Topological states of matter such as quantum spin liquids (QSLs) are of great interest because of their remarkable predicted properties including protection of quantum information and the emergence of Majorana fermions. Such QSLs, however, have proven difficult to identify experimentally. The most promising approach is to study their exotic nature via the wavevector and intensity dependence of their dynamical response in neutron scattering. A major search has centered on iridate materials which are proposed to realize the celebrated Kitaev model on a honeycomb lattice -a prototypical topological QSL system in two dimensions (2D). The difficulties of iridium for neutron measurements have, however, impeded progress significantly. Here we provide experimental evidence that a material based on ruthenium, α-RuCl 3 realizes the same Kitaev physics but is highly amenable to neutron investigation. Our measurements confirm the requisite strong spin-orbit coupling, and a low temperature 2 magnetic order that matches the predicted phase proximate to the QSL. We also show that stacking faults, inherent to the highly 2D nature of the material, readily explain some puzzling results to date. Measurements of the dynamical response functions, especially at energies and temperatures above that where interlayer effects are manifest, are naturally accounted for in terms of deconfinement physics expected for QSLs. Via a comparison to the recently calculated dynamics from gauge flux excitations and Majorana fermions of the pure Kitaev model we propose α-RuCl 3 as the prime candidate for experimental realization of fractionalized Kitaev physics.Exotic physics associated with frustrated quantum magnets is an enduring theme in condensed matter research. The formation of quantum spin liquids (QSL) The Kitaev model consists of a set of spin-1/2 moments � ���⃗ � arrayed on a honeycomb lattice. The Kitaev couplings, of strength K in eqn.(1) are highly anisotropic with a different spin component interacting for each of the three bonds of the honeycomb lattice. In actual materials a Heisenberg interaction (J) is also generally expected to be present, giving rise to the Heisenberg-Kitaev (H-K) Hamiltonian given by 11 .where, for example, m is the component of the spin directed along the bond connecting spins (i,j). The QSL phase of the pure Kitaev model (J=0), for both ferro and antiferromagnetic K, is stable for relatively small Heisenberg perturbations.Remarkably the Hamiltonian (1) has been proposed to accurately describe octahedrallycoordinated magnetic systems, Fig. 1 21 -27 . Whilst these studies lend support to the material as a potential Kitaev material, conflicting results centering on the low temperature magnetic properties have hindered progress. To resolve this we undertake a comprehensive evaluation of the magnetic and spin orbit properties of α-RuCl 3 , and further measure the dynamical response establishing this as a material proximate to the widely searched for quantum spin liquid.We begin by investigating the crystal and m...

We show that, in contrast with conventional normal metal-insulator-superconductor (NIS) junctions, the tunneling conductance of a NIS junction in graphene is an oscillatory function of the effective barrier strength of the insulating region, in the limit of a thin barrier. The amplitude of these oscillations is maximum for aligned Fermi surfaces of the normal and superconducting regions and vanishes for a large Fermi surface mismatch. The zero-bias tunneling conductance, in sharp contrast to its counterpart in conventional NIS junctions, becomes maximum for a finite barrier strength. We also suggest experiments to test these predictions.

Motivated by recent experiments on β−Li2IrO3, we study the phase diagram of the Heisenberg-Kitaev model on a three dimensional lattice of tri-coordinated Ir 4+ , dubbed the hyperhoneycomb lattice by Takagi et. al.The lattice geometry of this material, along with Ir 4+ ions carrying J eff = 1/2 moments, suggests that the Heisenberg-Kitaev model may effectively capture the low energy spin-physics of the system in the strongcoupling limit. Using a combination of semiclassical analysis, exact solution and slave-fermion mean field theory, we find, in addition to the spin-liquid, four different magnetically ordered phases depending on the parameter regime. All four magnetic phases-the Néel, the polarized ferromagnet, the skew-stripy and the skewzig-zag, have collinear spin ordering. The three dimensional Z2 spin liquid, which extends over an extended parameter regime around the exactly solvable Kitaev point, has a gapless Majorana mode with a deformed Fermi-circle (co-dimensions, dc = 2). We discuss the effect of the magnetic field and finite temperature on different phases that may be relevant for future experiments. arXiv:1308.6592v2 [cond-mat.str-el]

We explore the nature of the quantum phase transition between a magnetically ordered state with collinear spin pattern and a gapless Z 2 spin liquid in the Heisenberg-Kitaev model. We construct a slave particle mean-field theory for the Heisenberg-Kitaev model in terms of complex fermionic spinons. It is shown that this theory, formulated in the appropriate basis, is capable of describing the Kitaev spin liquid as well as the transition between the gapless Z 2 spin liquid and the so-called stripy antiferromagnet. Within our mean-field theory, we find a discontinuous transition from the Z 2 spin liquid to the stripy antiferromagnet. We argue that subtle spinon confinement effects, associated with the instability of gapped U (1) spin liquid in two spatial dimensions, play an important role at this transition. The possibility of an exotic continuous transition is briefly addressed.