We investigate the double-layer electron system in a parabolic quantum well at filling factor nu=2 in a tilted magnetic field using capacitance spectroscopy. The competition between two ground states is found at the Zeeman splitting appreciably smaller than the symmetric-antisymmetric splitting. Although at the transition point the system breaks up into domains of the two competing states, the activation energy turns out to be finite, signaling the occurrence of a new insulator-insulator quantum phase transition. We interpret the obtained results in terms of a predicted canted antiferromagnetic phase.
We investigate the double-layer electron system in a parabolic quantum well at filling factor nu=2 in a tilted magnetic field using capacitance spectroscopy. The competition between two ground states is found at the Zeeman splitting appreciably smaller than the symmetric-antisymmetric splitting. Although at the transition point the system breaks up into domains of the two competing states, the activation energy turns out to be finite, signaling the occurrence of a new insulator-insulator quantum phase transition. We interpret the obtained results in terms of a predicted canted antiferromagnetic phase.
We perform a Hartree-Fock calculation in order to describe the ground state of a vertical double quantum dot in the absence of magnetic fields parallel to the growth direction. Intradot and interdot exchange interactions determine the singlet or triplet character of the system as the tunneling is tuned. At finite Zeeman splittings due to in-plane magnetic fields, we observe a quantum phase transition from a ferromagnetic to a symmetric phase through a canted antiferromagnetic state. The latter is obtained even at zero Zeeman energy for an odd number of electrons.
We study the nature of the many-body electron states (and quantum phase transitions between them) in a double-quantum-well structure under a strong external magnetic field as a function of the materials parameters that define the two-layer system, namely, the thickness of individual layers, the separation between them, the individual well potentials confining the electrons, and the potential barrier between them. Motivated by two recent experiments, we consider two different situations, one with (almost) no quantum tunneling between the wells, and the other with substantial interwell quantum tunneling. We use the spherical system finite-size exact diagonalization technique for our calculations. By calculating the overlap of our exact small-system numerical wave functions with various (postulated) analytic wave functions, we comment on the nature of the incompressibility for various Landau-level filling factors (\ensuremath{\nu}). We investigate, in particular details, the possibility of \ensuremath{\nu}=1/2 (i.e., 1/4 average occupancy in each well), and, 1 (i.e., 1/2 occupancy in each well) incompressible states where \ensuremath{\nu} is the total filling factor for the system. We also provide results for the \ensuremath{\nu}=2/3 situation. Our conclusion, based on our use of realistic system parameters in our calculations, is that in both the recent experimental realizations of the \ensuremath{\nu}=1/2 fractional quantum Hall effect, the relevant ground state is the so-called ``331'' state which is stabilized by the competition between intrawell and interwell electron-electron correlations.We calculate for various double-quantum-well structural parameters and magnetic fields the \ensuremath{\nu}=1/2 excitation spectra and the energy gaps, and compare it with the recent experimental data, obtaining excellent quantitative agreement. We provide a detailed quantum phase diagram for the \ensuremath{\nu}=1 state as a function of the interwell Coulomb interaction and the symmetric-antisymmetric single-particle gap, and find that the \ensuremath{\nu}=1 quantum Hall effect observed in the two recent experiments, in contrast to the \ensuremath{\nu}=1/2 effect, belongs in some sense to two different universality classes. We also predict the existence of a reentrant \ensuremath{\nu}=1 quantum Hall effect in double-quantum-well systems.
We use the time-dependent Hartree Fock approximation to study the collective-mode spectra of $\ensuremath{\nu}=2$ quantum Hall bilayers in tilted magnetic fields, allowing for charge imbalance as well as tunneling between the two layers. In a previous companion paper to this work, we studied the zero-temperature global phase diagram of this system, which was found to include symmetric and ferromagnetic phases as well as a first-order transition between two canted phases with spontaneously broken U(1) symmetry. We further found that this first-order transition line ends in a quantum critical point within the canted region. In the current work, we study the excitation spectra of all of these phases and pay particular attention to the behavior of the collective modes near the phase transitions. We find, most interestingly, that the first-order transition between the two canted phases is signaled by a near softening of a magnetoroton minimum. Many of the collective-mode features explored here should be accessible experimentally in light-scattering experiments.
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 $\ensuremath{\nu}=4N\ifmmode\pm\else\textpm\fi{}1,$ 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 $\ensuremath{\nu}=4N+2,$ 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.
We analyze the transitions that a magnetic field provokes in the ground state of an artificial homonuclear diatomic molecule. For that purpose, we have performed numerical diagonalizations for a double quantum dot around the regime of filling factor two. We present phase diagrams in terms of tunneling and Zeeman couplings, and confinement strength. We identify a series of transitions from ferromagnetic to symmetric states through a set of canted states with antiferromagnetic coupling between the two quantum dots.
We present details of earlier studies [Zheng et al., Phys. Rev. Lett. 78, 310 (1997) and Das Sarma et al., 79, 917 (1997)] and additional results on double-layer quantum Hall systems at a total filling $\ensuremath{\nu}=2{\ensuremath{\nu}}_{1}$, where a single layer at filling ${\ensuremath{\nu}}_{1}$ forms a ferromagnetic, fully spin-polarized, gapped incompressible quantum Hall state. For the case ${\ensuremath{\nu}}_{1}=1$, a detailed Hartree-Fock analysis is carried out on a realistic, microscopic Hamiltonian. Apart from the state continuously connected to the ground state of two well-separated layers, we find two double-layer quantum Hall phases: one with a finite interlayer antiferromagnetic spin ordering in the plane orthogonal to the applied field (the ``canted'' state), and the other a spin singlet. The quantum transitions between the various quantum Hall states are continuous, and are signaled by the softening of collective intersubband spin-density excitations. For the case of general ${\ensuremath{\nu}}_{1}$, closely related results are obtained by a semi-phenomenological continuum quantum field theory description of the low-lying spin excitations using a nonlinear $\ensuremath{\sigma}$ model. Because of its broken symmetry, the canted phase supports a linearly dispersing Goldstone mode and has a finite-temperature Kosterlitz-Thouless transition. We present results on the form of the phase diagram, the magnitude of the canted order parameter, the collective excitation dispersions, the specific heat, the form of the dynamic light-scattering spectrum at finite temperature, and the Kosterlitz-Thouless critical temperature. Our findings are consistent with recent experimental results.