Abstract:
Motivated by the recent synthesis of two insulating Li$_2$IrO$_3$ polymorphs, where Ir$^{4+}$ $S_{eff}$=1/2 moments form 3D ("harmonic") honeycomb structures with threefold coordination, we study magnetic Hamiltonians on the resulting $\beta$-Li$_2$IrO$_3$ hyperhoneycomb lattice and $\gamma$-Li$_2$IrO$_3$ stripyhoneycomb lattice. Experimentally measured magnetic susceptibilities suggest that Kitaev interactions, predicted for the ideal 90$^\circ$ Ir-O-Ir bonds, are sizable in these materials. We first consider pure Kitaev interactions, which lead to an exactly soluble 3D quantum spin liquid (QSL) with emergent Majorana fermions and Z$_2$ flux loops. Unlike 2D QSLs, the 3D QSL is stable to finite temperature, with $T_c \approx |K|/100$. On including Heisenberg couplings, exact solubility is lost. However, by noting that the shortest closed loop $\ell$ is relatively large in these structures, we construct an $\ell\rightarrow \infty$ approximation by defining the model on the Bethe lattice. The phase diagram of the Kitaev-Heisenberg model on this lattice is obtained directly in the thermodynamic limit, using tensor network states and the infinite-system time-evolving-block-decimation (iTEBD) algorithm. Both magnetically ordered and gapped QSL phases are found, the latter being identified by an entanglement fingerprint.

Abstract:
We calculate angle-dependent magnetoresistance oscillations (AMRO) for interlayer transport of cuprate superconductors in the presence of ($\pi,\pi$) order. The order reconstructs the Fermi surface, creating magnetic breakdown junctions; we show how such magnetic breakdown effects can be incorporated into calculations of interlayer conductivity for this system. We successfully fit experimental data with our model, and these fits suggest a connection between ($\pi,\pi$) order and the anisotropic scattering observed in overdoped cuprates. This work paves the way for the use of AMRO as a tool to distinguish different kinds of ordered states.

Abstract:
Systematic measurements of the resistivity, heat capacity, susceptibility and Hall coefficient are presented for single crystal samples of the electron-doped superconductor Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$. These data delineate an $x-T$ phase diagram in which the single magnetic/structural phase transition that is observed for undoped BaFe$_2$As$_2$ at 134 K apparently splits into two distinct phase transitions, both of which are rapidly suppressed with increasing Co concentration. Superconductivity emerges for Co concentrations above $x \sim 0.025$, and appears to coexist with the broken symmetry state for an appreciable range of doping, up to $x \sim 0.06$. The optimal superconducting transition temperature appears to coincide with the Co concentration at which the magnetic/structural phase transitions are totally suppressed, at least within the resolution provided by the finite step size between crystals prepared with different doping levels. Superconductivity is observed for a further range of Co concentrations, before being completely suppressed for $x \sim 0.018$ and above. The form of this $x-T$ phase diagram is suggestive of an association between superconductivity and a quantum critical point arising from suppression of the magnetic and/or structural phase transitions.

Abstract:
Within the Landau paradigm of continuous phase transitions, ordered states of matter are characterized by a broken symmetry. Although the broken symmetry is usually evident, determining the driving force behind the phase transition is often a more subtle matter due to coupling between otherwise distinct order parameters. In this paper we show how measurement of the divergent nematic susceptibility of an iron pnictide superconductor unambiguously distinguishes an electronic nematic phase transition from a simple ferroelastic distortion. These measurements also reveal an electronic nematic quantum phase transition at the composition with optimal superconducting transition temperature.

Abstract:
We present results of angle-dependent magnetoresistance measurements and direct optical images of underdoped Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ which reveal partial detwinning by action of a 14T magnetic field. Driven by a substantial magneto-elastic coupling, this result provides evidence for an electronic origin of the lattice distortion in underdoped iron pnictides. The observed anisotropy in these partially detwinned samples implies a substantial in-plane electronic anisotropy in the broken symmetry state, with a smaller resistivity along the antiferromagnetic ordering direction.

Abstract:
Electrical resistivity measurements of detwinned single crystals of the representative iron arsenide Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ reveal a dramatic in-plane anisotropy associated with the tetragonal-to-orthorhombic structural transition that precedes the onset of long-range antiferromagnetic order. These results indicate that the structural transition in this family of compounds is fundamentally electronic in origin.

Abstract:
We have studied the interlayer resistivity of the prototypical quasi-two-dimensional organic superconductor $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$ as a function of temperature, current and magnetic field, within the superconducting state. We find a region of non-zero resistivity whose properties are strongly dependent on magnetic field and current density. There is a crossover to non-Ohmic conduction below a temperature that coincides with the 2D vortex solid -- vortex liquid transition. We interpret the behaviour in terms of a model of current- and thermally-driven phase slips caused by the diffusive motion of the pancake vortices which are weakly-coupled in adjacent layers, giving rise to a finite interlayer resistance.

Abstract:
We have introduced defects into clean samples of the organic superconductor $\kappa$-(BEDT-TTF)$_2$Cu(SCN)$_2$ in order to determine their effect on the temperature dependence of the conductivity and the critical temperature $T_{\rm c}$. We find a violation of Matthiessen's rule that can be explained by a model of the conductivity involving a defect-assisted interlayer channel which acts in parallel with the band-like conductivity. We observe an unusual dependence of $T_{\rm c}$ on residual resistivity which is not consistent with the generalised Abrikosov-Gor'kov theory for an order parameter with a single component, providing an important constraint on models of the superconductivity in this material.

Abstract:
Superconducting quantum interference device (SQUID) microscopy shows stripes of increased diamagnetic susceptibility in underdoped, but not overdoped, single crystals of Ba(Fe1-xCox)2As2. These stripes of increased diamagnetic susceptibility are consistent with enhanced superfluid density on twin boundaries. Individual vortices avoid pinning on or crossing the stripes, and prefer to travel parallel to them. These results indicate a relationship between superfluid density, local strain, and frustrated magnetism, and demonstrate two mechanisms for enhancing critical currents.

Abstract:
Shubnikov de Haas (SdH) oscillations and Angle Resolved PhotoEmission Spectroscopy (ARPES) are used to probe the Fermi surface of single crystals of Bi2Se3. We find that SdH and ARPES probes quantitatively agree on measurements of the effective mass and bulk band dispersion. In high carrier density samples, the two probes also agree in the exact position of the Fermi level EF, but for lower carrier density samples discrepancies emerge in the position of EF. In particular, SdH reveals a bulk three-dimensional Fermi surface for samples with carrier densities as low as 10^17cm-3. We suggest a simple mechanism to explain these differences and discuss consequences for existing and future transport studies of topological insulators.