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Comptes Rendus Physique

Quantum transitions in bilayer states

Vincent Pasquier

Published Jan 1, 2002• 0 citations
Publisher

Abstract

The possible phase transitions when two layers at filling factor ν t =1 are gradually separated are studied in this article. In the bosonic case the system should undergo a pairing transition from a Fermi liquid to an incompressible state. In the Fermionic case, the state evolves from an incompressible (1,1,1) state to a Fermi liquid. It is speculated that there is an intermediate phase involving charge two quasiparticles.

DOI
10.1016/s1631-0705(02)01365-8

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Quantum transition in bilayer states

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The possible phase transitions when two layers at filling factor ν t =1 are gradually separated are studied in this article. In the bosonic case the system should undergo a pairing transition from a Fermi liquid to an incompressible state. In the Fermionic case, the state evolves from an incompressible (1,1,1) state to a Fermi liquid. It is speculated that there is an intermediate phase involving charge two quasiparticles.
I study the possible phase transitions when two layers at filling factor νt=1ν_t=1νt​=1 are gradually separated. In the bosonic case the system should undergo a pairing transition from a Fermi liquid to an incompressible state. In the Fermionic case, the state evolves from an incompressible (1,1,1)(1,1,1)(1,1,1) state to a Fermi liquid. I speculate that there is an intermediate phase involving charge two quasiparticles.
The phase diagram of a quantum Hall bilayer at total filling ν = 1 contains an incompressible superfluid for small distances d between the layers, as well as the compressible phase corresponding to two uncoupled Fermi liquids for large d. Using exact diagonalization on the sphere and torus geometry, we investigate a long-standing question of the nature of the transition between the two regimes, and the possibility for the existence of a paired phase in the transition region. We find considerable evidence for a direct transition between the superfluid and the Fermi liquid phase, based in particular on the behavior of the ground state energy on the sphere (including appropriate finite-size corrections) as a function of d. At the critical distance dC ≈ 11.6ℓB the topological number ("shift") of the ground state changes, suggesting that tuning the layer separation d in experiment likely leads to a direct transition between the superfluid and the Fermi liquid phase.
We show that the wave functions that describe the ground states of putative p-wave-paired phases in quantum Hall bilayers, like the Pfaffian at νT = 1/2 or the paired phase at νT = 1, are more likely to describe the excited states of Fermi liquids at these filling factors. We point out to the close competition between Fermi liquid and paired phases, which leads to the conclusion that in the experiments only direct transitions from the correlated 111 and 331 states into Fermi liquid(s) are likely to be observed.
The Quantum Hall Bilayers (QHB) at filling factor $\ensuremath{\nu}=1$ represents a competition between Bose-Einstein condensation (BEC) at small distances between layers and fermionic condensation, whose influence grows with distance and results in two separate Fermi liquid states for the underlying quasiparticles at very large (or infinite) distances. The question that can be raised is whether, at intermediate distances between layers, a distinct phase exists or if a singular transition occurs, with the possibility that this happens at infinite distances. Here, using a dipole representation for fermionic quasiparticles, we find support for the latter scenario: Within a large and relevant range of distances, BEC condensation, identified as Cooper sss-wave pairing of dipole quasiparticles, prevails over both Cooper ppp-wave pairing and sss-wave excitonic pairing of the same quasiparticles.
We construct a class of composite fermion states for bilayer electron systems in a strong transverse magnetic field, and determine quantitatively the phase diagram as a function of the layer separation, layer thickness, and electron density, while neglecting interlayer tunneling. We find, in general, that there are several transitions, and that the incompressible phases are separated by compressible ones. The paired states of composite fermions, described by Pfaffian wave functions, are also considered.
We study the phase diagram of quantum Hall bilayer systems with total filing ν_{T}=1/2+1/2 of the lowest Landau level as a function of layer distances d. Based on numerical exact diagonalization calculations, we obtain three distinct phases, including an exciton superfluid phase with spontaneous interlayer coherence at small d, a composite Fermi liquid at large d, and an intermediate phase for 1.1<d/l_{B}<1.8 (l_{B} is the magnetic length). The transition from the exciton superfluid to the intermediate phase is identified by (i) a dramatic change in the Berry curvature of the ground state under twisted boundary conditions on the two layers and (ii) an energy level crossing of the first excited state. The transition from the intermediate phase to the composite Fermi liquid is identified by the vanishing of the exciton superfluid stiffness. Furthermore, from our finite-size study, the energy cost of transferring one electron between the layers shows an even-odd effect and possibly extrapolates to a finite value in the thermodynamic limit, indicating the enhanced intralayer correlation. Our identification of an intermediate phase and its distinctive features shed new light on the theoretical understanding of the quantum Hall bilayer system at total filling ν_{T}=1.