While the behavior of strongly interacting two-dimensional electrons in high magnetic fields is by now well understood, our understanding of the three-dimensional (3D) case is comparatively rudimentary. Illuminating this disparity are recent experiments on 3D bismuth, where unanticipated transport and magnetization structure—including hysteresis—persist even when all carriers are expected to reside in the lowest Landau level. Motivated by these findings, we derive a low-energy Hamiltonian for the hole and three Dirac electron pockets in bismuth which, crucially, encodes an unconventional Zeeman effect generated by spin-orbit coupling. We show that (1) this Zeeman coupling strongly suppresses the quantum limit for the Dirac electrons, giving rise to the observed magnetization structure, and (2) the hysteresis coincides with one of the pockets emptying its second Landau level, which is where Coulomb effects are most pronounced. Incorporating interactions, we find instabilities toward charge-density-wave and Wigner crystal phases and propose that hysteresis arises from a first-order transition out of the latter.

We present time-dependent density matrix renormalization group simulations $\left(t\text{-DMRG}\right)$ at finite temperatures. It is demonstrated how a combination of finite-temperature $t\text{-DMRG}$ and time-series prediction allows for an easy and very accurate calculation of spectral functions in one-dimensional quantum systems, irrespective of their statistics for arbitrary temperatures. This is illustrated with spin structure factors of $XX$ and $XXX$ spin-$\frac{1}{2}$ chains. For the $XX$ model we can compare against an exact solution, and for the $XXX$ model (Heisenberg antiferromagnet) against a Bethe ansatz solution and quantum Monte Carlo data.

We uncover the constitutive relation of graphene and probe the physics of its optical phonons by studying its Raman spectrum as a function of uniaxial strain. We find that the doubly degenerate $E_{2g}$ optical mode splits in two components: one polarized along the strain and the other perpendicular. This splits the $G$ peak into two bands, which we call $G^{+}$ and $G^{-}$, by analogy with the effect of curvature on the nanotube $G$ peak. Both peaks redshift with increasing strain and their splitting increases, in excellent agreement with first-principles calculations. Their relative intensities are found to depend on light polarization, which provides a useful tool to probe the graphene crystallographic orientation with respect to the strain. The 2D and $2{\text{D}}^{\prime }$ bands also redshift but do not split for small strains. We study the Grüneisen parameters for the phonons responsible for the $G$, $D$, and $D^{\prime }$ peaks. These can be used to measure the amount of uniaxial or biaxial strain, providing a fundamental tool for nanoelectronics, where strain monitoring is of paramount importance

Several recent works on quantum criticality beyond the Landau-Ginzburg-Wilson paradigm have led to a number of field theories, potentially important for certain two-dimensional magnetic insulating systems, where criticality is not very well understood. This situation highlights the need for nonperturbative information about criticality in two spatial dimensions (three space-time dimensions), which is a longstanding challenge. As a step toward addressing these issues, we present evidence that the O(4) vector model is dual to a theory of Dirac fermions coupled to both SU(2) and U(1) gauge fields. Both field theories arise as low-energy long-wavelength descriptions of a frustrated $XY$ model on the triangular lattice. Abelian boson-vortex duality of the lattice model, together with the emergence of larger non-Abelian symmetry at low energies, leads to this rare example of duality in two spatial dimensions involving non-Abelian global symmetry and fermions but without supersymmetry. The duality can also be viewed as a bosonization of the Dirac fermion gauge theory.

Four-terminal resistances, both longitudinal and diagonal, of a locally gated graphene device are measured in the quantum-Hall (QH) regime. In sharp distinction from previous two-terminal studies [J. R. Williams et al., Science 317, 638 (2007); B. Özyilmaz et al., Phys. Rev. Lett. 99, 166804 (2007)], asymmetric QH resistances are observed, which provide information on reflection as well as transmission of the QH edge states. Most quantized values of resistances are well analyzed by the assumption that all edge states are equally populated. Contrary to the expectation, however, a 5/2 transmission of the edge states is also found, which may be caused by incomplete mode mixing and/or by the presence of counterpropagating edge states. This four-terminal scheme can be conveniently used to study the edge-state equilibration in locally gated graphene devices as well as monolayer and multilayer graphene hybrid structures.

We discuss the superconductor-to-normal phase transition in an infinite-layered, type-II superconductor in the limit where the Josephson coupling between layers is negligible. We model each layer as a neutral gas of thermally excited pancake vortices and assume that the dominant interlayer coupling is the electromagnetic interaction between the screening currents induced by these vortices. Our main result, obtained by exactly solving the leading order renormalization group (RG) flow, is that the phase transition in this model is a Kosterlitz-Thouless transition despite being a three-dimensional system. While the transition itself is driven by the unbinding of two-dimensional pancake vortices, an RG analysis of the low temperature phase and a mean-field theory of the high temperature phase reveal that both phases possess three-dimensional correlations. An experimental consequence is that the jump in the measured in-plane superfluid stiffness, a universal quantity in $2d$ Kosterlitz-Thouless theory, receives a small nonuniversal correction (of order 1% in ${\text{Bi}}_2{\text{Sr}}_2{\text{CaCu}}_2{\text{O}}_{8+x}$). This overall picture places some claims expressed in the literature on a more secure analytical footing and resolves some conflicting views.

Using first-principles density-functional theory we predict a ferroelectric ground state—driven by the off-centering of the magnetic ${\text{Mn}}^{4+}$ ion—in perovskite-structure ${\text{BaMnO}}_3$. Our finding is surprising since the competition between energy-lowering covalent bond formation and energy-raising Coulombic repulsions usually only favors off-centering on the perovskite $B$ site for nonmagnetic $d^0$ ions. We explain this tendency for ferroelectric off-centering by analyzing the changes in electronic structure between the centrosymmetric and polar states and by calculating the Born effective charges; we find anomalously large values for Mn and O consistent with our calculated polarization of $12.8\mu \text{C}/{\text{cm}}^2$. Finally, we suggest possible routes by which the perovskite phase may be stabilized over the usual hexagonal phase to enable a practical realization of a single-phase multiferroic.

We study the steady state of driven elastic strings in disordered media below the depinning threshold. In the low-temperature limit, for a fixed sample, the steady state is dominated by a single configuration, which we determine exactly from the transition pathways between metastable states. We obtain the dynamical phase diagram in this limit. At variance with a thermodynamic phase transition, the depinning transition is not associated with a divergent length scale of the steady state below threshold, but only of the transient dynamics. We discuss the distribution of barrier heights, and check the validity of the dynamic phase diagram at small but finite temperatures using Langevin simulations. The phase diagram continues to hold for broken statistical tilt symmetry. We point out the relevance of our results for experiments of creep motion in elastic interfaces.

Monoclinic CuO is anomalous both structurally as well as electronically in the $3d$ transition metal oxide series. All the others have the cubic rocksalt structure. Here we report the synthesis and electronic property determination of a tetragonal (elongated rocksalt) form of CuO created using an epitaxial thin-film deposition approach. In situ photoelectron spectroscopy suggests an enhanced charge-transfer gap $\Delta$ with the overall bonding more ionic. As an end member of the $3d$ transition monoxides, its magnetic properties should be that of a high $T_N$ antiferromagnet.

We compare a fully quantum-mechanical numerical calculation of the conductivity of graphene to the semiclassical Boltzmann theory. Considering a disorder potential that is smooth on the scale of the lattice spacing, we find quantitative agreement between the two approaches away from the Dirac point. At the Dirac point the two theories are incompatible at weak disorder, although they may be compatible for strong disorder. Our numerical calculations provide a quantitative description of the full crossover between the quantum and semiclassical graphene transport regimes.

Thin films of lead have been grown on the Cu(111) surface and their structure and phonon dispersion curves have been investigated with high-resolution helium atom scattering. The diffraction pattern of the first monolayer (ML) indicates a $p\left(4\times 4\right)$ structure. Films consisting of $N=3$, 4, 5, and bulklike 50 ML all have a regular $\left(1\times 1\right)$ structure with the same lattice constant as the bulk and small superimposed $p\left(4\times 4\right)$ peaks for the thinnest films. The time-of-flight spectra reveal an unusually large number of inelastic peaks for all the films. The results have been analyzed in terms of dispersion curves which exhibit more than $\frac{1}{2}$ the total number of expected two $N$ modes active in the planar scattering geometry. Dispersion curves for an unannealed 5 ML film are also reported. A force-constant model fitted to the bulk dispersion curves can only qualitatively reproduce some of the data but help to explain some features. Along the $\overline{\Gamma }-\overline{K}$ direction, a Kohn anomaly is identified for the 3, 4, and 5 ML films at nearly the same wave vector as in the bulk along the equivalent direction.

We have employed soft and hard x-ray resonant magnetic scattering and polarized neutron diffraction to study the magnetic interface and the bulk antiferromagnetic domain state of the archetypal epitaxial ${\text{Ni}}_{81}{\text{Fe}}_{19}\left(111\right)/\text{CoO}\left(111\right)$ exchange biased bilayer. The combination of these scattering methods provides unprecedented detailed insights into the still incomplete understanding of some key manifestations of the exchange bias effect. We show that the several orders of magnitude difference between the expected and measured value of exchange bias field is caused by an anisotropic in-plane orientation of antiferromagnetic domains. Irreversible changes in their configuration lead to a training effect. This is directly seen as a change in the magnetic half-order Bragg peaks after magnetization reversal. The antiferromagnetic domain size is extracted from the width of the $\left(\frac{1}{2}\frac{1}{2}\frac{1}{2}\right)$ antiferromagnetic peak by both neutron and x-ray scattering and is determined to be 30 nm in size. A reduced blocking temperature as compared to the measured antiferromagnetic ordering temperature clearly corresponds to the blocking of antiferromagnetic domains. Moreover, an excellent correlation between the size of the antiferromagnetic domains, exchange bias field, and frozen-in spin ratio is found, providing a comprehensive understanding of the origin of exchange bias in epitaxial systems.

The growth and elementary properties of $p$-type ${\text{Bi}}_2{\text{Se}}_3$ single crystals are reported. Based on a hypothesis about the defect chemistry of ${\text{Bi}}_2{\text{Se}}_3$, the $p$-type behavior has been induced through low-level substitutions (1% or less) of Ca for Bi. Scanning tunneling microscopy is employed to image the defects and establish their charge. Tunneling and angle-resolved photoemission spectra show that the Fermi level has been lowered into the valence band by about 400 meV in ${\text{Bi}}_{1.98}{\text{Ca}}_{0.02}{\text{Se}}_3$ relative to the $n$-type material. $p$-type single crystals with $ab$-plane Seebeck coefficients of $+180\mu \text{V}/\text{K}$ at room temperature are reported. These crystals show an anomalous peak in the Seebeck coefficient at low temperatures, reaching $+120\mu \text{V}{\text{K}}^{-1}$ at 7 K, giving them a high thermoelectric power factor at low temperatures. In addition to its interesting thermoelectric properties, $p$-type ${\text{Bi}}_2{\text{Se}}_3$ is of substantial interest for studies of technologies and phenomena proposed for topological insulators.

We model and evaluate the Peltier and Seebeck effects in magnetic multilayer nanostructures by a finite-element theory of thermoelectric properties. We present analytical expressions for the thermopower and the current-induced temperature changes due to Peltier cooling/heating. The thermopower of a magnetic element is in general spin polarized, leading to spin-heat coupling effects. Thermoelectric effects in spin valves depend on the relative alignment of the magnetization directions and are sensitive to spin-flip scattering as well as inelastic collisions in the normal-metal spacer.

We present studies of the magnetic field distribution around the vortices in ${\text{LuNi}}_2{\text{B}}_2\text{C}$. Small-angle neutron scattering measurements of the vortex lattice (VL) in this material were extended to unprecedentedly large values of the scattering vector $q$, obtained both by using high magnetic fields to decrease the VL spacing and by using higher order reflections. A square VL, oriented with the nearest-neighbor direction along the crystalline [110] direction, was observed up to the highest measured field. The first-order VL form factor, $\left|F\left(q_{10}\right)\right|$, was found to decrease exponentially with increasing magnetic field. Measurements of the higher-order form factors, $\left|F\left(q_{hk}\right)\right|$, reveal a significant in-plane anisotropy and also allow for a real-space reconstruction of the VL field distribution.

Measuring the transport of electrons through a graphene sheet necessarily involves contacting it with metal electrodes. We study the adsorption of graphene on metal substrates using first-principles calculations at the level of density-functional theory. The bonding of graphene to Al, Ag, Cu, Au, and Pt (111) surfaces is so weak that its unique “ultrarelativistic” electronic structure is preserved. The interaction does, however, lead to a charge transfer that shifts the Fermi level by up to 0.5 eV with respect to the conical points. The crossover from $p$-type to $n$-type doping occurs for a metal with a work function $\sim 5.4\text{eV}$, a value much larger than the work function of free-standing graphene, 4.5 eV. We develop a simple analytical model that describes the Fermi-level shift in graphene in terms of the metal substrate work function. Graphene interacts with and binds more strongly to Co, Ni, Pd, and Ti. This chemisorption involves hybridization between graphene $p_z$ states and metal $d$ states that opens a band gap in graphene, and reduces its work function considerably. The supported graphene is effectively $n$-type doped because in a current-in-plane device geometry the work-function lowering will lead to electrons being transferred to the unsupported part of the graphene sheet.

We consider the two-dimensional Hubbard model on the honeycomb lattice, as a model for single-layer graphene with screened Coulomb interactions; at half filling and weak coupling, we construct its ground-state correlations by a convergent multiscale expansion, rigorously excluding the presence of magnetic or superconducting instabilities or the formation of a mass gap. The Fermi velocity, which can be written in terms of a convergent series expansion, remains close to its noninteracting value and turns out to be isotropic; as a consequence, the Dirac cones are isotropic at low energies. On the contrary, the interaction produces an asymmetry between the two components of the charge velocity, in contrast to the predictions based on relativistic or continuum approximations.

Recent experiments on triangular lattice organic Mott insulators have found evidence for a two-dimensional (2D) spin liquid in close proximity to the metal-insulator transition. A Gutzwiller wave function study of the triangular lattice Heisenberg model with a four-spin ring exchange term appropriate in this regime has found that the projected spinon Fermi sea state has a low variational energy. This wave function, together with a slave particle-gauge theory analysis, suggests that this putative spin liquid possesses spin correlations that are singular along surfaces in momentum space, i.e., “Bose surfaces.” Signatures of this state, which we will refer to as a “spin Bose metal” (SBM), are expected to manifest in quasi-one-dimensional (quasi-1D) ladder systems: the discrete transverse momenta cut through the 2D Bose surface leading to a distinct pattern of 1D gapless modes. Here, we search for a quasi-1D descendant of the triangular lattice SBM state by exploring the Heisenberg plus ring model on a two-leg triangular strip (zigzag chain). Using density matrix renormalization group (DMRG) supplemented by variational wave functions and a bosonization analysis, we map out the full phase diagram. In the absence of ring exchange the model is equivalent to the $J_1\text{−}{J}_2$ Heisenberg chain, and we find the expected Bethe-chain and dimerized phases. Remarkably, moderate ring exchange reveals a new gapless phase over a large swath of the phase diagram. Spin and dimer correlations possess singular wave vectors at particular “Bose points” (remnants of the 2D Bose surface) and allow us to identify this phase as the hoped for quasi-1D descendant of the triangular lattice SBM state. We use bosonization to derive a low-energy effective theory for the zigzag spin Bose metal and find three gapless modes and one Luttinger parameter controlling all power law correlations. Potential instabilities out of the zigzag SBM give rise to other interesting phases such as a period-3 valence bond solid or a period-4 chirality order, which we discover in the DMRG. Another interesting instability is into a spin Bose-metal phase with partial ferromagnetism (spin polarization of one spinon band), which we also find numerically using the DMRG.

Inhomogeneous broadening due to isotopic randomness in natural Si has been shown to cause a broadening of many of the ground-state to excited-state infrared-absorption transitions of the shallow donor phosphorus and acceptor boron. Previously, it had been thought that the observed linewidths of shallow impurity transitions in silicon were at their fundamental lifetime limit. We report improved high-resolution infrared-absorption studies of these transitions in new samples of isotopically enriched ${}^{28}\text{S}\text{i}$, ${}^{29}\text{S}\text{i}$, and ${}^{30}\text{S}\text{i}$. Some of the transitions in ${}^{28}\text{S}\text{i}$ show the narrowest linewidths ever reported for shallow donor and acceptor absorption transitions, and many higher excited states are now observed. The improved samples of ${}^{29}\text{S}\text{i}$ and ${}^{30}\text{S}\text{i}$ result in revised values for the dependence of shallow donor and acceptor binding energies on the average Si mass.

We present a simpler derivation of the exact solution of a spin polaron in a ferromagnet and generalize it to complex lattices and/or longer-range exchange interactions. As a specific example, we analyze a two-dimensional ${\text{MnO}}_2$-like lattice (as in the ferromagnetic layers in ${\text{LaMnO}}_3$) and discuss the properties of the resulting spin polaron in various regimes. At strong couplings the solution is reminiscent of the Zhang-Rice singlet, however the electronic wave function involved in the singlet is dependent on the momentum of the singlet, and multiple bands may appear.