Intrinsic Gap and Exciton Condensation in the ${\nu }_T=1$ Bilayer System

We investigate the quasiparticle excitation of the bilayer quantum Hall (QH) system at a total filling factor ${\nu }_T=1$ in the limit of negligible interlayer tunneling under a tilted magnetic field. We show that the intrinsic quasiparticle excitation is of purely pseudospin origin and solely governed by the inter- and intralayer electron interactions. A model based on exciton formation successfully explains the quantitative behavior of the quasiparticle excitation gap, demonstrating the existence of a link between the excitonic QH state and the composite fermion liquid. Our results provide a new insight into the nature of the phase transition between the two states.

Figure 1

(a) Longitudinal $R_{xx}$ and Hall $R_{xy}$ resistances as a function of the perpendicular magnetic field $B_{\perp }$ for two tilt angles $\theta =0°$ (dashed lines) and 55° (solid lines) at the fixed $d/{\ell }_B=2.04$. Inset: activation measurements of $R_{xx}$ at $d/{\ell }_B=2.04$ for six different tilt angles between $\theta =33°$ and 65°. (b) Quasiparticle excitation gap $\Delta$ as a function of total magnetic field $B$ for $\theta =0°$, 33°, 42°, 48°, 55°, 61°, and 65°. Different symbols correspond to different values of $d/{\ell }_B$.

Figure 2

Quasiparticle excitation gap $\Delta$ as a function of $B_{\perp }$, measured at different tilted angles. Inset: calculated energies of the QH (solid line) and partially polarized compressible states (dashed lines), $E_{\mathrm{QH}}$ and $E_{\mathrm{CF}}^{\mathrm{PP}}$, respectively, the latter for different angles. The energies refer to the fully polarized compressible state $E_{\mathrm{CF}}$ (horizontal line).

Figure 3

Normalized gap $\Delta /E_C$ as a function of $d/{\ell }_B$ measured at $\theta =0°$, 33°, 42°, 48°, 55°, 61°, and 65°. The solid line is the gap obtained from the model (without fitting parameters). The inset shows how the gap $\Delta$ opens around the Fermi level ($\equiv E_{\mathrm{CF}}$) with decreasing $d/{\ell }_B$.