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

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 (QH) regime of wide parabolic wells and zero width double well (bilayer) systems. Spin, isospin (associated with the layer index in the bilayer systems), 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 (un)polarized QH states, but also several many-body states that are only slightly higher in energy (within the Hartree-Fock theory) 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 phase). In a bilayer system at the filling factor $\nu =4N\pm 1,$ where N is an integer, we obtain an isospin spiral stripe phase in addition to the known (in)commensurate phases and the stripe phase without isospin winding. We do not find a charge or spin density wave instability in the bilayer system at $\nu =4N+2,$ 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 field) may lead to interesting quantum phases and transitions among them.