with an omission in the Acknowledgments. ''J. H. and R. W. acknowledge support from the DOE-BES (Grant No. DE-FG02-05ER46237) and computing time on NERSC supercomputers.'' has been added to the Acknowledgments as of 30 March 2012. Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

The 2007 discovery of quantized conductance in HgTe quantum wells delivered the field of topological insulators (TIs) its first experimental confirmation. While many three-dimensional TIs have since been identified, HgTe remains the only known two-dimensional system in this class. Difficulty fabricating HgTe quantum wells has, moreover, hampered their widespread use. With the goal of breaking this logjam, we provide a blueprint for stabilizing a robust TI state in a more readily available two-dimensional material-graphene. Using symmetry arguments, density functional theory, and tight-binding simulations, we predict that graphene endowed with certain heavy adatoms realizes a TI with substantial band gap. For indium and thallium, our most promising adatom candidates, a modest 6% coverage produces an estimated gap near 80 K and 240 K, respectively, which should be detectable in transport or spectroscopic measurements. Engineering such a robust topological phase in graphene could pave the way for a new generation of devices for spintronics, ultra-low-dissipation electronics, and quantum information processing.

Electrons hopping on the sites of a two-dimensional Lieb lattice and three-dimensional edge centered cubic (perovskite) lattice are shown to form topologically non-trivial insulating phases when spin-orbit coupling is introduced. These simple models on lattices with cubic symmetry show a Dirac-like structure in the excitation spectrum but with the unusual feature that there is a dispersionless band through the center of the spectrum and only a single Dirac cone per Brillouin zone.arXiv:1004.5172v1 [cond-mat.mes-hall]

We explore the possible particle-hole instabilities that can arise in a system of massless Dirac fermions on both the honeycomb and π-flux square lattices with short range interactions. Through analytical and numerical studies we show that these instabilities can result in a number of interesting phases. In addition to the previously identified charge and spin density wave phases and the exotic 'quantum anomalous Hall' (Haldane) phase, we establish the existence of the dimerized 'Kekulé' phase over a significant portion of the phase diagram and discuss the possibility of its spinful counterpart, the 'spin Kekulé' phase. On the π-flux square lattice we also find various stripe phases, which do not occur on the honeycomb lattice. The Kekulé phase is described by a Z3 order parameter whose singly quantized vortices carry fractional charge ±e/2. On the π-flux lattice the analogous dimerized phase is described by a Z4 order parameter. We perform a fully self-consistent calculation of the vortex structure inside the dimerized phase and find that close to the core the vortex resembles a familiar superconducting U(1) vortex, but at longer length scales a clear Z4 structure emerges with domain walls along the lattice diagonals.

We propose a two-dimensional time-reversal invariant system of essentially non-interacting electrons on a square lattice that exhibits configurations with fractional charges ±e/2. These are vortex-like topological defects in the dimerization order parameter describing spatial modulation in the electron hopping amplitudes. Charge fractionalization is established by a simple counting argument, analytical calculation within the effective lowenergy theory, and by an exact numerical diagonalization of the lattice Hamiltonian. We comment on the exchange statistics of fractional charges and possible realizations of the system.Introduction.-It is now well-known that fractional quantum numbers can arise as the collective excitations of a manybody system. The canonical example of such fractionalization is a 2D electron gas (2DEG) placed in a transverse magnetic field in the fractional quantum Hall regime. At odd inverse filling factors, ν −1 > 1, the many-body ground state is described by a strongly-correlated Laughlin wave function and the time-reversal symmetry is broken. The excitations carry the fractional charge νe (Ref. 1) and exhibit fractional (Abelian) statistics.2 The search for other systems that exhibit fractionalization is ongoing. Two important questions in this search are whether strong correlations or a broken timereversal symmetry is necessary for fractionalization to happen.