Probing Vortex Unbinding via Dipole Fluctuations

We develop a numerical method for detecting a vortex unbinding transition in a two-dimensional system by measuring large scale fluctuations in the total vortex dipole moment ${\vec P}$ of the system. These are characterized by a quantity $\cal F$ which measures the number of configurations in a simulation for which the either $P_x$ or $P_y$ is half the system size. It is shown that $\cal F$ tends to a non-vanishing constant for large system sizes in the unbound phase, and vanishes in the bound phase. The method is applied to the XY model both in the absence and presence of a magnetic field. In the latter case, the system size dependence of $\cal F$ suggests that there exist three distinct phases, one unbound vortex phase, a logarithmically bound phase, and a linearly bound phase.Comment: 6 pages, 2 figure

Band topology and quantum spin Hall effect in bilayer graphene

We consider bilayer graphene in the presence of spin orbit coupling, to assess its behavior as a topological insulator. The first Chern number $n$ for the energy bands of single and bilayer graphene is computed and compared. It is shown that for a given valley and spin, $n$ in a bilayer is doubled with respect to the monolayer. This implies that bilayer graphene will have twice as many edge states as single layer graphene, which we confirm with numerical calculations and analytically in the case of an armchair terminated surface. Bilayer graphene is a weak topological insulator, whose surface spectrum is susceptible to gap opening under spin-mixing perturbations. We also assess the stability of the associated topological bulk state of bilayer graphene under various perturbations. Finally, we consider an intermediate situation in which only one of the two layers has spin orbit coupling, and find that although individual valleys have non-trivial Chern numbers, the spectrum as a whole is not gapped, so that the system is not a topological insulator.Comment: 9 pages. 9 figures include

Collective charge density fluctuations in superconducting layered systems with bilayer unit cells

Collective modes of bilayered superconducting superlattices (e.g., YBCO) are investigated within the conserving gauge-invariant ladder diagram approximation including both the nearest interlayer single electron tunneling and the Josephson-type Cooper pair tunneling. By calculating the density-density response function including Coulomb and pairing interactions, we examine the two collective mode branches corresponding to the in-phase and out-of-phase charge fluctuations between the two layers in the unit cell. The out-of-phase collective mode develops a long wavelength plasmon gap whose magnitude depends on the tunneling strength with the mode dispersions being insensitive to the specific tunneling mechanism (i.e., single electron or Josephson). We also show that in the presence of tunneling the oscillator strength of the out-of-phase mode overwhelms that of the in-phase-mode at $k_{\|} = 0$ and finite $k_z$, where $k_z$ and $k_{\|}$ are respectively the mode wave vectors perpendicular and along the layer. We discuss the possible experimental observability of the phase fluctuation modes in the context of our theoretical results for the mode dispersion and spectral weight.Comment: 9 pages, 3 figure

Theory of Phonon Shakeup Effects on Photoluminescence from the Wigner Crystal in a Strong Magnetic Field

We develop a method to compute shakeup effects on photoluminescence from a strong magnetic field induced two-dimensional Wigner crystal. Only localized holes are considered. Our method treats the lattice electrons and the tunneling electron on an equal footing, and uses a quantum-mechanical calculation of the collective modes that does not depend in any way on a harmonic approximation. We find that shakeup produces a series of sidebands that may be identified with maxima in the collective mode density of states, and definitively distinguishes the crystal state from a liquid state in the absence of electron-hole interaction. In the presence of electron-hole interaction, sidebands also appear in the liquid state coming from short-range density fluctuations around the hole. However, the sidebands in the liquid state and the crystal state have different qualitative behaviors. We also find a shift in the main luminescence peak, that is associated with lattice relaxation in the vicinity of a vacancy. The relationship of the shakeup spectrum with previous mean-field calculations is discussed.Comment: 14 pages, uuencoded postscript file for entire paper, also available at (click phd14) http://rainbow.uchicago.edu/~ldz/paper/paper.htm

Collective Modes of Quantum Hall Stripes

The collective modes of striped phases in a quantum Hall system are computed using the time-dependent Hartree-Fock approximation. Uniform stripe phases are shown to be unstable to the formation of modulations along the stripes, so that within the Hartree-Fock approximation the groundstate is a stripe crystal. Such crystalline states are generically gapped at any finite wavevector; however, in the quantum Hall system the interactions of modulations among different stripes is found to be remarkably weak, leading to an infinite collection of collective modes with immeasurably small gaps. The resulting long wavelength behavior is derivable from an elastic theory for smectic liquid crystals. Collective modes for the phonon branch are computed throughout the Brillouin zone, as are spin wave and magnetoplasmon modes. A soft mode in the phonon spectrum is identified for partial filling factors sufficiently far from 1/2, indicating a second order phase transition. The modes contain several other signatures that should be experimentally observable.Comment: 36 pages LaTex with 11 postscript figures. Short animations of the collective modes can be found at http://www.physique.usherb.ca/~rcote/stripes/stripes.ht

Testing for Majorana Zero Modes in a Px+iPy Superconductor at High Temperature by Tunneling Spectroscopy

Directly observing a zero energy Majorana state in the vortex core of a chiral superconductor by tunneling spectroscopy requires energy resolution better than the spacing between core states $\Delta^2/eF$. We show that nevertheless, its existence can be decisively tested by comparing the temperature broadened tunneling conductance of a vortex with that of an antivortex even at temperatures $T >> \Delta^2/eF$.Comment: 5 pages, 4 figure

Signature of Quantum Hall Effect Skyrmions in Tunneling: A Theoretical Study

We present a theoretical study of the $I-V$ tunneling characteristic between two parallel two-dimensional electron gases in a perpendicular magnetic field when both are near filling factor $\nu=1$. Finite-size calculations of the single-layer spectral functions in the spherical geometry and analytical expressions for the disk geometry in the thermodynamic limit show that the current in the presence of skyrmions reflects in a direct way their underlying structure. It is also shown that fingerprints of the electron-electron interaction pseudopotentials are present in such a current.Comment: 4 pages, 1 figur

Skyrme Crystal In A Two-Dimensional Electron Gas

The ground state of a two-dimensional electron gas at Landau level filling factors near $\nu =1$ is a Skyrme crystal with long range order in the positions and orientations of the topologically and electrically charged elementary excitations of the $\nu=1$ 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.Comment: 3 pages, latex, 3 figures available upon request from [email protected]

Shape Deformation driven Structural Transitions in Quantum Hall Skyrmions

The Quantum Hall ground state away from $\nu = 1$ can be described by a collection of interacting skyrmions. We show within the context of a nonlinear sigma model, that the classical ground state away from $\nu = 1$ is a skyrmion crystal with a generalized N\'eel order. We show that as a function of filling $\nu$, the skyrmion crystal undergoes a triangle to square to triangle transition at zero temperature. We argue that this structural transition, driven by a change in the shape of the individual skyrmions, is stable to thermal and quantum fluctuations and may be probed experimentally.Comment: 4 pages (REVTEX) and 4 .eps figure

Majorana fermions of a two-dimensional Px+iPy superconductor

To investigate Majorana fermionic excitations of a $p_x+ip_y$ superconductor, the Bogoliubov-de-Gennes equation is solved on a sphere for two cases: (i) a vortex-antivortex pair at opposite poles and (ii) an edge near the south pole and an antivortex at the north pole. The vortex cores support a state of two Majorana fermions, the energy of which decreases exponentially with the radius of the sphere, independently of a moderate disorder potential. The tunneling conductance of an electron into the superconductor near the position of a vortex is computed for finite temperature, and is compared to the case of an {\it s}-wave superconductor. The zero bias conductance peak of the antivortex is half that of the vortex. This effect can be used as a probe of the order parameter symmetry, and as a direct measurement of the Majorana fermion.Comment: 15 pages, 17 figure