We present a theory of the quantum Griffiths phases associated with the ferromagnetic quantum phase transition in disordered metals. For Ising spin symmetry, we study the dynamics of a single rare region within the variational instanton approach. For Heisenberg symmetry, the dynamics of the rare region is studied using a renormalization group approach. In both cases, the rare region dynamics is even slower than in the usual quantum Griffiths case because the order parameter conservation of an itinerant ferromagnet hampers the relaxation of large magnetic clusters. The resulting quantum Griffiths singularities in ferromagnetic metals are stronger than power laws. For example, the low-energy density of states $\rho \left(\epsilon \right)$ takes the asymptotic form $\exp \left[{\{-\tilde{\lambda }\log ({\epsilon }_0/\epsilon )\}}^{3/5}\right]/\epsilon$ with $\tilde{\lambda }$ being nonuniversal. We contrast these results with the antiferromagnetic case in which the systems show power-law quantum Griffiths singularities in the vicinity of the quantum critical point. We also compare our result with existing experimental data of ferromagnetic alloy ${\mathrm{Ni}}_x{\mathrm{V}}_{1-x}$.

SrPt${}_2$As${}_2$ single crystals with CaBe${}_2$Ge${}_2$-type structure were synthesized by self-melting technique. X-ray diffraction, transmission electron microscopy, electrical resistivity, magnetic susceptibility, specific heat, and optical spectroscopy measurements were conducted to elucidate the properties of SrPt${}_2$As${}_2$. SrPt${}_2$As${}_2$ single crystals undergo a structural phase transition well above room temperature (about 450 K) and become superconducting at 5.18 K. The superconducting and structural phase transition temperatures are reduced by 6$\%$ iridium doping. Both the pure SrPt${}_2$As${}_2$ and the Ir-doped single crystals are demonstrated to be highly metallic with rather high plasma frequencies. In particular, the optical spectroscopy measurement revealed two gaplike suppression structures: a stronger one at high energy near 12 000 cm${}^{-1}$ ($\sim$1.5 eV), and a less prominent one at lower energy near 3200 cm${}^{-1}$ ($\sim$0.4 eV) for the pure compound. We elaborate that the former is related to the correlation effect, while the latter could be attributed to the partial energy gap formation associated with structural phase transition.

We have performed broadband zero-field and magneto-infrared spectroscopy of the three dimensional topological insulator Bi${}_{0.91}$Sb${}_{0.09}$. The zero-field results allow us to measure the value of the direct band gap between the conducting $L_a$ and valence $L_s$ bands. Under applied field in the Faraday geometry ($k\parallel H\parallel \text{C1}$), we measured the presence of a multitude of Landau level (LL) transitions, all with frequency dependence $\omega \propto \sqrt{H}$. We discuss the ramification of this observation for the surface and bulk properties of topological insulators.

We present highly subwavelength magnetic metamaterials designed for operation at radio frequencies (rf's). A dual-layer design consisting of independent planar spiral elements enables the experimental demonstration of a unit cell size $\left(a\right)$ that is $\sim$700 times smaller than the resonant wavelength $\left({\lambda }_0\right)$. Simulations indicate that utilization of a conductive via to connect spiral layers permits further optimization and we achieve a unit cell that is ${\lambda }_0/a\sim 2000$. Magnetic metamaterials are characterized by a time domain method which permits determination of the complex magnetic response. Numerical simulations are performed to support experimental data and we find excellent agreement. These designs make metamaterial low-frequency experimental investigations practical and suggest their use for the study of magnetoinductive waves, levitation, and to further enable potential rf applications.

We present ac susceptibility and specific-heat measurements taken on samples of LiHo${}_x$Y${}_{1-x}$F${}_4$ in the dilute limit: $x=0.018$, 0.045, 0.080, and 0.12. Susceptibility measurements show glassy behavior including wide absorption spectra that continually broaden with decreasing temperature. Dynamical scaling analyses show evidence of finite-temperature spin-glass transitions, the temperatures of which match those of recent theoretical work. A surprisingly long intrinsic time constant is observed in these samples and is found to be inversely correlated with the concentration of magnetic moments $x$. Our results support the picture that this behavior is largely a single-ion effect, related to the random transverse fields generated by the off-diagonal component of the dipolar interaction and significantly slowed by the important nuclear hyperfine interaction. Specific-heat measurements show broad features due to the electronic spins on top of a large Schottky-like nuclear contribution. Unusually, the peak position of the electronic component is found to be largely concentration independent, unlike the glass transition temperature.

The phantom force is an apparently repulsive force, which can dominate the atomic contrast of an AFM image when a tunneling current is present. We described this effect with a simple resistive model, in which the tunneling current causes a voltage drop at the sample area underneath the probe tip. Because tunneling is a highly local process, the areal current density is quite high, which leads to an appreciable local voltage drop that in turn changes the electrostatic attraction between tip and sample. However, Si(111)-7$\times$7 has a metallic surface state and it might be proposed that electrons should instead propagate along the surface state, as through a thin metal film on a semiconducting surface, before propagating into the bulk. In this paper, we first measure the phantom force on a sample that displays a metallic surface state [here, Si(111)-7$\times$7] using tips with various radii. If the metallic surface state would lead to a constant electrostatic potential on the surface, we would expect a direct dependence of the phantom force with tip radius. In a second set of experiments, we study H/Si(100), a surface that does not have a metallic surface state. We conclude that a metallic surface state does not suppress the phantom force, but that the local resistance $R_s$ has a strong effect on the magnitude of the phantom force.

We show that a three-dimensional topological insulator doped with magnetic impurities in the bulk can have a regime where the surface is magnetically ordered but the bulk is not. This is in contrast to conventional materials where bulk ordered phases are typically more robust than surface ordered phases. The difference originates from the topologically protected gapless surface states characteristic of topological insulators. We study the problem using a mean-field approach in two concrete models that give the same qualitative result, with some interesting differences. Our findings could help explain recent experimental results showing the emergence of a spectral gap in the surface state of Bi${}_2$Se${}_3$ doped with Mn or Fe atoms, but with no measurable bulk magnetism.

The competition between intertube hopping processes and density-density interactions is investigated in one-dimensional quantum dipolar bosons systems of $N$ coupled tubes at zero temperature. Using a phenomenological bosonization approach, we show that the resulting competition leads to an exotic quantum phase transition described by a U(1) $\times$ ${\mathbb{Z}}_N$ conformal field theory with a fractional central charge. The emerging ${\mathbb{Z}}_N$ parafermionic critical degrees of freedom are highly nontrivial in terms of the original atoms or polar molecules of the model. We further determine the main physical properties of the quantum-critical point in a double-tube system which has central charge $c=3/2$. In triple-tube systems, we show that the competition between the two antagonistic processes is related to the physics of the two-dimensional ${\mathbb{Z}}_3$ chiral Potts model. This work opens the possibility to study the exotic properties of the ${\mathbb{Z}}_N$ parafermions in the context of ultracold quantum Bose gases.

We derive an approximate analytical solution of the self-consistency equations of the bosonic dynamical mean-field theory (B-DMFT) in the strong-coupling limit. The approach is based on a linked-cluster expansion in the hybridization function of normal bosons around the atomic limit. The solution is used to compute the phase diagram of the bosonic Hubbard model for different lattices. We compare our results with numerical solutions of the B-DMFT equations and numerically exact methods, respectively. The very good agreement with those numerical results demonstrates that our approach captures the essential physics of correlated bosons both in the Mott insulator and in the superfluid phase. Close to the transition into the superfluid phase the momentum distribution function at zero momentum is found to be strongly enhanced already in the normal phase. The linked-cluster expansion also allows us to compute dynamical properties such as the spectral function of bosons. The evolution of the spectral function across the transition from the normal to the superfluid phase is seen to be characteristically different for the interaction driven and density driven transition, respectively.

Employing a classical density-functional description of liquid environments, we introduce a rigorous method for the diffusion quantum Monte Carlo calculation of free energies and thermodynamic averages of solvated systems that requires neither thermodynamic sampling nor explicit solvent electrons. We find that this method yields promising results and small convergence errors for a set of test molecules. It is implemented readily and is applicable to a range of challenges in condensed matter, including the study of transition states of molecular and surface reactions in liquid environments.

We systematically investigate magnetic reversal of permalloy islands in a square spin-ice geometry with in situ Lorentz microscopy. Differential phase imaging reveals the presence of a flux channel similar to a Dirac string between the magnetic charge monopoles during the reversal. Analysis of the phase images shows that positively and negatively charged monopoles always move together with the flux channel. Statistical analysis of monopole populations and system correlations shows the emergence of a highly frustrated state for low magnetizations. This state is explained by a strong influence of charge ordering, which limits monopole densities.

Using ultrahigh magnetic fields up to 170 T and polarized midinfrared radiation with tunable wavelengths from 9.22 to 10.67 $\mu$m, we studied cyclotron resonance in large-area graphene grown by chemical vapor deposition. Circular polarization dependent studies reveal strong $p$-type doping for as-grown graphene, and the dependence of the cyclotron resonance on radiation wavelength allows for a determination of the Fermi energy. Thermal annealing shifts the Fermi energy to near the Dirac point, resulting in the simultaneous appearance of hole and electron cyclotron resonance in the magnetic quantum limit, even though the sample is still $p$-type, due to graphene's linear dispersion and unique Landau level structure. These high-field studies therefore allow for a clear identification of cyclotron resonance features in large-area, low-mobility graphene samples.

A number of recent experiments have used torsional oscillators to study the behavior of solid helium. The oscillator frequencies increased at temperatures below 200 mK, an effect attributed to decoupling of a fraction of the helium mass—the signature of a “supersolid” phase. However, helium's shear modulus also increases below 200 mK and the frequency of a torsional oscillator depends on its elastic properties, as well as on its inertia. In many experiments helium is introduced via a hole in the torsion rod, where its shear modulus contributes to the stiffness of the rod. In oscillators with relatively large torsion rod holes, changes in the helium's shear modulus could produce the entire low temperature frequency shifts that have been interpreted as mass decoupling. For these oscillators we also find that the known elastic properties of helium in the torsion rod can explain the observed TO amplitude dependence (which has been interpreted as a critical velocity) and the TO dissipation peak. However, in other oscillators these elastic effects are small and the observed frequency changes must have a different origin.

It has been suggested that after being gapped by a small symmetry-breaking field, the Majorana quasiparticles localized on the surface of a class DIII topological insulator will exhibit a thermal Hall effect that arises from a gravitational Chern-Simons term. We critically examine this idea, and argue that the thermogravitational Hall effect is more complicated than its familiar analog. A conventional Hall current is generated by a uniform electric field, but computing the flux from the gravitational Chern-Simons functional shows that gravitational field gradients—i.e., tidal forces—are needed to induce an energy-momentum flow. We relate the resulting surface energy-momentum flux to a domain-wall gravitational anomaly via the Callan-Harvey inflow mechanism. We stress that the gauge invariance of the combined bulk-plus-boundary theory ensures that the current in the domain wall always experiences a “covariant” rather than “consistent” anomaly. We use this observation to confirm that the tidally induced energy-momentum current exactly accounts for the covariant gravitational anomaly in $(1+1)$-dimensional domain-wall fermions. The same anomaly arises whether we write the Chern-Simons functional in terms of the Christoffel symbol or in terms of the spin connection.

Superlattices (SLs) in monolayer and bilayer graphene, formed by spatially periodic potential variations, lead to a modified bandstructure with extra finite-energy and zero-energy Dirac fermions with tunable anisotropic velocities. We theoretically show that transport in a weak perpendicular (orbital) magnetic field allows one to not only probe the number of emergent Dirac points but also yields further information about their dispersion. For monolayer graphene, we find that a moderate magnetic field can lead to a strong reversal of the transport anisotropy imposed by the SL potential, an effect that arises due to the SL-induced dispersion of the zero-energy Landau levels. This effect may find useful applications in switching or other devices. For bilayer graphene, we discuss the structure of Landau level wave functions and local density of states in the presence of a uniform bias, as well as in the presence of a kink in the bias that leads to topologically bound “edge states.” We consider implications of these results for scanning tunneling spectroscopy measurements, valley filtering, and impurity-induced breakdown of the quantum Hall effect in bilayer graphene.

We investigate the pairing in iron pnictides in the coexistence phase, which displays both superconducting and antiferromagnetic orders. By solving the pairing problem on the Fermi surface reconstructed by long-range magnetic order, we find that the pairing interaction necessarily becomes angle dependent, even if it was isotropic in the paramagnetic phase, which results in an angular variation of the superconducting gap along the Fermi surfaces. We find that the gap has no nodes for a small antiferromagnetic order parameter $M$, but may develop accidental nodes for intermediate values of $M$, when one pair of the reconstructed Fermi surface pockets disappears. For even larger $M$, when the other pair of reconstructed Fermi pockets is gapped by long-range magnetic order, superconductivity still exists, but the quasiparticle spectrum becomes nodeless again. We also show that the application of an external magnetic field facilitates the formation of nodes. We argue that this mechanism for a nodeless-nodal-nodeless transition explains recent thermal conductivity measurements of hole-doped (Ba${}_{1-x}$K${}_x$)Fe${}_2$As${}_2$ [J-Ph. Read et al., e-print arXiv:1105.2232].

We have experimentally studied the nonlinear nature of electrical conduction in monolayer graphene devices on silica substrates. This nonlinearity manifests itself as a nonmonotonic dependence of the differential resistance on applied dc voltage bias across the sample. At temperatures below $\sim$70 K, the differential resistance exhibits a peak near zero bias that can be attributed to self-heating of the charge carriers. We show that the shape of this peak arises from a combination of different energy dissipation mechanisms of the carriers. The energy dissipation at higher carrier temperatures depends critically on the length of the sample. For samples longer than 10 $\mu$m the heat loss is shown to be determined by optical phonons at the silica-graphene interface.

The Heusler-derived multiferroic alloy Ni${}_{50-x}$Co${}_x$Mn${}_{40}$Sn${}_{10}$ has recently been shown to exhibit, at just above room temperature, a highly reversible martensitic phase transformation with an unusually large magnetization change. In this work the nature of the magnetic ordering above and below this transformation has been studied in detail in the critical composition range $x$ $=$ 6–8 via temperature-dependent (5–600 K) magnetometry and small-angle neutron scattering (SANS). We observe fairly typical paramagnetic to long-range-ordered ferromagnetic phase transitions on cooling to 420–430 K, with the expected critical spin fluctuations, followed by first-order martensitic phase transformations to a nonferromagnetic state below 360–390 K. The static magnetization reveals complex magnetism in this low-temperature nonferromagnetic phase, including a Langevin-like field dependence, distinct spin freezing near 60 K, and significant exchange bias effects, consistent with superparamagnetic blocking of ferromagnetic clusters of nanoscopic dimensions. We demonstrate that these spin clusters, whose existence has been hypothesized in a variety of martensitic alloys exhibiting competition between ferromagnetic and antiferromagnetic exchange interactions, can be directly observed by SANS. The scattering data are consistent with a liquidlike spatial distribution of interacting magnetic clusters with a mean center-to-center spacing of 12 nm. Considering the behavior of the superparmagnetism, cooling-field and temperature-dependent exchange bias, and magnetic SANS, we discuss in detail the physical form and origin of these spin clusters, their intercluster interactions, the nature of the ground-state magnetic ordering in the martensitic phase, and the implications for our understanding of such alloy systems.

Electron doping of a 122-type iron pnictide BaFe${}_2$As${}_2$ by substituting the Ba site with an aliovalent ion (indirect doping), which had been unsuccessful by conventional solid-state synthesis methods, was achieved by a nonequilibrium film growth process. The substitution with La was substantiated by a systematic shrinkage of the $c$-axis lattice parameter due to the smaller ionic radius of La${}^{3+}$ than that of Ba${}^{2+}$. A negative Hall coefficient indicated that the majority carriers were electrons, as is consistent with this aliovalent ion doping. The La substitution suppressed an antiferromagnetic transition and induced bulk superconductivity at a maximum onset critical temperature ($T_{\mathrm{c}}$) of 22.4 K. The electronic phase diagram for (Ba${}_{1-x}$La${}_x$)Fe${}_2$As${}_2$ was built, which revealed that the indirect electron doping at the Ba site with La [(Ba${}_{1-x}$La${}_x$)Fe${}_2$As${}_2$] exhibits almost the same $T_{\mathrm{c}}$- doping level relation as that of the direct electron doping at the Fe site with Co [Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$]. This finding clarified that $T_{\mathrm{c}}$ in 122-type compounds is not affected by a crystallographic doping site, which is in sharp contrast to the 1111-type compounds, $RE$FeAsO ($RE$ $=$ rare earth). It is tentatively attributed to the differences in their dimensionality of electronic structures and electron pairing symmetries.

We study the Anderson impurity problem in a mesoscopic setting, namely the “Anderson box,” in which the impurity is coupled to finite reservoir having a discrete spectrum and large sample-to-sample mesoscopic fluctuations. Note that both the weakly coupled and strong coupling Anderson impurity problems are characterized by a Fermi-liquid theory with weakly interacting quasiparticles. We study how the statistical fluctuations in these two problems are connected, using random matrix theory and the slave boson mean-field approximation (SBMFA). First, for a resonant level model such as results from the SBMFA, we find the joint distribution of energy levels with and without the resonant level present. Second, if only energy levels within the Kondo resonance are considered, the distributions of perturbed levels collapse to universal forms for both orthogonal and unitary ensembles for all values of the coupling. These universal curves are described well by a simple Wigner-surmise-type toy model. Third, we study the fluctuations of the mean-field parameters in the SBMFA, finding that they are small. Finally, the change in the intensity of an eigenfunction at an arbitrary point is studied, such as is relevant in conductance measurements. We find that the introduction of the strongly coupled impurity considerably changes the wave function but that a substantial correlation remains.