Intrinsic Gap and Exciton Condensation in the ĖT = 1 Bilayer System
Paula Giudici, Koji Muraki, Norio Kumada, and Toshimasa Fujisawa
Physical Science Laboratory
@A system comprising two layers of two-dimensional electron systems (2DES) closely separated at a distance of 20-30 nm, termed a bilayer electron system, exhibits unusual properties not seen in single-layer systems. In particular, for a system where macroscopically degenerate discrete levels (Landau levels), formed in each layer by a magnetic field applied perpendicular to the 2D plane, are half filled by electrons (i.e., total filling factor ĖT = 1) and the interlayer distance d is small enough so that the interlayer interaction is strong, many interesting phenomena, including dissipationless flow of electrical current oppositely directed in the two layers suggestive of excitonic superfluidity , have been reported. On the other hand, when d is large enough so that the two layers behave independently, the system exhibits a metallic behavior, which is believed to reflect the Fermi surface formed by composite particles consisting of electrons and magnetic flux quanta.
@The nature of the quantum phase transition between these largely dissimilar quantum states has long been a subject of both theoretical and experimental interest. However, in a recent study  we have shown that, in the standard experimental conditions, where a GaAs double quantum well is subjected to a perpendicular magnetic field, the metallic phase is not fully spin polarized and, as a result, the experimentally observed transition is governed by the Zeeman energy, which results in a first order transition with different nature than that of a quantum phase transition expected for an ideal spinless system. In this study, by tilting the magnetic field with respect to the sample normal and thereby enhancing the Zeeman energy, we investigated the nature of the intrinsic phase transition without any spin effects . As the Zeeman energy is increased, the energy gap of the excitonic phase saturates at a value (intrinsic gap) that depends solely on the ratio between the interlayer distance d and the in-plane electron distance lB (Fig. 1) and its amplitude coincides with twice the energy difference between the two states (Fig. 2). These results suggest that this phase transition is of second order and the condensate is formed from the metallic state through exciton formation.
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 P. Giudici, K. Muraki, N. Kumada, and T. Fujisawa, Phys. Rev. Lett 104 (2010) 056802.
Fig.. 1. Energy gap of the excitonic phase at different d/lB
plotted as a function of the total magnetic field.
Fig.. 2. Intrinsic gap vs d/lB and comparison with
twice the energy difference (solid line).