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 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.

arXiv:cond-mat/0401044Physical Review BSep 24, 20044 citations

On the quantum phase transition of a quantum Hall liquid

Adriaan M. J. Schakel

Nuclear Physics BOct 1, 19954 citations

Quantum Hall charge density waves under anisotropy: from first-order to continuous transitions

Yuchi He, Kang Yang, M. O. Goerbig +1 more

We investigate the quantum Hall charge density wave states in the $N=2$ Landau level under mass anisotropy. In the absence of anisotropy, there are two first-order phase transitions between the Wigner crystal, the $2$ -electron bubble phase, and the stripe phase. By adding mass anisotropy, our analytical and numerical studies show that the $2$ -electron bubble phase disappears and the stripe phase significantly enlarges its domain in the phase diagram. Meanwhile, a regime of stripe crystals that may be observed experimentally is unveiled after the bubble phase gets out. Upon increase of the anisotropy, the energy of the phases at the transitions becomes progressively smooth as a function of the filling. We conclude that all first-order phase transitions are replaced by continuous phase transitions, providing a possible realisation of continuous quantum crystalline phase transitions.We investigate the quantum Hall charge density wave states in the $N=2$ Landau level under mass anisotropy. In the absence of anisotropy, there are two first-order phase transitions between the Wigner crystal, the $2$-electron bubble phase, and the stripe phase. By adding mass anisotropy, our analytical and numerical studies show that the $2$-electron bubble phase disappears and the stripe phase significantly enlarges its domain in the phase diagram. Meanwhile, a regime of stripe crystals that may be observed experimentally is unveiled after the bubble phase gets out. Upon increase of the anisotropy, the energy of the phases at the transitions becomes progressively smooth as a function of the filling. We conclude that all first-order phase transitions are replaced by continuous phase transitions, providing a possible realisation of continuous quantum crystalline phase transitions.

Bulletin of the American Physical SocietyOct 1, 20200 citations

Two-dimensional Ising physics in quantum Hall ferromagnets

Tomas Jungwirth, Allan H. MacDonald, Edward H. Rezayi

Physica E Low-dimensional Systems and NanostructuresJan 1, 20024 citations

We investigate the quantum Hall charge density wave states in the

N=2

Landau level under mass anisotropy. In the absence of anisotropy, there are two first-order phase transitions between the Wigner crystal, the

2

-electron bubble phase, and the stripe phase. By adding mass anisotropy, our analytical and numerical studies show that the

2

-electron bubble phase disappears and the stripe phase significantly enlarges its domain in the phase diagram. Meanwhile, a regime of stripe crystals that may be observed experimentally is unveiled after the bubble phase gets out. Upon increase of the anisotropy, the energy of the phases at the transitions becomes progressively smooth as a function of the filling. We conclude that all first-order phase transitions are replaced by continuous phase transitions, providing a possible realisation of continuous quantum crystalline phase transitions.