Collective modes of CP(3) Skyrmion crystals in quantum Hall ferromagnets

The two-dimensional electron gas in a bilayer quantum Hall system can sustain an interlayer coherence at filling factor nu=1 even in the absence of tunneling between the layers. This system has low-energy charged excitations which may carry textures in real spin or pseudospin. Away from filling factor nu =1 a finite density of these is present in the ground state of the 2DEG and forms a crystal. Depending on the relative size of the various energy scales, such as tunneling (Delta_SAS), Zeeman coupling (Delta_Z) or electrical bias (Delta_b), these textured crystal states can involve spin, pseudospin, or both intertwined. In this article, we present a comprehensive numerical study of the collective excitations of these textured crystals using the GRPA. For the pure spin case, at finite Zeeman coupling the state is a Skyrmion crystal with a gapless phonon mode, and a separate Goldstone mode that arises from a broken U(1) symmetry. At zero Zeeman coupling, we demonstrate that the constituent Skyrmions break up, and the resulting state is a meron crystal with 4 gapless modes. In contrast, a pure pseudospin Skyrme crystal at finite tunneling has only the phonon mode. For Delta_SAS=0, the state evolves into a meron crystal and supports an extra gapless U(1) mode in addition to the phonon. For a CP(3) Skyrmion crystal, we find a U(1) gapless mode in the presence of the symmetry-breaking fields. In addition, a second mode with a very small gap is present in the spectrum.Comment: 16 pages and 12 eps figure

SU(4) Skyrmions and Activation Energy Anomaly in Bilayer Quantum Hall Systems

The bilayer QH system has four energy levels in the lowest Landau level, corresponding to the layer and spin degrees of freedom. We investigate the system in the regime where all four levels are nearly degenerate and equally active. The underlying group structure is SU(4). At $\nu =1$ the QH state is a charge-transferable state between the two layers and the SU(4) isospin coherence develops spontaneously. Quasiparticles are isospin textures to be identified with SU(4) skyrmions. The skyrmion energy consists of the Coulomb energy, the Zeeman energy and the pseudo-Zeeman energy. The Coulomb energy consists of the self-energy, the capacitance energy and the exchange energy. At the balanced point only pseudospins are excited unless the tunneling gap is too large. Then, the SU(4) skyrmion evolves continuously from the pseudospin-skyrmion limit into the spin-skyrmion limit as the system is transformed from the balanced point to the monolayer point by controlling the bias voltage. Our theoretical result explains quite well the experimental data due to Murphy et al. and Sawada et al. on the activation energy anomaly induced by applying parallel magnetic field.Comment: 22 pagets, 6 figures, the final version to be published in PR

Composite bosons in bilayer nu = 1 system: An application of the Murthy-Shankar formalism

We calculate the dispersion of the out-of-phase mode characteristic for the bilayer nu = 1 quantum Hall system applying the version of Chern-Simons theory of Murthy and Shankar that cures the unwanted bare electron mass dependence in the low-energy description of quantum Hall systems. The obtained value for the mode when d, distance between the layers, is zero is in a good agreement with the existing pseudospin picture of the system. For d nonzero but small we find that the mode is linearly dispersing and its velocity to a good approximation depends linearly on d. This is in agreement with the Hartree-Fock calculations of the pseudospin picture that predicts a linear dependance on d, and contrary to the naive Hartree predictions with dependence on the square-root of d. We set up a formalism that enables one to consider fluctuations around the found stationary point values. In addition we address the case of imbalanced layers in the Murthy-Shankar formalism.Comment: 10 pages, 1 figur

Spatial stochastic resonance in 1D Ising systems

The 1D Ising model is analytically studied in a spatially periodic and oscillatory external magnetic field using the transfer-matrix method. For low enough magnetic field intensities the correlation between the external magnetic field and the response in magnetization presents a maximum for a given temperature. The phenomenon can be interpreted as a resonance phenomenon induced by the stochastic heatbath. This novel "spatial stochastic resonance" has a different origin from the classical stochastic resonance phenomenon.Comment: REVTex, 5 pages, 3 figure

A call to action: Temporal trends of COVID-19 deaths in the South African Muslim community

Letter by Omar on letter by Jassat et al. (Jassat W, Brey Z, Parker S, et al. A call to action: Temporal trends of COVID-19 deaths in the South African Muslim community. S Afr Med J 2021;111(8):692-694. https://doi.org/10.7196/SAMJ.2021.v111i8.15878); and response by Jassat et al

Stripes in Quantum Hall Double Layer Systems

We present results of a study of double layer quantum Hall systems in which each layer has a high-index Landau level that is half-filled. Hartree-Fock calculations indicate that, above a critical layer separation, the system becomes unstable to the formation of a unidirectional coherent charge density wave (UCCDW), which is related to stripe states in single layer systems. The UCCDW state supports a quantized Hall effect when there is tunneling between layers, and is {\it always} stable against formation of an isotropic Wigner crystal for Landau indices $N \ge 1$. The state does become unstable to the formation of modulations within the stripes at large enough layer separation. The UCCDW state supports low-energy modes associated with interlayer coherence. The coherence allows the formation of charged soliton excitations, which become gapless in the limit of vanishing tunneling. We argue that this may result in a novel {\it ``critical Hall state''}, characterized by a power law $I-V$ in tunneling experiments.Comment: 10 pages, 8 figures include

Conductance Through Graphene Bends and Polygons

We investigate the transmission of electrons between conducting nanoribbon leads oriented at multiples of 60 degrees with respect to one another, connected either directly or through graphene polygons. A mode-matching analysis suggests that the transmission at low-energies is sensitive to the precise way in which the ribbons are joined. Most strikingly, we find that armchair leads forming 120-degree angles can support either a large transmission or a highly suppressed transmission, depending on the specific geometry. Tight-binding calculations demonstrate the effects in detail, and are also used to study transmission at higher energies as well as for zigzag ribbon leads.Comment: 14 pages, 21 figure

Microscopic Functional Integral Theory of Quantum Fluctuations in Double-Layer Quantum Hall Ferromagnets

We present a microscopic theory of zero-temperature order parameter and pseudospin stiffness reduction due to quantum fluctuations in the ground state of double-layer quantum Hall ferromagnets. Collective excitations in this systems are properly described only when interactions in both direct and exchange particle-hole channels are included. We employ a functional integral approach which is able to account for both, and comment on its relation to diagrammatic perturbation theory. We also discuss its relation to Gaussian fluctuation approximations based on Hubbard-Stratonovich-transformation representations of interactions in ferromagnets and superconductors. We derive remarkably simple analytical expressions for the correlation energy, renormalized order parameter and renormalized pseudospin stiffness.Comment: 15 pages, 5 figure

Enhancement of spin orbit coupling at manganite surfaces

Spin orbit coupling in magnetic systems lacking inversion symmetry can give rise to nontrivial spin textures. Magnetic thin films and heterostructures are potential candidates for the formation of skyrmions and other noncollinear spin configurations as inversion symmetry is inherently lost at their surfaces and interfaces. However, manganites, in spite of their extraordinarily rich magnetic phase diagram, have not yet been considered of interest within this context as their spin orbit coupling is assumed to be negligible. We demonstrate here, by means of angular dependent x ray linear dichroism experiments and theoretical calculations, the existence of a noncollinear antiferromagnetic ordering at the surface of ferromagnetic La2 3Sr1 3MnO3 thin films whose properties can only be explained by an unexpectedly large enhancement of the spin orbit interaction. Our results reveal that spin orbit coupling, usually assumed to be very small in manganites, can be significantly enhanced at surfaces and interfaces adding a new twist to the possible magnetic orders that can arise in electronically reconstructed system