We study the low energy edge states of bilayer graphene in a strong perpendicular magnetic field. Several possible simple boundaries geometries related to zigzag edges are considered. Tight-binding calculations reveal three types of edge state behaviors: weakly, strongly, and non-dispersive edge states. These three behaviors may all be understood within a continuum model, and related by nonlinear transformations to the spectra of quantum Hall edge-states in a conventional two-dimensional electron system. In all cases, the edge states closest to zero energy include a hole-like edge state of one valley and a particle-like state of the other on the same edge, which may or may not cross depending on the boundary condition. Edge states with the same spin generically have anticrossings that complicate the spectra, but which may be understood within degenerate perturbation theory. The results demonstrate that the number of edge states crossing the Fermi level in clean, undoped bilayer graphene depends both on boundary conditions and the energies of the bulk states.

We analyze the thermal phases of a non critical holographic model of QCD. The model is based on a six dimensional background of N c non extremal D4 branes wrapping a spacial circle of radius R and the compactified Euclidean time direction of radius β = 1/T . We place in this background stacks of N f D4 and anti-D4 flavor probe branes with a separation distance L at large radial direction. The analysis of the DBI effective action yields the following phase diagram: At low temperature the system is in a confining phase with broken chiral symmetry. In the high temperature deconfining phase chiral symmetry can be either restored for L > L c = 1.06R or broken for L < L c . All of these phase transitions are of first order. We analyze the spectrum of the low-spin and high-spin mesons. High spin mesons above certain critical angular momentum "melt". We detect (no) drag for ( mesons) quarks moving in hot quark-gluon fluid. The results resemble the structure and properties of the thermal Sakai-Sugimoto model derived in hep-th/0604161.Recently the phases of thermal holographic QCD (HQCD) have been analyzed [1] in the context of the model of Sakai and Sugimoto [2,3]. It was found out that the confinement/deconfinement and chiral symmetry breaking/restoring phase transitions are first order transitions and they do not necessarly coincide with each other. The system may admit an intemediate deconfined phase with broken chiral symmetry.The mesonic world at these phases was later investigated in [4]. The temperature dependence of low-spin as well as high-spin meson masses was shown to exhibit a pattern familiar from the lattice. The Goldstone bosons associated with chiral symmetry breaking were shown to disappear above the chiral symmetry restoration temperature. The dissociation temperature of mesons as a function of their spin was determined, showing that at a fixed quark mass, mesons with larger spins dissociate at lower temperatures. It was further shown that unlike quarks, large-spin mesons do not experience drag effects when moving through the quark gluon fluid. They do, however, have a maximum velocity for fixed spin, beyond which they dissociate.HQCD models based on critical string theories suffer from the major drawback of incorporating undesired KK modes. Whereas the modes associated with the S 5 in the string theory on AdS 5 × S 5 are essential to describe the dual N = 4 SYM theory, the KK modes in models of HQCD do not correspond to modes of the gauge theory. Moreover, the mass scale of those KK modes is the same as that of the glueballs and hadrons and there is no known method to disentangle the two scales. The most natural way to overcome this problem is to consider strings in non-critical dimensions so as to minimize the set of KK modes. Since the pioneering paper of Polyakov [5]. there have been many attempts to write down an non-critical string model of QCD [6]- [10]. The main problem with non-critical holography is the fact that the corresponding SUGRA backgrounds have curvature of order one and there is no wa...

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We consider the zero-filled quantum-Hall ferromagnetic state of bilayer graphene subject to a kink-like perpendicular electric field, which generates domain walls in the electronic state and lowenergy collective modes confined to move along them. In particular, it is shown that two pairs of collective helical modes are formed at opposite sides of the kink, each pair consisting of modes with identical helicities. We derive an effective field-theoretical model of these modes in terms of two weakly coupled anisotropic quantum spin-ladders, with parameters tunable through control of the electric and magnetic fields. This yields a rich phase diagram, where due to the helical nature of the modes, distinct phases possess very different charge conduction properties. Most notably, this system can potentially exhibit a transition from a superfluid to an insulating phase.PACS numbers: 73.22.Gk, 73.43.Lp, 72.80.Vp, 75.10.Pq, 75.10.Jm Among the most intriguing electronic properties of graphene is the emergence of novel collective states in the quantum Hall (QH) regime [1]. In particular, the peculiar ν = 0 QH states in both monolayer graphene (MLG) [2][3][4] and bilayer graphene (BLG) [5] suggest that Coulomb interactions lift the degeneracies of the half-filled zero energy Landau level. The multitude of discrete degrees of freedom (two valleys (K,K ) and two spin states in MLG, and an additional layer index in BLG) dictates a rich variety of possible exchange-induced broken symmetry states [6][7][8], as generalizations of the spontaneously polarized ferromagnetic state of an ordinary two-dimensional (2D) electron gas [9]. These can be controlled by external fields: in MLG, primarily by tuning the Zeeman energy via a strong parallel magnetic field [10]; in BLG, the orbital isospin degeneracies can be lifted by applying a perpendicular electric field [11].The unique features of the broken symmetry ν = 0 QH states are most prominently manifested by the nature of their collective excitations. While in the standard QH ferromagnet the elementary charge excitations are Skyrmions [9], more complex forms of spin-textures have been predicted in graphene, e.g. charge-2e Skyrmions in BLG [12]. Yet more remarkably, the particle-hole symmetry of the bulk spectrum allows the formation of charge conducting edge modes associated with kinks in the effective Zeeman field, where it changes sign across a line. These can be realized near physical edges of the graphene ribbon [13][14][15], or in the interior of a BLG sheet subject to non-uniform gating [16][17][18].The coherent domain wall (DW) forming in the spin/isospin configuration near such a kink supports a gapless collective mode, which possesses a onedimensional (1D) dynamics along the kink of a helical character. The latter arises from the constraint relating a spin/isospin texture to the charge degree of freedom [9]. This yields a mapping to a helical Luttinger liquid (HLL), with a single flavor encoding spin and charge related by duality, in analogy with the edge states of 2D topol...

We derive an effective field-theoretical model for the one-dimensional collective mode associated with a domain wall in a quantum Hall ferromagnetic state, as realized in confined graphene systems at zero filling. To this end we consider the coupling of a quantum spin ladder forming near a kink in the Zeeman field to the spin fluctuations of a neighboring spin polarized two-dimensional environment. It is shown, in particular, that such coupling may induce anisotropy of the exchange coupling in the legs of the ladder. Furthermore, we demonstrate that the resulting ferromagnetic spin-1/2 ladder, subject to a kinked magnetic field, can be mapped to an antiferromagnetic spin chain at zero magnetic field.