Topological Exciton Fermi Surfaces in Two-Component Fractional Quantized Hall Insulators

A wide variety of two-dimensional electron systems allow for independent control of the total and relative charge density of two-component fractional quantum Hall (FQH) states. In particular, a recent experiment on bilayer graphene (BLG) observed a continuous transition between a compressible and incompressible phase at total filling ${\nu }_T=\frac{1}{2}$ as charge is transferred between the layers, with the remarkable property that the incompressible phase has a finite interlayer polarizability. We argue that this occurs because the topological order of ${\nu }_T=\frac{1}{2}$ systems supports a novel type of interlayer exciton that carries Fermi statistics. If the fermionic excitons are lower in energy than the conventional bosonic excitons (i.e., electron-hole pairs), they can form an emergent neutral Fermi surface, providing a possible explanation of an incompressible yet polarizable state at ${\nu }_T=\frac{1}{2}$. We perform exact diagonalization studies that demonstrate that fermionic excitons are indeed lower in energy than bosonic excitons. This suggests that a “topological exciton metal” hidden inside a FQH insulator may have been realized experimentally in BLG. We discuss several detection schemes by which the topological exciton metal can be experimentally probed.

Figure 1

(a) The top panel shows the energy per electron $E(N_1=N_e,N_0=0)/N_e\to e_0$ when all electrons are in the $N=1$ layer. The odd-even effect [36] confirms that the Pfaffian ground state occurs for $N_e$ even, while $N_e$ odd corresponds to the ${\psi }_{\mathrm{NF}}$ excited state. Extrapolating the energy difference in $1/N_e$, we obtain the neutral fermion gap ${\mathrm{\Delta }}_{\mathrm{NF}}\sim 0.018$. In the bottom panel, we transfer one electron from the $N=1$ to the $N=0$ layer and measure the energy relative to the vacuum, $E_{ex}(N_e)=E(N_e-1,1)-e_0{N}_e$. There is again an odd-even effect, but reversed: the bosonic exciton (blue, $N_e=2m$) is considerably higher in energy than the fermionic exciton (red, $N_e=2m+1$). (b) The $f$-exc pair correlation function between the $N=0$, 1 layers, $g_{01}(r)$, shows that the electron and hole bind together into an exciton of size $\sim 4{\ell }_B$.