Striped states in quantum Hall effect: Deriving a low-energy theory from Hartree-Fock

Lopatnikova, Anna; Simon, Steven H.; Halperin, Bertrand I.; Wen, Xiao-Gang

doi:10.1103/physrevb.64.155301

Cited by 28 publications

(56 citation statements)

References 18 publications

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“…Most microscopic theories for the anisotropic state at ν = 9/2 (and in higher Landau levels) were built on this proposal. [27][28][29][30][31][32][33] The resulting picture of the stripe state is an array of "sliding" Luttinger liquids.…”

Section: 18mentioning

confidence: 99%

Nematic quantum phase transition of composite Fermi liquids in half-filled Landau levels and their geometric response

2016

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We present a theory of the isotropic-nematic quantum phase transition in the composite Fermi liquid arising in half-filled Landau levels. We show that the quantum phase transition between the isotropic and the nematic phase is triggered by an attractive quadrupolar interaction between electrons, as in the case of conventional Fermi liquids. We derive the theory of the nematic state and of the phase transition. This theory is based on the flux attachment procedure which maps an electron liquid in half-filled Landau levels into the composite Fermi liquid close to a nematic transition. We show that the local fluctuations of the nematic order parameters act as an effective dynamical metric interplaying with the underlying Chern-Simons gauge fields associated with the flux attachment. Both the fluctuations of the Chern-Simons gauge field and the nematic order parameter can destroy the composite fermion quasiparticles and drive the system into a non-Fermi liquid state. The effective field theory for the isotropic-nematic phase transition is shown to have z = 3 dynamical exponent due to the Landau damping of the dense Fermi system. We show that there is a Berry phase type term which governs the effective dynamics of the nematic order parameter fluctuations, which can be interpreted as a non-universal "Hall viscosity" of the dynamical metric. We also show that the effective field theory of this compressible fluid has a Wen-Zee-type term. Both terms originate from the time-reversal breaking fluctuation of the Chern-Simons gauge fields. We present a perturbative (one-loop) computation of the Hall viscosity and also show that this term is also obtained by a Ward identity. We show that the topological excitation of the nematic fluid, the disclination, carries an electric charge. We show that a resonance observed in radio-frequency conductivity experiments can be interpreted as a Goldstone nematic mode gapped by lattice effects.

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Section: 18mentioning

confidence: 99%

Nematic quantum phase transition of composite Fermi liquids in half-filled Landau levels and their geometric response

2016

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“…[34,35,36,37,38,39,40]). Recent work on these interesting phases of the two-dimensional electron gas has revealed that magnetic symmetry plays a crucial role in low-energy dynamics of these states.…”

Section: Discussionmentioning

confidence: 99%

Non-commutative Chern–Simons for the quantum Hall system and duality

2002

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The quantum Hall system is known to have two mutually dual Chern-Simons descriptions, one associated with the hydrodynamics of the electron fluid, and another associated with the statistics. Recently, Susskind has made the claim that the hydrodynamic Chern-Simons theory should be considered to have a non-commutative gauge symmetry. The statistical Chern-Simons theory has a perturbative momentum expansion. In this paper, we study this perturbation theory and show that the effective action, although commutative at leading order, is non-commutative. This conclusion is arrived at through a careful study of the three-point function of ChernSimons gauge fields. The non-commutative gauge symmetry of this system is thus a quantum symmetry, which we show can only be fully realized only through the inclusion of all orders in perturbation theory. We discuss the duality between the two non-commutative descriptions.

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“…2,3͒ and the first experimental observation in high Landau levels via the magnetoresistance anisotropy measurement in 1999. 4,5 Many related phenomena, e.g., transport via internal edge state excitations, [6][7][8] liquid crystal phases, 1,9 reorientation of stripe directions, [10][11][12] and reentrant integer quantum Hall effect, 13 have been widely explored both theoretically and experimentally in this context. Stripe formation at fractional filling factors ϭ(2Nϩ1)/(4Nϩ4) corresponding to the composite fermion filling factor *ϭN ϩ1/2 was also proposed to have energy lower than the conventional Laughlin liquid, composite-fermion Fermi sea, or paired composite-fermion state.…”

Section: Introductionmentioning

confidence: 99%

Spontaneous symmetry breaking and exotic quantum orders in integer quantum Hall systems under a tilted magnetic field

2003

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We use the microscopic Hartree-Fock approximation to investigate various quantum phase transitions associated with possible spontaneous symmetry breaking induced by a tilted magnetic field in the integral quantum Hall ͑QH͒ regime of wide parabolic wells and zero width double well ͑bilayer͒ systems. Spin, isospin ͑asso-ciated with the layer index in the bilayer systems͒, and orbital dynamics all play important roles in the quantum phase transitions being studied. We propose a general class of variational wave functions that describe several types of parity, spin, and translational symmetry breaking, including spin and charge density wave phases. In wide well systems at odd filling factors, we find a many-body state of broken parity symmetry for weak in-plane magnetic fields and an isospin skyrmion stripe phase, which simultaneously has isospin and charge modulation, for strong in-plane fields. In wide well systems at even filling factors, we find direct first order transitions between simple ͑un͒polarized QH states, but also several many-body states that are only slightly higher in energy ͑within the Hartree-Fock theory͒ than the ground state in strong in-plane field region. We suggest that going beyond the approximations used in this paper one may be able to stabilize such many-body phases with broken symmetries ͑most likely the skyrmion stripe phase͒. In a bilayer system at the filling factor ϭ4NϮ1, where N is an integer, we obtain an isospin spiral stripe phase in addition to the known ͑in͒com-mensurate phases and the stripe phase without isospin winding. We do not find a charge or spin density wave instability in the bilayer system at ϭ4Nϩ2, except for the known commensurate canted antiferromagnetic phase. Zero temperature quantum phase diagrams for these systems are calculated in the parameter regime of experimental interest. We discuss the symmetry properties of our predicted quantum phase diagrams and give a unified picture of these novel many-body phases. We point out how quantum level crossing phenomena in many situations ͑tuned by the applied tilted magnetic field͒ may lead to interesting quantum phases and transitions among them.

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Striped states in quantum Hall effect: Deriving a low-energy theory from Hartree-Fock

Cited by 28 publications

References 18 publications

Nematic quantum phase transition of composite Fermi liquids in half-filled Landau levels and their geometric response

Nematic quantum phase transition of composite Fermi liquids in half-filled Landau levels and their geometric response

Non-commutative Chern–Simons for the quantum Hall system and duality

Spontaneous symmetry breaking and exotic quantum orders in integer quantum Hall systems under a tilted magnetic field

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