Bosonization Approach for Bilayer Quantum Hall Systems atνT=1

Abstract

We develop a non-perturbative bosonization approach for bilayer quantum Hall systems at νT = 1, which allows us to systematically study the existence of an exciton condensate in these systems. An effective boson model is derived and the excitation spectrum is calculated both in the Bogoliubov and in the Popov approximations. In the latter case, we show that the ground state of the system is an exciton condensate only when the distance between the layers is very small compared to the magnetic length, indicating that the system possibly undergoes another phase transition before the incompressible-compressible one. The effect of a finite electron interlayer tunnelling is included and a quantitative phase diagram is proposed.

Trial wave functions forν=12+12quantum Hall bilayers

“…Conversely, for small enough spacing between the two layers the ground state is known to be the interlayer coherent "111 state", which we can think of as a composite boson (CB), or interlayer exciton condensate, 4 with strong interlayer correlations and intralayer correlations which are weaker than those of the composite fermion Fermi sea. 1 While the nature of these two limiting states is reasonably well understood, the nature of the states at intermediate d is less understood and has been an active topic of both theoretical 3,5,6,7,8,9,10,11,12,13,14,15,16 and experimental interest. 17,18,19,20,21,22,23,24,25,26,27 Although there are many interesting questions remaining that involve more complicated experimental situations, within the current work we always consider a zero temperature bilayer system with zero tunnelling between the two layers and no disorder.…”

Finite-momentum condensate of magnetic excitons in a bilayer quantum Hall system

“…12 This analogy motivated us to employ the bosonization scheme 13 to study the bilayer QHS at ν T = 1. Our main finding in this first study 14 was that a zero-momentum BEC of magnetic excitons is stable only for d 0.4 (zero interlayer tunneling case). Such a result is in quite good agreement with the exact diagonalization calculations on finite-size systems, which show that the overlap between the exact ground state and the 111 state is close to unit only for d 0.5 .…”

“…In this paper, we revisit the bilayer QHS within the bosonization formalism 13,14 focusing on the intermediate d/ region. We propose that within this bosonic scheme, the ground state of the system can be seen as a finite-momentum BEC of magnetic excitons.…”

“…3), we show that such a BEC is indeed a stable solution for certain values of d/ provided that the excitation spectrum is gapped. Here, the boson-boson interaction potential (14) plays an important role in the stability of this phase. In the following, we consider 0.1 Q 2 and 0.1 d 4 .…”

Excitonic gap generation in thin-film topological insulators

“…particle-hole bound states in bilayer systems [18][19][20][21][22]. At the microscopic level, Hubbard-like Hamitonians have been employed in the study of exciton condensation in monolayer [23] and bilayer graphene [24], bilayer quantum Hall systems [18,25,26] and in 3D thin-film TIs in the class AII [27][28][29]. In the latter case, the electron-hole pairs residing on the surface states can condense to form a topological exciton condensate.…”