Collective Edge Modes near the onset of a graphene quantum spin Hall state

Graphene subject to a strong, tilted magnetic field exhibits an insulator-metal transition tunable by tilt-angle, attributed to the transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) bulk state at filling factor zero. We develop a theoretical description for the spin and valley edge textures in the two phases, and the implied evolution in the nature of edge modes through the transition. In particular, we show that the CAF has gapless neutral modes in the bulk, but supports gapped charged edge modes. At the transition to the FM state the charged edge modes become gapless and are smoothly connected to the helical edge modes of the FM state. Possible experimental consequences are discussed.Comment: 5 pages, 2 figure

Collective Bulk and Edge Modes through the Quantum Phase Transition in Graphene at ν=0\nu=0

Undoped graphene in a strong, tilted magnetic field exhibits a radical change in conduction upon changing the tilt-angle, which can be attributed to a quantum phase transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) bulk state at filling factor $\nu=0$. This behavior signifies a change in the nature of the collective ground state and excitations across the transition. Using the time-dependent Hartree-Fock approximation, we study the collective neutral (particle-hole) excitations in the two phases, both in the bulk and on the edge of the system. The CAF has gapless neutral modes in the bulk, whereas the FM state supports only gapped modes in its bulk. At the edge, however, only the FM state supports gapless charge-carrying states. Linear response functions are computed to elucidate their sensitivity to the various modes. The response functions demonstrate that the two phases can be distinguished by the evolution of a local charge pulse at the edge.Comment: 15 pages, 23 figure

Valley-kink in Bilayer Graphene at ν=0\nu=0: A Charge Density Signature for Quantum Hall Ferromagnetism

We investigate interaction-induced valley domain walls in bilayer graphene in the $\nu=0$ quantum Hall state, subject to a perpendicular electric field that is antisymmetric across a line in the sample. Such a state can be realized in a double-gated suspended sample, where the electric field changes sign across a line in the middle. The non-interacting energy spectrum of the ground state is characterized by a sharp domain wall between two valley-polarized regions. Using the Hartree-Fock approximation, we find that the Coulomb interaction opens a gap between the two lowest-lying states near the Fermi level, yielding a smooth domain wall with a kink configuration in the valley index. Our results suggest the possibility to visualize the domain wall via measuring the charge density difference between the two graphene layers, which we find exhibits a characteristic pattern. The width of the kink and the resulting pattern can be tuned by the interplay between the magnetic field and gate electric fields

Emergence of helical edge conduction in graphene at the \nu=0 quantum Hall state

The conductance of graphene subject to a strong, tilted magnetic field exhibits a dramatic change from insulating to conducting behavior with tilt-angle, regarded as evidence for the transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) \nu=0 quantum Hall state. We develop a theory for the electric transport in this system based on the spin-charge connection, whereby the evolution in the nature of collective spin excitations is reflected in the charge-carrying modes. To this end, we derive an effective field theoretical description of the low-energy excitations, associated with quantum fluctuations of the spin-valley domain wall ground-state configuration which characterizes the two-dimensional (2D) system with an edge. This analysis yields a model describing a one-dimensional charged edge mode coupled to charge-neutral spin-wave excitations in the 2D bulk. Focusing particularly on the FM phase, naively expected to exhibit perfect conductance, we study a mechanism whereby the coupling to these bulk excitations assists in generating back-scattering. Our theory yields the conductance as a function of temperature and the Zeeman energy - the parameter that tunes the transition between the FM and CAF phases - with behavior in qualitative agreement with experiment.Comment: 16 pages, 1 figur

Colored Non-Crossing Euclidean Steiner Forest

Given a set of $k$-colored points in the plane, we consider the problem of finding $k$ trees such that each tree connects all points of one color class, no two trees cross, and the total edge length of the trees is minimized. For $k=1$, this is the well-known Euclidean Steiner tree problem. For general $k$, a $k\rho$-approximation algorithm is known, where $\rho \le 1.21$ is the Steiner ratio. We present a PTAS for $k=2$, a $(5/3+\varepsilon)$-approximation algorithm for $k=3$, and two approximation algorithms for general~$k$, with ratios $O(\sqrt n \log k)$ and $k+\varepsilon$

Magnetic quantum tunnelling in Fe8 with excited nuclei

We investigate the effect of dynamic nuclear spin fluctuation on quantum tunneling of the magnetization (QTM) in the molecular magnet Fe8 by increasing the nuclei temperature using radio frequency (RF) pulses before the hysteresis loop measurements. The RF pulses do not change the electrons spin temperature. Independently we show that the nuclear spin-spin relaxation time T2 has strong temperature dependence. Nevertheless, we found no effect of the nuclear spin temperature on the tunneling probability. This suggests that in our experimental conditions only the hyperfine field strength is relevant for QTM. We demonstrate theoretically how this can occur.Comment: 4 pages, 4 figure

Nernst Effect as a Signature of Quantum Fluctuations in Quasi-1D Superconductors

We study a model for the transverse thermoelectric response due to quantum superconducting fluctuations in a two-leg Josephson ladder, subject to a perpendicular magnetic field B and a transverse temperature gradient. The off-diagonal Peltier coefficient (\alpha_{xy}) and the Nernst effect are evaluated as functions of B and the temperature T. The Nernst effect is found to exhibit a prominent peak close to the superconductor-insulator transition (SIT), which becomes progressively enhanced at low T. In addition, we derive a relation to diamagnetic response: \alpha_{xy}= -M/T_0, where M is the equilibrium magnetization and T_0 a plasma energy in the superconducting legs.Comment: An extended (and hopefully more comprehensible) version of an earlier postin

Correlated disordered interactions on Potts models

Using a weak-disorder scheme and real-space renormalization-group techniques, we obtain analytical results for the critical behavior of various q-state Potts models with correlated disordered exchange interactions along d1 of d spatial dimensions on hierarchical (Migdal-Kadanoff) lattices. Our results indicate qualitative differences between the cases d-d1=1 (for which we find nonphysical random fixed points, suggesting the existence of nonperturbative fixed distributions) and d-d1>1 (for which we do find acceptable perturbartive random fixed points), in agreement with previous numerical calculations by Andelman and Aharony. We also rederive a criterion for relevance of correlated disorder, which generalizes the usual Harris criterion.Comment: 8 pages, 4 figures, to be published in Physical Review