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arXiv:1809.02679 · Physical review. B./Physical review. B

Exciton condensation in quantum Hall bilayers at total filling νT=5

Zheng Zhu, Shao-Kai Jian, D. N. Sheng

Published May 20, 2019• 5 citations
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Abstract

Quantum Hall bilayers have proven to be an inexhaustible platform for emerging exotic states and novel phase transitions in the strongly correlated arena. Here, the authors study coupled quantum Hall bilayers at half-filled first excited Landau levels by varying the layer distance. The authors find a continuous transition between the exciton superfluid phase and two copies of the Moore-Read state. This transition breaks symmetry and changes topology simultaneously, providing an exotic example of a quantum phase transition beyond the Landau paradigm.

DOI
10.1103/physrevb.99.201108

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Quantum Hall bilayers have proven to be an inexhaustible platform for emerging exotic states and novel phase transitions in the strongly correlated arena. Here, the authors study coupled quantum Hall bilayers at half-filled first excited Landau levels by varying the layer distance. The authors find a continuous transition between the exciton superfluid phase and two copies of the Moore-Read state. This transition breaks symmetry and changes topology simultaneously, providing an exotic example of a quantum phase transition beyond the Landau paradigm.
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.
Deconfined quantum critical points (DQCPs) represent an unconventional class of quantum criticality beyond the Landau-Ginzburg-Wilson-Fisher paradigm. Nevertheless, both their theoretical identification and experimental realization remain challenging. Here we report compelling evidence of a DQCP in quantum Hall bilayers with half-filled n=2n=2n=2 Landau levels in each layer, based on large-scale variational uniform matrix product state (VUMPS) simulations and exact diagonalization (ED). By systematically analyzing the ground-state fidelity, low-lying energy spectra, exciton superfluid and stripe order parameters, and ground-state energy derivatives, we identify a direct and continuous quantum phase transition between two distinct symmetry-breaking phases by tuning the layer separation: an exciton superfluid phase with spontaneous U(1)U(1)U(1) symmetry breaking at small separation, and a unidirectional charge density wave with broken translational symmetry at large separation. Our results highlight quantum Hall bilayers as an ideal platform for realizing and experimentally probing DQCPs under precisely tunable interactions.
XY* transitions represent one of the simplest examples of unconventional quantum criticality, in which fractionally charged excitations condense into a superfluid and display novel features that combine quantum criticality and fractionalization.Nevertheless, their experimental realization is challenging.Here we propose to study the XY* transition in quantum Hall bilayers at filling ðν 1 ; ν 2 Þ ¼ ð 1 3 ; 2 3 Þ where the exciton condensate (EC) phase plays the role of the superfluid.Supported by exact diagonalization calculation, we argue that there is a continuous transition between an EC phase at small bilayer separation to a pair of decoupled fractional quantum Hall states at large separation.The transition is driven by condensation of a fractional exciton, a bound state of a Laughlin quasiparticle and quasihole, and is in the XY* universality class.The fractionalization is manifested by unusual properties including a large anomalous exponent and fractional universal conductivity, which can be conveniently measured through interlayer tunneling and counterflow transport, respectively.We also show that the edge is likely to realize the newly predicted extraordinary log boundary criticality.Our work highlights the promise of quantum Hall bilayers as an ideal platform for exploring exotic bulk and boundary critical behaviors that are amenable to immediate experimental exploration in dual-gated bilayer systems.The XY* critical theory can be generalized to a bilayer system with an arbitrary Abelian state in one layer and its particle-hole partner in the other layer.Therefore, we anticipate many distinct XY* transitions corresponding to the different Laughlin states and Jain sequences in the single-layer case.
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 construct a mapped bilayer quantum Hall system to realize the proposal that two nearly flatbands have opposite Chern numbers. For the C = ±1 case, the two Landau levels of the bilayer experience opposite magnetic fields. We consider a mapped bilayer quantum Hall system at total filling ν t = 1 2 + 1 2 where the intralayer interaction is repulsive and the interlayer interaction is attractive. We take exact diagonalization (ED) calculations on a torus to study the phase transition when the separation distance d/lB is driven. The critical point at d c/lB = 0.68 is characterized by a collapse of degeneracy and a crossing of energy levels. In the region d/lB < d c/lB , the states of each level are highly degenerate. The pair-correlation function indicates electrons with opposite pseudo-spins are strong correlated at r = 0. We find an exciton stripe phase composed of bound pairs. The ferromagnetic ground state is destroyed by the strong effective attractive potential. An electron composite-Fermion (eCF) and a hole composite Fermion (hCF) are tightly bound. In the region d/lB > d c/lB , a crossover from the d → d c limit to the large d limit is observed. The electron and hole composite Fermion liquids (CFL) are realized by composite Fermions (CF) which attach opposite fluxes, respectively.
We discuss monolayer and bilayer quantum Hall systems in which each layer is a half-filled Landau level (LL) system. In the mean field approximation of the Son's formalism, there is a common pairing structure that underlines the possibilities for paired ground states in both systems. We argue that the particle-hole (PH) Pfaffian state in the (particle-hole symmetric) half-filled LL of a monolayer, and analogous state in the PH symmetric bilayer (in which each layer is half-filled LL) can be considered as critical states, i.e., states that cannot describe a phase under PH symmetry. We point out that the inclusion of a PH symmetry breaking (like LL mixing) may stabilize the PH Pfaffian in a monolayer. In the bilayer case, in numerical experiments on a sphere, by choosing the PH symmetric shift, we can stabilize the interlayer correlated (111) excitonic state or critical state, for any distance between the layers, but in general, with no bias, the evolution of the bilayer includes other phases.