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 regime of wide parabolic wells and zero width double well (bilayer) systems. We propose a general class of variational wavefunctions that describe several types of parity, spin, and translational symmetry breaking, including spin and charge density wave phases. 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. A conceptually new aspect of our theory is the predicted possibility for the spontaneous breaking of parity symmetry, which indicates a ``ferroelectric'' quantum order in integer quantum Hall systems and has not been considered in the literature before.
Highlights
Unidirectional charge density wave orderalso called stripe orderin quantum HallQHsystems has been extensively studied1 since the first theoretical prediction in 1996 ͑Refs. 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,6–8 liquid crystal phases,1,9 reorientation of stripe directions,10–12 and reentrant integer quantum Hall effect,13 have been widely explored both theoretically and experimentally in this context
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
We develop a detailed theory in this paper for possible spontaneous symmetry breaking and associated exotic quantum order in both wide-well and double-well integer quantum Hall systems by considering the symmetry properties of the realistic system Hamiltonians
Summary
Unidirectional charge density wave orderalso called stripe orderin quantum HallQHsystems has been extensively studied since the first theoretical prediction in 1996 ͑Refs. 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, liquid crystal phases, reorientation of stripe directions, and reentrant integer quantum Hall effect, have been widely explored both theoretically and experimentally in this context. Following our earlier work based on the collective mode dispersion, in this paper we carry out the ground state energetic calculation within the Hartree-Fock approximation to obtain and describe these exotic phases, which break isospin rotation, parity, and/or translational symmetries. Based on our HF calculation results, we suggest the existence of skyrmion stripe phase, breaking both spin rotational and translational symmetries near the degenerate point of W2Ј systems, may be responsible for the resistance anisotropy observed recently in Ref. 15. ͑Including four rather than two levels in many-body wave functions was shown to be crucial for establishing the many-body canted antiferromagnetic state in bilayer systems at ϭ2.33͒ We will divide the Hartree-Fock variational energies and the related numerical results into the following four sections: wide well systems at ϭ2Nϩ1 ͑Sec. IVand at ϭ2Nϩ2 ͑Sec. V; double well systems at total filling factor ϭ4Nϩ1 ͑Sec. VIand at ϭ4Nϩ2 ͑Sec. VII. Many analytic details discussed in the main text are shown in Appendix
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