Talks

A systematic method to construct 4d N=2 supersymmetric theories by compactifying M5-branes on a Riemann surface was found by Gaiotto last year. This suggests that any physical quantity of the 4d theory should be reflected in another physical quantity of the 2d theory living on the Riemann surface. Indeed, one finds that the instanton partition function of the 4d theories equals the conformal blocks of the 2d theory. I would like to illustrate this construction through explicit examples.

Many putative explanations in physics rely on idealized models of physical systems. These explanations are inconsistent with standard philosophical accounts of explanation. A common view holds that idealizations can underwrite explanation nonetheless, but only when they are what have variously been called Galilean, approximative, traditional or controllable. Controllability is the least vague of these categories, and this paper focuses on the relation between controllability and explanation. Specifically, it argues that the common view is an untenable half-measure. It gives the example of a simple pendulum with quadratic damping, an uncontrollable idealization that makes use of singular limits and for which the behaviour at the limit is qualitatively new—but a system whose behaviour is fully explained in terms of the idealization. It shows that uncontrollable idealizations can have explanatory capacities (and in a way distinct from Batterman’s “asymptotic explanation”).

We point out and explicitly demonstrate a close connection that exists between featureless Mott insulators and fractional quantum Hall liquids. Using magnetic Wannier states as the single-particle basis in the lowest Landau level (LLL), we demonstrate that the Hamiltonian of interacting bosons in the LLL maps onto a Hamiltonian of a featureless Mott insulator on triangular lattice, formed by the magnetic Wannier states. The Hamiltonian is remarkably simple and consists only of short-range repulsion and ring-exchange terms.

The heavy fermion URu2Si2 boasts a 25 year old mystery. Its ''hidden order'' phase transition at Tc=17.5K has eluded the onslaught of theory and experiment to describe the complex underlying mechanism. Whether the transition is due to conventional ordering of k-space heavy electrons or to a change in hybridization of the r-space states at each magnetic-moment-contributing U atom is unknown. Addressing the problem requires a probe which can simultaneously measure the real space and momentum space structure, making spectroscopic imaging STM (SI-STM) the natural choice. SI-STM studies of URu2Si2 above Tc reveal the first images of the Fano lattice electronic structure, the real-space spectroscopic manifestation of a periodic array of localized Kondo resonances at the U sites. Below Tc, however, a hybridization gap opens in the density of states. Quasiparticle interference imaging reveals a concurrent rapid splitting of a light symmetric k-space band to form two new heavy bands exhibiting momentum space anisotropy. Thus, the ''hidden order'' state emerges directly from the Fano lattice electronic structure and exhibits characteristics of alterations in the hybridization of states at each U atom.

Soft materials are dynamical by nature and the study of the dynamics of soft materials is an exciting, rich area of current interest. During macromolecular self-assembly, as occurs in block copolymers, long structural relaxation timescales due to collective molecular motion are often seen. How microstructure influences the dynamics, the existence and lifetime of metastable states, and the dynamics of long-lived non-equilibrium structures are all poorly-understood issues. I will discuss our dynamical simulations that address these questions in the context of the nucleation of one microstructured phase out of another in a block copolymer melt.

Frustrated pyrochlore magnets with Ising-like moments have attracted much attention due to the spin ice and spin liquid disordered states these materials display at low temperatures. We recently focused attention on Er2Ti2O7 and Yb2Ti2O7 which possess local XY, or planar, moments on the pyrochlore lattice - a network of corner sharing tetrahedra. I will describe our neutron scattering experiments in which magnetic long range order is destroyed by application of a (110) magnetic field in the XY antiferromagnetic pyrochlore Er2Ti2O7, and experiments in which unexpected field-induced magnetic order is observed in its ferromagnetic counterpart, Yb2Ti2O7.

In correlated electron systems, electrons can organize themselves in states that are analogous to classical liquid crystal phases. The search for such phases in solid state systems, in particular for the quantum version of an anisotropic liquid crystal state, dubbed electronic nematic phase, has been of great interest. For example, anisotropic metal bounded by two consecutive meta-magnetic transitions was reported in bilayer Ruthenates, and anisotropic neutron scattering patterns were observed in high temperature Cuprates In this talk, I will review theoretical development of the nematic phase and present relevant experimental issues. The interplay with other competing orders and avoided quantum criticality will be also discussed.

I will discuss NMR study of two types of iron based superconductors, electron doped Ba(Fe,Co)2As2 and stoichiometric FeSe. The primary focus will be on normal state spin fluctuations and its possible relation with the superconducting mechanism, and the pairing symmetry as probed by NMR.

Recent theory and experiment have revealed that strong spin-orbit coupling (SOC) can have dramatic qualitative effects on weakly interacting electrons. For instance, it leads to a distinct phase of matter, the topological band insulator. I will discuss the combined effects of SOC and strong electron correlation. For a ''strong'' Mott insulator, in which the electrons are well localized, SOC can compete with exchange interactions, leading to quenching of orbital degeneracy and even an instance of quantum criticality. For intermediate correlations, SOC has both quantitative and qualitative effects upon the Mott transition. An illustrative example of Ir-based pyrochlores will be presented, suggesting a rich interplay of correlations and SOC, and the possibility of distinct new electronic phases such a ''topological Mott insulator''.