No abstract

The ground state of a two-dimensional electron gas at Landau level filling factors near ν = 1 is a Skyrme crystal with long range order in the positions and orientations of the topologically and electrically charged elementary excitations of the ν = 1 ferromagnetic ground state. The lowest energy Skyrme crystal is a square lattice with opposing postures for topological excitations on opposite sublattices. The filling factor dependence of the electron spin-polarization, calculated for the square lattice Skyrme crystal, is in excellent agreement with recent experiments.PACS number 73.20.Dx The incompressible [1] ground state of a twodimensional electron gas (2DEG) at Landau level filling factor ν = 1 is ferromagnetic. (Here ν ≡ N/N φ is the ratio of the number of electrons to the orbital degeneracy of a Landau level; N φ = AB/Φ 0 = A/(2πℓ 2 ) where A is the area of the system, Φ 0 is the magnetic flux quantum, and B is the magnetic field strength.) Recently it has been shown [2-5] that, in the limit of weak Zeeman coupling, the lowest energy charged excitations of this state are spin-textures known as skyrmions. [6]. Skyrmions are the lowest energy topologically charged spin-texture excitations of the SU(2) non-linear σ (NLσ) model which describes the long wavelength properties of isotropic ferromagnets. The equivalence of physical charge and topological charge in the present system is a consequence [2,5] of the quantum Hall effect [1] and is responsible for the dominating role of skyrmions in determining many physical properties.Pioneering studies of skyrmions in the quantum Hall regime relied on NLσ models generalized [2,5] to account for Zeeman coupling to the spin and for the Hartree (electrostatic) interactions present when the charge density is non-uniform. States in the NLσ model are specified by a space-dependent unit vector which describes the local orientation of the spin magnetic moment. A skyrmion is characterized by the sign of its topological charge, by its size, and by the global orientation of the spin; with no Zeeman or Hartree coupling the energy of an isolated skyrmion is independent of all three. When Zeeman coupling is included the spin moment outside a skyrmion aligns with the field (m z = 1), the spin moment at the center of a skyrmion is oriented in opposition to the field (m z = −1). The perpendicular component (m ⊥ ) of the spin-moment, which must be non-zero as m z changes from −1 to 1, has a vortex at the skyrmion center. The global azimuthal orientation of m ⊥ is, importantly for the work described here, still arbitrary. Because the spinmoment is reversed in the interior of a skyrmion, Zeeman coupling favors small skyrmions. On the other hand the Hartree self-interaction energy of the skyrmion favors large skyrmions so that an optimal skyrmion size is established.[2] For Zeeman coupling strengths typical of physical systems the estimated skyrmion size is comparable to microscopic lengths, motivating a microscopic approach. Recently [7], using a microscopic Hartree-Fock approximation, w...

Interaction driven integer quantum Hall effects are anticipated in graphene bilayers because of the near-degeneracy of the eight Landau levels which appear near the neutral system Fermi level. We predict that an intra-Landau-level cyclotron resonance signal will appear at some odd-integer filling factors, accompanied by collective modes which are nearly gapless and have approximate k 3/2 dispersion. We speculate on the possibility of unusual localization physics associated with these modes.PACS numbers: 76.40.+b,75.30.Ds Introduction-Because the Zeeman spin-splitting in most two-dimensional electron systems (2DES's) is much smaller than the Landau level separation, the magnetic band spectrum usually consists of narrowly-spaced doublets. When one of these doublets is half-filled and disorder is weak, Coulomb interaction physics leads to ferromagnetism i.e. to spontaneous spin polarization in the absence of a Zeeman field [1,2,3]. In some circumstances [4] other approximate Landau level degeneracies occur, often associated with layer degrees of freedom. These can also lead to broken symmetries which induce quasiparticle gaps and hence interaction driven integer quantum Hall effects. The case of bilayer 2DES's is particularly interesting because the which layer degree of freedom doubles Landau level degeneracies and leads to exciton condensation [5,6] at odd filling factors and to canted anti-ferromagnetic states [7] at even filling factors. In this Letter, we address the still richer case of graphene bilayer 2DES's in which chiral bands lead to an additional degeneracy doubling [8] at the Fermi energy of a neutral system. Bilayer graphene's Landau level octet is already apparent in present experiments [9] through the 8×(e 2 /h) Hall conductivity jump between well formed plateaus at Landau level filling factors ν = −4 and ν = +4. We anticipate that when external magnetic fields are strong enough or disorder is weak enough [10], interactions will drive quantum Hall effects at the octet's seven intermediate integer filling factors. We predict that these quantum Hall ferromagnets (QHFs) will exhibit unusual intraLandau-level cyclotron modes at odd filling factors, and that the collective mode excitations at these filling factors are nearly gapless even when there is no continuous symmetry breaking. Because the conductivity has Drude weight centered near zero-energy, we speculate that localization physics and quantum-Hall related transport phenomena will also be anomalous. Graphene Bilayer Landau Levels-When trigonal warping [11] and Zeeman coupling are neglected, the low energy properties of Bernal stacked unbalanced bilayer graphene are determined by electron-electron interactions and by a band Hamiltonian [8] H = H 0 + H ext where

At Landau level filling factors near n 1, quantum Hall ferromagnets form a Skyrme crystal state with quasi-long-range translational and noncollinear magnetic order. We develop an effective low energy theory which explains the presence of magnetic excitations in these systems at energies below the Larmor gap (D) and that predicts a dramatic enhancement of the nuclear spin relaxation rate by a factor of 10 3 . The effective theory predicts a rich set of quantum and classical phase transitions. Based in part on accurate time-dependent Hartree-Fock calculations of the ordered state collective excitation spectrum, we discuss aspects of the T -n-D Skyrme crystal phase diagram. [S0031-9007(97) PACS numbers: 73.40. Hm, 64.60.Cn, At Landau level filling factor n 1͞m (with m an odd integer), the ground state of a two-dimensional electron system (2DES) is an incompressible strong ferromagnet [1], i.e., it has complete spin alignment even in the limit of vanishing Zeeman coupling strength and it has a gap for charged excitations. Quantum Hall ferromagnets have the unusual property [2-4] that their topologically nontrivial spin texture excitations (Skyrmions) carry charge. This property profoundly affects their physics. In particular, the ground state at filling factors slightly away from n 1͞m contains a finite density of Skyrmions, and these are expected [5][6][7] to crystallize, at least when they are sufficiently dilute.In an external field the spin-wave modes of a collinear ferromagnet have an excitation gap equal to the Zeeman energy. On the other hand, a noncollinear magnet can have two Goldstone modes [8], and one of these can remain gapless in an external field. The Skyrme crystal state has noncollinear magnetic order [5]. A single Skyrmion spin texture has its spins aligned with the Zeeman field at infinity, reversed at the center of the Skyrmion, and has nonzero XY spin components at intermediate distances which have a vortex-like configuration [2,6]. The classical (or quantum mean-field) energy of a Skyrmion is independent of the angle w which defines the global orientation of the XY spin components. This extra U͑1͒ degree of freedom for a single Skyrmion leads to broken symmetry in the crystal ground state and hence to a spin wave mode which remains gapless in the presence of the Zeeman field. The existence of this gapless spin mode (presumably in overdamped form in a Skyrme liquid state) dramatically alters the low temperature physics, manifesting itself in both rapid nuclear spin relaxation [9] and giant apparent specific heat [10].In this Letter we address the impact of thermal and quantum fluctuations on the physics of Skyrme crystals. We propose a rich zero temperature phase diagram in which quantum fluctuations destroy the magnetic order of the Skyrme crystal for some values of n and Zeeman coupling strength. Where order exists in the ground state, we estimate the finite temperature Kosterlitz-Thouless phase transition temperatures. Our analysis is based on a boson Hubbard model, which we argue describes ...

No abstract