Fig. 3: Localized QH exciton on an antidot.

a Top gate-dependent transverse resistance showing quasi-periodic valleys on the \({f}^{{\prime} }=-1\) plateau. Inset: shift of resistance oscillations under varying magnetic fields. The curves are displaced on the y-axis for clarity. b Color-mapped antidot tunneling conductance versus doping inside and outside the antidot. The yellow dotted straight lines trace the random jumps in conductance peak traces along constant top gate voltages. The black dotted curves are guides to the eyes for the anti-crossing-like features, which are associated with tunneling through the electron-hole pairing states. The yellow dotted rectangle highlights a pronounced exciton state, which is discussed quantitatively in the text. c Antidot tunneling conductance curves inside the yellow dotted rectangle in (b), shifted in the y-axis direction for clarity. The dashed lines highlight the evolution of the position of the conductance peaks. d Qualitative schematic showing gate tuning of the antidot levels for the outer (hole) and inner (electron) antidot modes. The red and blue lines correspond to electron- and hole-associated levels, respectively. Bottom right plot: the energy levels spread out with increasing magnitude of top gate voltage. Due to the energy offset between the \({f}^{{\prime} }=\pm 1\) Landau levels (\({\varepsilon }_{g}\)), the electron- and hole- antidot levels can cross each other, resulting in resonances and pairing. Here we highlight the shift of an electron level and a hole level (thick red and blue lines in the \(E({V}_{{TG}})\) plot and the red and blue solid circles in the Landau level diagrams) under changing top gate voltage, with corresponding Landau level diagrams at top gate voltages of 0, \({V}_{1}\) and \({V}_{2}\) shown in panels ①, ②, and ③. Panel ① inset: device schematic where Landau level diagrams are along the dotted line. The blue and the apricot regions illustrate the antidot/couplers and the bulk regions, respectively.