Spin exchange in quantum rings and wires in the Wigner-crystal limit

We present a controlled method for computing the exchange coupling in strongly correlated one-dimensional electron systems. It is based on the asymptotically exact relation between the exchange constant and the pair-correlation function of spinless electrons. Explicit results are obtained for thin quantum rings with realistic Coulomb interactions, by calculating this function via a many-body instanton approach.Comment: 7 pages, 2 figures. Changes in the text and figures to improve readability; added reference

Solitonic Excitations in Linearly Coherent Channels of Bilayer Quantum Hall Stripes

In some range of interlayer distances, the ground state of the two-dimensional electron gas at filling factor nu =4N+1 with N=0,1,2,... is a coherent stripe phase in the Hartree-Fock approximation. This phase has one-dimensional coherent channels that support charged excitations in the form of pseudospin solitons. In this work, we compute the transport gap of the coherent striped phase due to the creation of soliton-antisoliton pairs using a supercell microscopic unrestricted Hartree-Fock approach. We study this gap as a function of interlayer distance and tunneling amplitude. Our calculations confirm that the soliton-antisoliton excitation energy is lower than the corresponding Hartree-Fock electron-hole pair energy. We compare our results with estimates of the transport gap obtained from a field-theoretic model valid in the limit of slowly varying pseudospin textures.Comment: 15 pages, 8 figure

Cyclotron resonance in a two-dimensional electron gas with long-range randomness

We show that the the cyclotron resonance in a two-dimensional electron gas has non-trivial properties if the correlation length of the disorder is larger than the de Broglie wavelength: (a) the lineshape assumes three different forms in strong, intermediate, and weak magnetic fields (b) at the transition from the intermediate to the weak fields the linewidth suddenly collapses due to an explosive growth in the fraction of electrons with a diffusive-type dynamics.Comment: A few typos correcte

Ground state phase diagram of 2D electrons in a high Landau level: - DMRG study

The ground state phase diagram of 2D electrons in a high Landau level (index N=2) is studied by the density matrix renormalization group method. Pair correlation functions are systematically calculated for various filling factors from v=1/8 to 1/2. It is shown that the ground state phase diagram consists of three different CDW states called stripe-phase, bubble-phase, and Wigner crystal. The boundary between the stripe and the bubble phases is determined to be v_c = 0.38, and that for the bubble phase and Wigner crystal is v_c = 0.24. Each transition is of first order.Comment: 4 pages, 6 figure

Local Geometry of the Fermi Surface and Magnetoacoustic Responce of Two-Dimensional Electron Systems in Strong Magnetic Fields

A semiclassical theory for magnetotrasport in a quantum Hall system near filling factor $\nu = 1/2$ based on the Composite Fermions physical picture is used to analyze the effect of local flattening of the Composite Fermion Fermi surface (CF-FS) upon magnetoacoustic oscllations. We report on calculations of the velocity shift and attenuation of a surface acoustic wave (SAW) which travels above the two-dimensional electron system, and we show that local geometry of the CF-FS could give rise to noticeable changes in the magnitude and phase of the oscillations. We predict these changes to be revealed in experiments, and to be used in further studies of the shape and symmetries of the CF-FS. Main conclusions reported here could be applied to analyze magnetotransport in quantum Hall systems at higher filling factors $\nu = 3/2, 5/2$ provided the Fermi-liquid-like state of the system.Comment: 7 pages, 2 figure

Skyrme and Wigner crystals in graphene

At low-energy, the band structure of graphene can be approximated by two degenerate valleys $(K,K^{\prime})$ about which the electronic spectra of the valence and conduction bands have linear dispersion relations. An electronic state in this band spectrum is a linear superposition of states from the $A$ and $B$ sublattices of the honeycomb lattice of graphene. In a quantizing magnetic field, the band spectrum is split into Landau levels with level N=0 having zero weight on the $B(A)$ sublattice for the $$ valley. Treating the valley index as a pseudospin and assuming the real spins to be fully polarized, we compute the energy of Wigner and Skyrme crystals in the Hartree-Fock approximation. We show that Skyrme crystals have lower energy than Wigner crystals \textit{i.e.} crystals with no pseudospin texture in some range of filling factor $\nu$ around integer fillings. The collective mode spectrum of the valley-skyrmion crystal has three linearly-dispersing Goldstone modes in addition to the usual phonon mode while a Wigner crystal has only one extra Goldstone mode with a quadratic dispersion. We comment on how these modes should be affected by disorder and how, in principle, a microwave absorption experiment could distinguish between Wigner and Skyrme crystals.Comment: 14 pages with 11 figure

A model of large volumetric capacitance in graphene supercapacitors based on ion clustering

Electric double layer supercapacitors are promising devices for high-power energy storage based on the reversible absorption of ions into porous, conducting electrodes. Graphene is a particularly good candidate for the electrode material in supercapacitors due to its high conductivity and large surface area. In this paper we consider supercapacitor electrodes made from a stack of graphene sheets with randomly-inserted "spacer" molecules. We show that the large volumetric capacitances C > 100 F/cm^3 observed experimentally can be understood as a result of collective intercalation of ions into the graphene stack and the accompanying nonlinear screening by graphene electrons that renormalizes the charge of the ion clusters.Comment: 13 pages, 5 figures; additional discussion and supporting calculations adde

Ground-state energy of the electron liquid in ultrathin wires

The ground-state energy and the density correlation function of the electron liquid in a thin one-dimensional wire are computed. The calculation is based on an approximate mapping of the problem with a realistic Coulomb interaction law onto exactly solvable models of mathematical physics. This approach becomes asymptotically exact in the limit of small wire radius but remains numerically accurate even for modestly thin wires.Comment: (v3) Replaced with the published version. 4 pages, 1 figur

Orientation of the Stripe Formed by the Two-Dimensional Electrons in Higher Landau Levels

Effect of periodic potential on the stripe phase realized in the higher Landau levels is investigated by the Hartree-Fock approximation. The period of the potential is chosen to be two to six times of the fundamental period of the stripe phase. It is found that the stripe aligns perpendicularly to the external potential in contrast to a naive expectation and hydrodynamic theory. Charge modulation towards the Wigner crystallization along the stripe is essential for the present unexpected new result.Comment: 5 pages, RevTex, two figures included in the tex