nu=\frac{9}{2}$, but remains a CFL over the entire displacement-field range at $\nu=\frac{15}{2}$.
• Figure S1: FQH states in the first excited LL of BLG in D1. $R_{xx}$ as a function of $\nu$ and $D$ for $4\leq\nu\leq8$ at $T = 10~\mathrm{mK}$ and $B = 12~\mathrm{T}$. Even-denominator FQH states appear at $\nu=\frac{9}{2}$ and $\nu=\frac{11}{2}$ at high displacement fields.