We report an unexpected anomaly in the zero-field Hall coefficient of two-dimensional electron systems in high-mobility GaAs/AlGaAs heterostructures. Our device layout allows the investigation of mesoscopic systems with variable Fermi energy as well as with tunable Hall probes. At very low temperature, both positive and negative deviations from the noninteracting Hall coefficient ${\gamma }_{\text{H}}^0$ are observed, which can be twice as large as ${\gamma }_{\text{H}}^0$ itself. A distinct regularity in the deviations and their temperature dependence are interpreted as the spontaneous formation of localized spins and their indirect exchange interaction.

The area and perimeter dependences of the Josephson-like interlayer tunneling signature of the coherent ${\nu }_T=1$ quantum Hall phase in bilayer two-dimensional electron systems is examined. Electrostatic top gates of various sizes and shapes are used to locally define distinct ${\nu }_T=1$ regions in the same sample. Near the phase boundary with the incoherent ${\nu }_T=1$ state at large layer separation, our results demonstrate that the tunneling conductance in the coherent phase is closely proportional to the total area of the tunneling region. This implies that tunneling at ${\nu }_T=1$ is a bulk phenomenon in this regime.

${\text{CaFe}}_2{\text{As}}_2$ has been synthesized and found to form in the tetragonal ${\text{ThCr}}_2{\text{Si}}_2$ structure with lattice parameters $a=3.912\left(68\right)\text{Å}$ and $c=11.667\left(45\right)\text{Å}$. Upon cooling through 170 K, ${\text{CaFe}}_2{\text{As}}_2$ undergoes a first-order structural phase transition to a low-temperature orthorhombic phase with a 2–3 K range of hysteresis and coexistence. This transition is clearly evident in microscopic, thermodynamic, and transport measurements. ${\text{CaFe}}_2{\text{As}}_2$ is the third member of the ${\text{AFe}}_2{\text{As}}_2$ $\left(A=\text{Ba},\text{Sr},\text{Ca}\right)$ family to exhibit such a dramatic phase transition and is a promising candidate for studies of doping induced superconductivity.

We introduce a one-dimensional valence bond solid (VBS) state with symplectic symmetry $\text{SP}\left(n\right)$ and construct the corresponding parent Hamiltonian. We argue that there is a gap in the spectrum. We calculate exactly the static correlation functions, which fall off exponentially. Hence the model introduced here shares all properties of the Haldane scenario for integer-spin quantum antiferromagnets. We further show that the VBS state possesses string order and discuss its generalization to higher dimensions.

The ordering temperature of a quasi-one-dimensional system, consisting of weakly interacting quantum spin-1/2 chains with antiferromagnetic spin-frustrating couplings (or zigzag ladder), is calculated. The results show that a quantum critical point between two phases of the one-dimensional subsystem plays a crucial role. If the one-dimensional subsystem is in the antiferromagneticlike phase in the ground state, similar to the phase of a spin chain without frustration, weak couplings yield magnetic ordering of the Néel type. For intrachain spin-frustrating interactions larger than the critical one (at which the quantum phase transition takes place), the quasi-one-dimensional spin system manifests a spiral magnetic incommensurate ordering. The obtained results of our quantum theory are compared with the quasiclassical approximations. The calculated features of magnetic ordering are expected to be generic for weakly-coupled quantum spin chains with gapless excitations and spin-frustrating nearest- and next-nearest-neighbor interactions.

DC and ac magnetization, resistivity, specific-heat, and neutron-diffraction data reveal that stoichiometric LaFePO is metallic and non-superconducting above $T=0.35\text{K}$, with $\gamma =12.5\frac{\text{mJ}}{\text{mol}{\text{K}}^2}$. Neutron-diffraction data at room temperature and $T=10\text{K}$ are well described by the stoichiometric, tetragonal ZrCuSiAs structure, and show no signs of structural distortions or long-range magnetic ordering to an estimated detectability limit of $0.07{\mu }_B/\text{Fe}$. We propose a model based on the shape of the iron-pnictide tetrahedron that explains the differences between LaFePO and LaFeAsO, the parent compound of the recently discovered high-Tc oxyarsenides, which, in contrast, shows both structural and spin-density wave transitions.

We present a mean-field theory of the Pomeranchuk instability in two dimensions, starting from a generic central interaction potential described in terms of a few microscopic parameters. For a significant range of parameters, the instability is found to be pre-empted by a first-order quantum phase transition. We provide the ground-state phase diagram in terms of our generic parameters.

We identify the donor level of interstitial hydrogen in GaAs, which is characterized by the activation enthalpy $E_C-E_t=0.13\text{eV}$. This level is the marker of two different but closely related defect structures, which are indistinguishable as far as their emission properties are concerned; however, discernible on the basis of their different dynamical behaviors are revealed by annealing studies. We interpret the two structures as regular bond center hydrogen $\text{H}\left(BC\right)$ and bond center hydrogen $\text{H}\left(B{C}^{\prime }\right)$, which is perturbed by the local strain from a neighbor point defect. We demonstrate negative-$U$ properties of the perturbed structure and infer that the corresponding acceptor $\text{H}\left(T^{\prime }\right)$ lies deep in the band gap. These results for interstitial hydrogen in GaAs are in every aspect analogous to the properties of interstitial hydrogen in Si.

We describe a computational method based on density functional theory in which the total electronic density is expressed as a sum over “atomic” densities or densities localized at atomic sites. The atomic densities are determined self-consistently from a variational treatment of the total energy, which includes terms to account for kinetic energy due to the overlapping densities from separate atomic sites. We call this method self-consistent atomic deformation. The self-consistent procedure involves formulation and calculation of a potential for each atomic site, solving a one-electron Schrödinger’s equation for each site and using these self-consistent potentials and densities to compute total energy and forces. The associated numerical methods employed are described in detail and illustrated for selected examples.

We propose a method to detect the geometric phase produced by the Dirac-type band structure of a triangular-lattice photonic crystal. The spectrum is known to have a conical singularity ($=\text{Dirac}$ point) with a pair of nearly degenerate modes near that singularity described by a spin-$\frac{1}{2}$ degree of freedom $\left(=\text{pseudospin}\right)$. The geometric Berry phase acquired upon rotation of the pseudospin is in general obscured by a large and unspecified dynamical phase. We use the analogy with graphene to show how complementary media can eliminate the dynamical phase. A transmission minimum results as a direct consequence of the geometric phase shift of $\pi$ acquired by rotation of the pseudospin over $360°$ around a perpendicular axis. We support our analytical theory based on the Dirac equation by a numerical solution of the full Maxwell equations.

Using real-time charge sensing and gate pulsing techniques we measure the ratio of the rates for tunneling into the excited and ground spin states of a single-electron quantum dot at an AlGaAs/GaAs interface in a magnetic field parallel to the interface. We find that the ratio decreases with increasing magnetic field until tunneling into the excited spin state is completely suppressed. However, we find that by adjusting the voltages on the surface gates to change the orbital configuration of the dot, we can restore tunneling into the excited spin state and that the ratio reaches a maximum when the dot is symmetric.

We develop a dynamical simulation model for magnetic iron where atoms are treated as classical particles with intrinsic spins. The atoms interact via scalar many-body forces as well as via spin orientation dependent forces of the Heisenberg form. The coupling between the lattice and spin degrees of freedom is described by a coordinate-dependent exchange function where the spin orientation dependent forces are proportional to the gradient of this function. The spin-lattice dynamics simulation approach extends the existing magnetic potential treatment to the case where the energy of interaction between the atoms depends on the relative noncollinear orientations of spins. An algorithm for integrating the linked spin-coordinate equations of motion is based on the second-order Suzuki-Trotter decomposition for noncommuting operators of evolution for coordinate and spin variables. The notions of the spin thermostat and the spin temperature are introduced through the combined application of the Langevin spin dynamics and the fluctuation-dissipation theorem. We investigate several applications of the method, performing microcanonical ensemble simulations of adiabatic spin-lattice relaxation of periodic arrays of $180°$ domain walls, and isothermal-isobaric ensemble dynamical simulations of thermally equilibrated homogeneous systems at various temperatures. The predicted isothermal magnetization curve agrees well with the experimental data for a broad range of temperatures. The equilibrium as well as time-correlation functions of spin orientations exhibit the presence of short-range magnetic order above the Curie temperature. Furthermore, short-range order spin fluctuations are shown to contribute to the thermal expansion of the material. Our analysis illustrates the significant part played by the spin degrees of freedom in the dynamics of motion of atoms in magnetic iron and iron-based alloys. It also shows that the spin-lattice dynamics algorithm developed in this paper offers a viable way of performing large-scale dynamical atomistic simulations of magnetic materials.

The Chalker-Coddington network model (introduced originally as a model for percolation in the quantum Hall effect) is known to map onto the two-dimensional Dirac equation. Here we show how the network model can be used to solve a scattering problem in a weakly doped graphene sheet connected to heavily doped electron reservoirs. We develop a numerical procedure to calculate the scattering matrix with the aide of the network model. For numerical purposes, the advantage of the network model over the honeycomb lattice is that it eliminates intervalley scattering from the outset. We avoid the need to include the heavily doped regions in the network model (which would be computationally expensive) by means of an analytical relation between the transfer matrix through the weakly doped region and the scattering matrix between the electron reservoirs. We test the network algorithm by calculating the conductance of an electrostatically defined quantum point contact and comparing with the tight-binding model of graphene. We further calculate the conductance of a graphene sheet in the presence of disorder in the regime where intervalley scattering is suppressed. We find an increase in conductance that is consistent with previous studies. Unlike the tight-binding model, the network model does not require smooth potentials in order to avoid intervalley scattering.

We have studied the effects of band filling and bandwidth-control on the chemical potential in perovskite manganites $R_{1-x}{A}_x{\text{MnO}}_3$ ($R$: rare earth, $A$: alkaline earth) by measurements of core-level photoemission spectra. A suppression of the doping-dependent chemical potential shift was observed in and around the CE-type charge-ordered composition range, indicating that there is charge self-organization such as stripe formation or its fluctuations. As a function of bandwidth, we observed a downward chemical potential shift with increasing bandwidth due to the reduction of the orthorhombic distortion. After subtracting the latter contribution, we found an upward chemical potential shift in the ferromagnetic metallic region $0.3<x<0.5$, which we attribute to the enhancement of double-exchange interaction involving the Jahn-Teller-split $e_g$ band.

We report on the observation of terahertz oscillations in an electron-hole plasma optically excited by a femtosecond pulse in the $\mu \text{m}$-sized slab of low-temperature-grown-GaAs (LT-GaAs) grown on the GaAs substrate. The frequency of oscillations is shown to be inversely proportional to the slab thickness. It is suggested that the LT-GaAs slab serves as a resonant cavity for traveling plasma waves, which have been generated as a consequence of the shock interaction of photoexcited electron plasma with the GaAs/LT-GaAs interface. The instantaneous diffusion of photoexcited plasma inward the material is driven by the density gradient over the Beer’s law distributed carrier population and is evidenced to be a main reason of the shock interaction in the localized plasma. The frequencies of oscillations observed are 3.5 times larger that the inverse electron transit time in the LT-GaAs slab, suggesting the “ballistic” regime for plasma wave propagation to occur. The oscillations have been observed in the photocurrent autocorrelation measurements. The dynamical electric field at the GaAs/LT-GaAs interface arising due to the instantaneous diffusion of photoexcited electrons inward the material was studied through the transient reflectivity change responses, which have been measured simultaneously with photocurrent.

We study the electronic surface states of the semiconducting alloy bismuth antimony $\left({\text{Bi}}_{1-x}{\text{Sb}}_x\right)$. Using a phenomenological tight-binding model, we show that the Fermi surface for the 111 surface states encloses an odd number of time-reversal-invariant momenta (TRIM) in the surface Brillouin zone. This confirms that the alloy is a strong topological insulator in the (1;111) ${\mathbb{Z}}_2$ topological class. We go on to develop general arguments which show that spatial symmetries lead to additional topological structure of the bulk energy bands, and impose further constraints on the surface band structure. Inversion-symmetric band structures are characterized by eight ${\mathbb{Z}}_2$ “parity invariants,” which include the four ${\mathbb{Z}}_2$ invariants defined by time-reversal symmetry. The extra invariants determine the “surface fermion parity,” which specifies which surface TRIM are enclosed by an odd number of electron or hole pockets. We provide a simple proof of this result, which provides a direct link between the surface-state structure and the parity eigenvalues characterizing the bulk. Using this result, we make specific predictions for the surface-state structure for several faces of ${\text{Bi}}_{1-x}{\text{Sb}}_x$. We next show that mirror-invariant band structures are characterized by an integer “mirror Chern number” $n_{\mathcal{M}}$, which further constrains the surface states. We show that the sign of $n_{\mathcal{M}}$ in the topological insulator phase of ${\text{Bi}}_{1-x}{\text{Sb}}_x$ is related to a previously unexplored ${\mathbb{Z}}_2$ parameter in the $L$ point $\mathbf{k}\cdot \mathbf{p}$ theory of pure bismuth, which we refer to as the “mirror chirality” $\eta$. The value of $\eta$ predicted by the tight-binding model for bismuth disagrees with the value predicted by a more fundamental pseudopotential calculation. This explains a subtle disagreement between our tight-binding surface-state calculation and previous first-principles calculations of the surface states of bismuth. This suggests that the tight-binding parameters in the Liu-Allen model of bismuth need to be reconsidered. Implications for existing and future angle-resolved photoemission spectroscopy (ARPES) experiments and spin-polarized ARPES experiments will be discussed.

We use a nanowire quantum dot to probe high-frequency current fluctuations in a nearby quantum point contact. The fluctuations drive charge transitions in the quantum dot, which are measured in real-time with single-electron detection techniques. The quantum point contact (GaAs) and the quantum dot (InAs) are fabricated in different material systems, which indicates that the interactions are mediated by photons rather than phonons. The large energy scales of the nanowire quantum dot allow radiation detection in the long-wavelength infrared regime.

Ultrafast electron dynamics in Pb/Si(111) quantum well structures have been investigated by femtosecond time-resolved two-photon photoemission spectroscopy. Three unoccupied quantum well states (or subbands) as well as an image potential state are identified and analyzed as a function of Pb thickness. Using 1.9 eV photon energy for optical excitation electron-hole pairs are formed in the Pb film and in the Si substrate. The hot electron population in the quantum well states exhibits a biexponential decay and both decay times increase when the energy difference to the Fermi level is reduced. The slower decay component with decay times of 130 and 900 fs is attributed to delayed filling of the states in the adlayer due to electronic relaxation in the Si(111) substrate. The faster decay (30–140 fs) is caused by electron-electron scattering in the Pb film. At a first glance, the extracted decay times increase toward the Fermi level as predicted by the Fermi-liquid theory. However, by investigation of the quantized electronic structure more detailed insight into scattering among defined subbands has been gained. The rise of the excited electron population in the lowest unoccupied quantum well state is delayed by 70 fs which occurs concomitantly with a decay in the second lowest state. We describe this simultaneous decay and rise in the two adjacent subbands by coupled rate equations and attribute it to intersubband scattering. Thereby, we demonstrate the importance of intersubband decay in low-dimensional metallic systems in addition to intraband scattering processes considered in Fermi-liquid theory and derived descriptions.

The superconducting properties of ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{7\text{−}\delta }$ (YBCO) are strongly dependent on atomic structure and composition. While the average structures of YBCO are well documented, the local oxygen concentration and ordering have received much less attention owing to the difficulty of experiments and analysis. We examined several samples of YBCO by quantitative high-resolution transmission electron microscopy and geometric phase analysis to determine their local atomic structure and symmetry. Our results reveal that adjacent domains separated by the (110) interfaces, commonly considered to be twin domains, can have different $a_o/b_o$ ratios. The domains, therefore, do not retain the ideal twinned configuration commonly expected for this system. Assuming the $a_o/b_o$ ratio is proportional to oxygen concentration, we suggest that these domains result from inhomogeneous oxygen distribution. Multiple measurements in both bulk and thin-film samples indicate that YBCO can consist of different phases, which may yield locally variable superconducting properties.

We study theoretically the zero-temperature phase transition in two dimensions from a Fermi liquid to a paramagnetic Mott insulator with a spinon Fermi surface. We show that the approach to the bandwidth-controlled Mott transition from the metallic side is accompanied by a vanishing quasiparticle residue and a diverging effective mass. The Landau parameters $F_s^0,F_a^0$ also diverge. Right at the quantum critical point there is a sharply defined “critical Fermi surface” but no Landau quasiparticle. The critical point has a $T\text{ln}1/T$ specific heat and a nonzero $T=0$ resistivity. We predict an interesting universal resistivity jump in the residual resistivity at the critical point as the transition is approached from the metallic side. The crossovers out of the critical region are also studied. Remarkably the initial crossover out of criticality on the metallic side is to a marginal Fermi liquid metal. At much lower temperatures there is a further crossover into the Landau Fermi liquid. The ratio of the two crossover scales vanishes when approaching the critical point. Similar phenomena are found in the insulating side. The filling-controlled Mott transition is also studied. Implications for experiments on the layered triangular lattice organic material $\kappa -{\left(\text{ET}\right)}_2{\text{Cu}}_2{\left(\text{CN}\right)}_3$ are discussed.