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

Abstract

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.

Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances

“…Several theoretical scenarios [22][23][24][25][26][27][28][29][30][31][32][33][34][35] have been proposed for understanding the transition between the exciton superfluid and CFL at intermediate layer distances. Due to its non-perturbative nature, controlled analytical method for this problem is still lacking, and numerical techniques have been playing an important role.…”

Tilt-Induced Anisotropic Phases in Wide GaAs Quantum Wells

“…However in bilayer systems the presence of interlayer coupling may allow for the formation of more exotic phases. Indeed, the possibility of coherent stripe phases has been studied theoretically [7][8][9][10][11][12][13]. In particular, a tilt-induced transition from a quantum Hall state to various isospin stripe phases at odd values of filling factor in the N≥1 Landau levels has been predicted to occur for certain system parameters [9][10][11].…”

Global phase diagram ofν=2quantum Hall bilayers in tilted magnetic fields

“…We note that Ref. 16 considered the possibility of nonuniform phases in bilayer quantum Hall systems at =2 in the case of equal electron densities in the two layers. The conclusion of that work was that charge or spin density wave phases were never stabilized in the realistic range of parameters.…”