We study the effect of nematic quantum critical fluctuations on quasiparticle interference. We show that nematic quantum critical fluctuations, which cause back and forth slushing of the d -wave nodes along the underlying Fermi surface, provide a natural mechanism for the accumulation of coherence that has been present in QPI experiments. © 2010 The American Physical Society.

We study the interplay between charge and spin ordering in electronic liquid crystalline states with a particular emphasis on fluctuating spin stripe phenomena observed in recent neutron scattering experiments. Based on a phenomenological model, we propose that charge nematic ordering is indeed behind the formation of temperature dependent incommensurate inelastic peaks near wave vector (π, π) in the dynamic structure factor of YBa2Cu3O6+y. We strengthen this claim by providing a compelling fit to the experimental data. © 2010 The American Physical Society.

We study the finite-temperature nature of a quantum phase transition between an Abelian and a non-Abelian topological phase in an exactly solvable model of the chiral spin liquid of Yao and Kivelson [Phys. Rev. Lett. 99, 247203 (2007)]. As it is exactly solvable, this model can serve as a testbed for developing better measures for describing topological quantum phase transitions.

This chapter is a progress report on the challenging yet promising frontier of quantum phase transitions (QPTs) in strongly correlated systems from the perspective of modern local probes and recent theoretical developments. The focus will be on our latest developments at this frontier. An outlook based on opportunities and questions emerging from these latest developments concludes the discussion. © Taylor & Francis Group.

Motivated by recent interest in spin-triplet superconductors, we investigate the vortex lattice structures for this class of unconventional superconductors. We discuss how the order parameter symmetry can give rise to U(1) × U(1) symmetry in the same sense as in spinor condensates, making half-quantum vortices (HQVs) topologically stable. We then calculate the vortex lattice structure of HQVs, with particular attention on the roles of the crystalline lattice, the Zeeman coupling and Meissner screening, all absent in spinor condensates.

We propose ways to create and detect fractionally charged excitations in integer quantum Hall edge states. The charge fractionalization occurs due to the Coulomb interaction between electrons propagating on different edge channels. The fractional charge of the solitonlike collective excitations can be observed in time-resolved or frequency-dependent shot noise measurements. © 2009 The American Physical Society.

In an externally applied magnetic field, ultrapure crystals of the bilayer compound Sr3 Ru2 O7 undergo a metamagnetic transition below a critical temperature, T, which varies as a function of the angle between the magnetic field H and the Ru-O planes. Moreover, T approaches zero when H is perpendicular to the planes. This putative "metamagnetic quantum critical point," however, is pre-empted by a nematic fluid phase with order one resistive anisotropy in the ab plane.

We study the scaling behavior of the entanglement entropy of two-dimensional conformal quantum critical systems, i.e., systems with scale-invariant wave functions. They include two-dimensional generalized quantum dimer models on bipartite lattices and quantum loop models, as well as the quantum Lifshitz model and related gauge theories. We show that under quite general conditions, the entanglement entropy of a large and simply connected subsystem of an infinite system with a smooth boundary has a universal finite contribution, as well as scale-invariant terms for special geometries.

We propose and analyze interedge tunneling in a quantum spin Hall corner junction as a means to probe the helical nature of the edge states. We show that electron-electron interactions in the one-dimensional helical edge states result in Luttinger parameters for spin and charge that are intertwined, and thus rather different from those for a quantum wire with spin rotation invariance. Consequently, we find that the four-terminal conductance in a corner junction has a distinctive form that could be used as evidence for the helical nature of the edge states.

We investigate the membrane aspect of graphene and its impact on the electronic properties. We show that rippling generates spatially varying electrochemical potential that is proportional to the square of the local curvature. This is due to the rehybridization effects and the change in the next-neighbor hopping caused by curvature. We estimate the electrochemical- potential variation associated with the rippling observed in recent scanning tunneling microscopy (STM) to be of order 30 meV. Further we show that the charge inhomogeneity in turn stabilizes ripple formation.