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Unconventional features of relativistic Dirac/Weyl quasi-particles in topological materials are most evidently manifested in the 2D quantum Hall effect (QHE), whose variety is further enriched by their spin and/or valley polarization.…
The $\nu = 1$ quantum Hall ground state in materials like GaAs is well known to be ferromagnetic in nature. The exchange part of the Coulomb interaction provides the necessary attractive force to align the electron spins spontaneously. The…
Monolayer graphene at charge neutrality in a quantizing magnetic field is a quantum Hall ferromagnet. Due to the spin and valley (near) degeneracies, there is a plethora of possible ground states. Previous theoretical work, based on a…
The collective modes of stripes in double layer quantum Hall systems are computed using the time-dependent Hartree-Fock approximation. It is found that, when the system possesses spontaneous interlayer coherence, there are two gapless…
We numerically investigate the quantum phases and phase transition in a system made of two species of fermionic atoms that interact with each other via $s$-wave Feshbach resonance, and are subject to rotation or a synthetic gauge field that…
We report on the dramatic evolution of the quantum Hall ferromagnet in the fractional quantum Hall regime at $\nu = 2/5$ filling. A large enhancement in the characteristic timescale gives rise to a dynamical transition into a novel…
We study a two-electron quantum dot molecule in a magnetic field by the direct diagonalization of the Hamiltonian matrix. The ground states of the molecule with the total spin S=0 and S=1 provide a possible realization for a qubit of a…
We study intersubband spin density collective modes in double-layer quantum Hall systems at $\nu=2$ within the time-dependent Hartree-Fock approximation. We find that these intersubband spin density excitations may soften under…
Two-dimensional electron gases in strong magnetic fields provide a canonical platform for realizing a variety of electronic ordering phenomena. Here we review the physics of one intriguing class of interaction-driven quantum Hall states:…
The phase diagram of diluted magnetic semiconductor quantum wells is investigated. The interaction between the carriers in the hole gas can lead to first order ferromagnetic transitions, which remain abrupt in applied fields. These…
We have experimentally confirmed the quantum Hall ferromagnetic state with Chern number \nu=0, characterized by the helical edge state, in a layered organic Dirac fermion system \alpha-(BEDT-TTF)_2I_3. The interlayer resistance saturates at…
Valley-polarized quantum Hall states in graphene are described by a Heisenberg O(3) ferromagnet model, with the ordering type controlled by the strength and sign of valley anisotropy. A mechanism resulting from electron coupling to…
We present the phase diagram of a ferromagnetic quantum Hall effect liquid in a narrow quantum well with vanishing single-particle Zeeman splitting, $\epsilon_{{\rm Z}}$ and pronounced spin-orbit coupling. Upon decreasing $\epsilon_{{\rm…
In a quantum Hall ferromagnet, the spin polarization of the two-dimensional electron system can be dynamically transferred to nuclear spins in its vicinity through the hyperfine interaction. The resulting nuclear field typically acts back…
We investigate the quantum phase transition of itinerant ferromagnets. It is shown that correlation effects in the underlying itinerant electron system lead to singularities in the order parameter field theory that result in an effective…
Quantum dots in the fractional quantum Hall regime are studied using a Hartree formulation of composite fermion theory. Under appropriate conditions the chemical potential of the dots will oscillate periodically with B due to the transfer…
In the quantum Hall regime of graphene, antiferromagnetic and spin-polarized ferromagnetic states at the zeroth Landau level compete, leading to a canted antiferromagnetic state depending on the direction and magnitude of an applied…
We derive an effective field-theoretical model for the one-dimensional collective mode associated with a domain wall in a quantum Hall ferromagnetic state, as realized in confined graphene systems at zero filling. To this end, we consider…
In a lattice model subject to a perpendicular magnetic field, when the lattice constant is comparable to the magnetic length, one enters the "Hofstadter regime," where continuum Landau levels become fractal magnetic Bloch bands. Strong…
Magnetic semiconductor quantum dots with a few carriers represent an interesting model system where ferromagnetic interactions can be tuned by voltage. By designing the geometry of a doped quantum dot, one can tailor the anisotropic quantum…