Fractional quantum Hall effect in a tilted magnetic field

Papić, Zlatko

doi:10.1103/physrevb.87.245315

Cited by 49 publications

(65 citation statements)

References 80 publications

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“…The distinct anisotropies of the electron mass and dielectric tensor lead to an extra degree of freedom in Laughlin's variational scheme for fractional Hall state: the optimal coordinate rescaling parameter for the fractional state. This was demonstrated in variational as well as numerical studies of the anisotropic problem 2 , and later generalized to the case of tilted magnetic fields, where rotational symmetry is also broken 4 .…”

Section: Introductionmentioning

confidence: 88%

Connection between Fermi contours of zero-field electrons and ν=12 composite fermions in two-dimensional systems

2017

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We investigate the relation between the Fermi sea (FS) of zero-field carriers in two-dimensional systems and the FS of the corresponding composite fermions which emerge in a high magnetic field at filling ν = 1 2 , as the kinetic energy dispersion is varied. We study cases both with and without rotational symmetry, and find that there is generally no straightforward relation between the geometric shapes and topologies of the two FSs. In particular, we show analytically that the composite Fermi liquid (CFL) is completely insensitive to a wide range of changes to the zero-field dispersion which preserve rotational symmetry, including ones that break the zero-field FS into multiple disconnected pieces. In the absence of rotational symmetry, we show that the notion of 'valley pseudospin' in many-valley systems is generically not transferred to the CFL, in agreement with experimental observations. We also discuss how a rotationally symmetric band structure can induce a reordering of the Landau levels, opening interesting possibilities of observing higherLandau-level physics in the high-field regime.

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Section: Introductionmentioning

confidence: 88%

Connection between Fermi contours of zero-field electrons and ν=12 composite fermions in two-dimensional systems

2017

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“…The very fact that the application of an inplane magnetic field can induce a strong resistance anisotropy in the ν = 5/2 state has been well known for a number of years [40][41][42]. While the initial goal of the in-plane magnetic field experiment was to investigate the spin polarization of the 5/2 state [43], it had been realized that, in combination of finite sample thickness, the in-plane magnetic field played a much more complicated role than just increasing the Zeeman splitting energy [44,45]. In general, the in-plane magnetic field was believed to weaken the 5/2 FQHE state by generating various anisotropic effects, which eventually induce a transition to the anisotropic compressible states observed in the third or higher Landau levels [46], which are believed to be the stripe states [47][48][49][50][51].…”

Section: Introductionmentioning

confidence: 99%

Bilayer mapping of the paired quantum Hall state: Instability toward anisotropic pairing

Jeong

Park

2015

Phys. Rev. B

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One of the most dominant candidates for the paired quantum Hall (QH) state at filling factor ν = 5/2 is the Moore-Read (MR) Pfaffian state. A salient problem, however, is that it does not occur exactly at the Coulomb interaction, but rather at a modified interaction, which favors particle-hole symmetry breaking. In an effort to find a better state, in this work, we investigate the possible connection between the paired QH state and the antisymmetrized bilayer ground state, which is inspired by the intriguing identity that the MR Pfaffian state is entirely equivalent to the antisymmetrized projection of the bilayer QH state called the Halperin (331) state, which is valid at interlayer distance, d, roughly equal to the magnetic length, lB. Specifically, by using exact diagonalization in the torus geometry, we show that the exact 5/2 state at a given Haldane pseudopotential variation is intimately connected with the antisymmetrized bilayer ground state at a corresponding d/lB via one-to-one mapping, which we call the bilayer mapping. One of the most important discoveries in this work is that the paired QH state occurring at the Coulomb interaction is mapped onto the antisymmetrized bilayer ground state at d ≫ lB, which is equivalent to the antisymmetrized product state of two composite fermion seas at quarter filling, not the MR Pfaffian state. While maintaining high overlap with the paired QH state, the antisymmetrized bilayer ground state at d ≫ lB exhibits an abrupt change under the influence of small anisotropy. This suggests that the paired QH state occurring at the Coulomb interaction might be susceptible to anisotropic instability, opening up the possibility of anisotropic px or py-wave pairing instead of px ± ipy-wave pairing in the MR Pfaffian/anti-Pfaffian state.

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“…The mass anisotropy has a qualitatively similar effect as the in-plane field 23,25,49,50 , but it is much simpler to model theoretically. By calculating energy spectra and the static structure factors, we demonstrate that the incompressible MR state transitions into a compressible state with increasing the mass anisotropy.…”

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confidence: 99%

Anisotropy-driven transition from the Moore-Read state to quantum Hall stripes

Zhu¹,

Sodemann²,

Fu³

2017

Phys. Rev. B

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We investigate the nature of the quantum Hall liquid in a half-filled second Landau level (n = 1) as a function of band mass anisotropy using numerical exact diagonalization (ED) and density matrix renormalization group (DMRG) methods. We find increasing the mass anisotropy induces a quantum phase transition from the MooreRead state to a charge density wave state. By analyzing the energy spectrum, guiding center structure factors and by adding weak pinning potentials, we show that this charge density wave is a uni-directional quantum Hall stripe, which has a periodicity of a few magnetic lengths and survives in the thermodynamic limit. We find smooth profiles for the guiding center occupation function that reveal the strong coupling nature of the array of chiral Luttinger liquids residing at the stripe edges.

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Fractional quantum Hall effect in a tilted magnetic field

Cited by 49 publications

References 80 publications

Connection between Fermi contours of zero-field electrons and ν=12 composite fermions in two-dimensional systems

Connection between Fermi contours of zero-field electrons and ν=12 composite fermions in two-dimensional systems

Bilayer mapping of the paired quantum Hall state: Instability toward anisotropic pairing

Anisotropy-driven transition from the Moore-Read state to quantum Hall stripes

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