Phase diagram of insulating crystal and quantum Hall states in ABC-stacked trilayer graphene

In the presence of a perpendicular magnetic field, ABC-stacked trilayer graphene's chiral band structure supports a 12-fold degenerate N=0 Landau level (LL). Along with the valley and spin degrees of freedom, the zeroth LL contains additional quantum numbers associated with the LL orbital index $$. Remote inter-layer hopping terms and external potential difference $\Delta_{B}$ between the layers lead to LL splitting by introducing a gap $$ between the degenerate zero-energy triplet LL orbitals. Assuming that the spin and valley degrees of freedom are frozen, we study the phase diagram of this system resulting from competition of the single particle LL splitting and Coulomb interactions within the Hartree-Fock approximation at integer filling factors. Above a critical value $\Delta_{LL}^{c}$ of the external potential difference i,e, for $|\Delta_{LL}| >\Delta_{LL}^{c}$, the ground state is a uniform quantum Hall state where the electrons occupy the lowest unoccupied LL orbital index. For $|\Delta_{LL}| <\Delta_{LL}^{c}$ (which corresponds to large positive or negative values of $\Delta_{B}$) the uniform QH state is unstable to the formation of a crystal state at integer filling factors. This phase transition should be characterized by a Hall plateau transition as a function of $\Delta_{LL}$ at a fixed filling factor. We also study the properties of this crystal state and discuss its experimental detection.Comment: 16 pages with 13 figure

Rectified voltage induced by a microwave field in a confined two-dimensional electron gas with a mesoscopic static vortex

We investigate the effect of a microwave field on a confined two dimensional electron gas which contains an insulating region comparable to the Fermi wavelength. The insulating region causes the electron wave function to vanish in that region. We describe the insulating region as a static vortex. The vortex carries a flux which is determined by vanishing of the charge density of the electronic fluid due to the insulating region. The sign of the vorticity for a hole is opposite to the vorticity for adding additional electrons. The vorticity gives rise to non-commuting kinetic momenta. The two dimensional electron gas is described as fluid with a density which obeys the Fermi-Dirac statistics. The presence of the confinement potential gives rise to vanishing kinetic momenta in the vicinity of the classical turning points. As a result, the Cartesian coordinate do not commute and gives rise to a Hall current which in the presence of a modified Fermi-Surface caused by the microwave field results in a rectified voltage. Using a Bosonized formulation of the two dimensional gas in the presence of insulating regions allows us to compute the rectified current. The proposed theory may explain the experimental results recently reported by J. Zhang et al.Comment: 14 pages, 2 figure

How does triple-Pomeranchukon coupling modify F<SUB>2</SUB>(&#969;)?

The deep-inelastic electroproduction process is studied in the presence of high-mass diffractive dissociation. The first-order correction, in triple-Pomeranchukon coupling, to the structure function F2(&#969;) is explicitly calculated as &#948;F2(&#969;)=0.013ln&#969; and &#948;F2(&#969;)=0.11&#215;ln(1+0.11ln&#969;) for large &#969;, corresponding to &#945;P'=0 and &#945;P'=0.25 GeV-2, respectively. It is also shown that the diffractive peak of the inclusive cross section for e(&#956;)+p&#8594;e'(&#956;')+p'+X is completely fixed by available parameters from p+p'&#8594;p"+X and electroproduction structure functions