Molecular dynamics simulations were performed on a first-principles-based effective Hamiltonian for $\text{Pb}\left({\text{Sc}}_{1/2}{\text{Nb}}_{1/2}\right){\text{O}}_3$ (PSN) with nearest neighbor Pb-O divacancy pairs. Simulations were performed for PSN with ideal chemical order, chemical short-range order, and random chemical disorder. Divacancy concentration vs temperature, $X_{\left[\text{Pb-O}\right]}$ vs $T$, phase diagrams were calculated, and they are shown to be topologically equivalent to the previously calculated hydrostatic pressure vs temperature diagram. In PSN with ideal chemical order, the Burns temperature defines an isotherm, which is analogous to the “Griffiths phase” in the magnetic dilution problem.

A variety of thermodynamic and transport measurements were made on high-quality single crystals of the Pr-based filled skutterudite compound ${\text{PrFe}}_4{\text{As}}_{12}$. Abrupt features in magnetization, ac susceptibility, specific heat, resistivity, thermoelectric power, and ultrasonic velocity reveal the onset of long range ferromagnetic order below ${\Theta }_C=18\text{K}$. The low-temperature magnetic susceptibility is characterized by a Curie–Weiss law with an effective moment of $3.52{\mu }_B/\text{f}\text{.u}\text{.}$ and a saturation magnetization of $2.3{\mu }_B/\text{f}\text{.u}\text{.}$, which is consistent with a magnetic ${\Gamma }_5$ triplet ground state. A gaplike reduction of the large electronic specific heat coefficient of $340\text{mJ}/\text{mol}{\text{K}}^2$ and several other features point to a strongly correlated electron behavior that is likely coupled to a change in magnetic and/or structural order near $T^{\ast }\simeq 12\text{K}$. Furthermore, this complex magnetic state is found to be strongly field dependent, as evidenced by a change in the easy axis at low fields and an additional contribution to thermal conductivity appearing only at high fields.

The distribution of charge induced by a gate voltage in a graphene strip is investigated. We analytically calculate the charge profile and demonstrate a strong (macroscopic) charge accumulation along the boundaries of a micrometer-wide strip. This charge inhomogeneity is especially important in the quantum Hall regime, where we predict the doubling of the number of edge states and the coexistence of two different types of such states. Applications to graphene-based nanoelectronics are discussed.

We investigate the influence of inhomogeneity in the pairing coupling constant $U\left(\vec{r}\right)$ on dirty BCS superconductors, focusing on $T_c$, the order parameter $\Delta \left(\vec{r}\right)$, and the energy gap $E_g\left(\vec{r}\right)$. Within mean-field theory, we find that when the length scale of the inhomogeneity is comparable to or larger than the coherence length, the ratio $2E_g∕T_c$ is significantly reduced from that of a homogeneous superconductor, while in the opposite limit, this ratio stays unmodified. In two dimensions, when strong phase fluctuations are included, the Kosterlitz-Thouless temperature $T_{\mathit{KT}}$ is also studied. We find that when the inhomogeneity length scale is much larger than the coherence length, $2E_g∕T_{\mathit{KT}}$ can be larger than the usual BCS value. We use our results to qualitatively explain recent experimental observation of a surprisingly low value of $2E_g∕T_c$ in thin films.

We have synthesized single crystals of ${\text{Yb}}_2{\text{Pt}}_2\text{Pb}$, which crystallize in the layered ${\text{U}}_2{\text{Pt}}_2\text{Sn}$-type structure, where planes of Yb ions lie on a triangular network. Here, we report the results of magnetization, specific heat, and electrical resistivity experiments. The lattice constants and high temperature magnetic susceptibility indicate that the Yb ions are trivalent, while the Schottky peaks in the specific heat show that the ground state is a well isolated doublet. A significant magnetic anisotropy is observed, with the ratio of susceptibilities perpendicular and parallel to the magnetic planes differing by as much as a factor of 30 at the lowest temperatures. Antiferromagnetic order occurs at a Néel temperature $T_N=2.07\text{K}$. Evidence of short range magnetic fluctuations is found in the magnetic susceptibility and electrical resistivity, which have broad peaks above $T_N$, and in the slow development of the magnetic entropy at $T_N$. Our experiments indicate that ${\text{Yb}}_2{\text{Pt}}_2\text{Pb}$ is a quasi-two-dimensional and localized moment system, where strong magnetic frustration may arise from the geometry of the underlying Shastry-Sutherland lattice.

We derive an analytical formula for the open-circuit voltage $\left(V_{\text{oc}}\right)$ of organic planar heterojunction solar cells under standard operating conditions. We find that the type of free carrier recombination at the interface between the donor and acceptor materials controls the slope of $V_{\text{oc}}$ vs incident light intensity. By using the same derivation, an equation for the resistance around $V_{\text{oc}}$ is obtained. From this, we investigate two parameters in more detail and compare them to experiments. The first is the work function of the cathode metal. We show that, within our model, $V_{\text{oc}}$ does not depend on this work function, while the cell resistance around $V_{\text{oc}}$ is strongly dependent on it. Second, we find that the asymptotic resistance around $V_{\text{oc}}$ is a third-order power function of the thickness of the organic layers (acceptor or donor). The model provides insights to achieve low-resistivity high open-circuit voltage organic solar cells.

We present a systematic study of the variations of the ${}^7\mathrm{Li}$ NMR properties versus magnetic defect concentration $n_{\text{defect}}$ within the spinel structure of polycrystalline powder samples ($n_{\text{defect}}=0.21$, 0.49, and $0.83\mathrm{mol}\%$) and a collection of small single crystals $(n_{\text{defect}}=0.38\mathrm{mol}\%)$ of $\mathrm{Li}{\mathrm{V}}_2{\mathrm{O}}_4$ in the temperature range from $0.5\text{to}4.2\mathrm{K}$. We also report static magnetization measurements and ac magnetic susceptibility measurements at $14\mathrm{MHz}$ on the samples at low temperatures. Both the ${}^7\mathrm{Li}$ NMR spectrum and nuclear spin-lattice relaxation rate are inhomogeneous in the presence of the magnetic defects. The ${}^7\mathrm{Li}$ NMR data for the powders are well explained by assuming that (i) there is a random distribution of magnetic point defects, (ii) the same heavy Fermi liquid is present in the samples containing the magnetic defects as in magnetically pure $\mathrm{Li}{\mathrm{V}}_2{\mathrm{O}}_4$, and (iii) the influences of the magnetic defects and of the Fermi liquid on the magnetization and NMR properties are separable. In the single crystals, somewhat different behaviors are observed, which are possibly due to a modification of the heavy Fermi liquid, to a lack of separability of the relaxation effects due to the Fermi liquid and the magnetic defects, to non-Fermi liquid behavior of the conduction electrons, and/or to quantum fluctuations of finite-size magnetic defects (magnetic droplets). Remarkably, the magnetic defects in the powder samples show evidence of spin freezing below $T\approx 1.0\mathrm{K}$, whereas in the single crystals with similar magnetic defect concentration, no spin freezing was found down to $T=0.5\mathrm{K}$. Thus, different types of magnetic defects and/or interactions between them appear to arise in the powders versus the crystals, which are possibly due to the substantially different synthesis conditions of the powders and crystals.

As recently shown, ${\text{HgBa}}_2{\text{Ca}}_{n-1}{\text{Cu}}_n{\text{O}}_y$ $\left(n\ge 6\right)$ cuprate superconductors have a critical temperature of about 100 K independent of $n$. This remarkable property can be explained by the very imbalanced distribution of carriers among the inequivalent ${\text{CuO}}_2$ planes in the unit cell. We discovered that these materials also have a common vortex melting line that resembles the theoretical melting lines of magnetically coupled pancake vortices. We suggest that there are two types of pancake pairs situated in the superconducting ${\text{CuO}}_2$ outer planes: those separated by the thin charge reservoir layer are strongly (Josephson) coupled, while those separated by the thick block of $\left(n-2\right)$ ${\text{CuO}}_2$ nonsuperconducting inner planes are weakly (magnetically) coupled, forming magnetically coupled pancake vortex molecules.

Homogeneous melting in the superheating regime is investigated by using molecular dynamics simulation of a Lennard-Jones model system. We show that the commonly observed catastrophic melting at the superheating limit is caused by fast heating rate. By keeping the system isothermally at temperatures below the superheating limit, we observe intense self-diffusion motions as the precursor of melting. The highly correlated atomic motions are related to the self-diffusion loops or rings. Two types of loops are observed, closed loop and open loop, where the latter is directly related to the homogeneous nucleation of the liquid phase. Homogeneous melting occurs when the number density of diffusion loops reaches a critical value. Our results suggest that homogeneous melting in the superheating regime is a first-order thermodynamic phase transition triggered by the self-diffusion loops when the kinetic constraint imposed by heating rate is lessened.

We present a gauge-invariant theory of the electromagnetic response of a chiral $p_x+i{p}_y$ superconductor in the clean limit. Due to the spontaneously broken time-reversal symmetry, the effective action of the system contains an anomalous term not present in conventional superconductors. As a result, the electromagnetic charge and current responses contain anomalous terms, which explicitly depend on the chirality of the superconducting order parameter. These terms lead to a number of unusual effects, such as coupling of the transverse currents to the collective plasma oscillations and a possibility of inducing the charge density by the magnetic field perpendicular to the conducting planes. We calculate the antisymmetric part of the conductivity tensor (the intrinsic Hall conductivity) and show that it depends on the wave vector of the electromagnetic field. We also show that the Mermin–Muzikar magnetization current and the Hall conductivity are strongly suppressed at high frequencies. Finally, we discuss the implications of the theory to the experiments in ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$.

Quantum pumping holds great potential for future applications in microtechnology and nanotechnology. Its main feature, which is the dissipationless charge transport, is theoretically possible via several different mechanisms. However, since no unambiguous verification has been experimentally demonstrated, the question of finding a viable mechanism for pumping remains open. Here, we study quantum pumping in an one dimensional electron waveguide with a single time-dependent barrier. The quantum pumping of electrons by using a potential barrier whose height and position are harmonically varied is analytically analyzed and by numerically solving the time-dependent Schrödinger equation. The pumped charge is analytically modeled by including two contributions in linear response theory. First, the scattering of electrons off a potential moving slowly through matter waves gives a contribution independent of the translational velocity of the potential. Second, Doppler-shifted scattering events give rise to a velocity dependent contribution, which is found in general to be small in comparison with the first one. The relative phase between the oscillations of the height and position is found to be the factor that determines to what extent either contribution is present.

We present a study on the structural, spectroscopic, conducting, and magnetic properties of ${\mathrm{Mg}}_5{\mathrm{C}}_{60}$, which is a two-dimensional (2D) fulleride polymer. The polymer phase is stable up to the exceptionally high temperature of $823\mathrm{K}$. The infrared and Raman studies suggest the formation of single bonds between the fulleride ions and possibly $\mathrm{Mg}\text{−}{\mathrm{C}}_{60}$ covalent bonds. ${\mathrm{Mg}}_5{\mathrm{C}}_{60}$ is a metal at ambient temperature, as shown by electron spin resonance and microwave conductivity measurements. The smooth transition from a metallic to a paramagnetic insulator state below $200\mathrm{K}$ is attributed to Anderson localization driven by structural disorder.

A recent experiment [M. Sigrist et al., Phys. Rev. Lett. 98, 036805 (2007)] reported switches between 0 and $\pi$ in the phase of Aharonov-Bohm (AB) oscillations of the two-terminal differential conductance through a two-dot ring with increasing voltage bias. Using a simple model, where one of the dots contains multiple interacting levels, these findings are explained as a result of transport through the interferometer being dominated at different biases by quantum dot levels of different “parities” (i.e., the sign of the overlap integral between the dot state and the states in the leads). The redistribution of electron population between different levels with bias leads to the fact that the number of switching events is not necessarily equal to the number of dot levels, in agreement with experiment. For the same reason, switching does not always imply that the parity of levels is strictly alternating. Lastly, it is demonstrated that the correlation between the first switching of the phase and the onset of the inelastic cotunneling, as well as the sharp (rather than gradual) change of phase when switching occurs, give reason to think that the present interpretation of the experiment is preferable to the one based on electrostatic AB effect.

The polarized reflectivity spectra of $\mathrm{Cd}\mathrm{Mo}{\mathrm{O}}_4$ single crystals with a scheelite structure and of $\mathrm{Cd}\mathrm{W}{\mathrm{O}}_4$ with a wolframite structure are measured in the $3–30\mathrm{eV}$ range by using synchrotron radiation. The spectra of optical constants for the crystallographic axes are derived by a Kramers–Kronig analysis. X-ray photoelectron spectroscopy (XPS) and the calculation of the electronic structure by using a discrete variational $X\alpha$ method are performed for $\mathrm{Cd}\mathrm{Mo}{\mathrm{O}}_4$. The calculation shows that the $\mathrm{Cd}4d$ state is localized at the bottom region of the $\mathrm{O}2p$ valence band, and the $\mathrm{Cd}5s$ state has a significant contribution to the bottom of the conduction band, composed of the $\mathrm{Mo}4d$ state. The XPS spectrum of $\mathrm{Cd}\mathrm{Mo}{\mathrm{O}}_4$ resembles that of $\mathrm{Cd}\mathrm{W}{\mathrm{O}}_4$. Unlike the XPS spectrum, the optical spectra of $\mathrm{Cd}\mathrm{Mo}{\mathrm{O}}_4$ resemble those of scheelite $\mathrm{Ca}\mathrm{Mo}{\mathrm{O}}_4$ rather than $\mathrm{Cd}\mathrm{W}{\mathrm{O}}_4$. An excitonic transition is observed as a weak shoulderlike structure in $\mathrm{Cd}\mathrm{W}{\mathrm{O}}_4$, while it is not appreciable in $\mathrm{Cd}\mathrm{Mo}{\mathrm{O}}_4$. These experimental results are discussed in comparison with the theoretical calculation of electronic structures. The remarkable anisotropy of the optical spectra in $\mathrm{Cd}\mathrm{Mo}{\mathrm{O}}_4$ is explained by taking into account the presence of the $\mathrm{Cd}5s$ state at the bottom of the conduction band. The dichroism of $\mathrm{Cd}\mathrm{W}{\mathrm{O}}_4$ is discussed in terms of the chain structure of $\mathrm{W}\mathrm{O}_6{}^{6-}$ octahedra in wolframite crystals. The present study indicates that the Cd metal states play a crucial role in the optical properties near the fundamental absorption edge in both $\mathrm{Cd}\mathrm{Mo}{\mathrm{O}}_4$ and $\mathrm{Cd}\mathrm{W}{\mathrm{O}}_4$.

Recent experiments have shown that it is possible to create an in-plane harmonic potential trap for a two-dimensional (2D) gas of exciton polaritons in a microcavity structure, and evidence has been reported of Bose-Einstein condensation of polaritons accumulated in this type of trap. We present here the theory of Bose-Einstein condensation (BEC) and superfluidity of the exciton polaritons in a harmonic potential trap. Along the way, we determine a general method for defining the superfluid fraction in a 2D trap, in terms of angular momentum representation. We show that in the continuum limit, as the trap becomes shallower, the superfluid fraction approaches the 2D Kosterlitz–Thouless limit, while the condensate fraction approaches zero, as expected.

Various aspects of the Aharonov–Bohm(AB)-type effects in antidot lattices in the quantum Hall (QH) regime are studied. Features associated with spin-resolved edge channels formed around the antidots are observed in the vicinity of the $\nu =2$ [$\nu$ being the Landau level (LL) filling factor] QH state. AB-type oscillations with anomalous periodicities lying between $h∕2e$ and $h∕3e$ are observed on the higher field side of the $\nu =2$ QH state. The phenomenon is interpreted basically as $h∕2e$ oscillation reported earlier for single antidot systems, but with important modification specific to the antidot array system. By tuning the negative front gate bias, different regimes of relative importance of the intra- and inter-LL tunnelings are explored.

The nitrogen-vacancy center in diamond is a promising candidate for realizing the spin qubits concept in quantum information. Even though this defect has been known for a long time, its electronic structure and other properties have not yet been explored in detail. We study the properties of the nitrogen-vacancy center in diamond through density functional theory within the local spin density approximation by using supercell calculations. While this theory is strictly applicable for ground state properties, we are able to give an estimate for the energy sequence of the excited states of this defect. We also calculate the hyperfine tensors in the ground state. The results clearly show that (i) the spin density and the appropriate hyperfine constants are spread along a plane and unevenly distributed around the core of the defect and (ii) the measurable hyperfine constants can be found within about $7\mathrm{\AA }$ from the vacancy site. These results have important implications on the decoherence of the electron spin which is crucial in realizing the spin qubits in diamond.

We study the effects of electron-electron interactions on the transport properties of a junction of three quantum wires enclosing a magnetic flux. The wires are modeled as single channel spin-$\frac{1}{2}$ Tomonaga–Luttinger liquids. The system exhibits a rich phase diagram as a function of the electronic interaction strength, which includes a chiral fixed point with an asymmetric current flow highly sensitive to the sign of the flux and another fixed point where pair tunneling dominates, which is similar to the case of spinless electrons. While in the case of spinless electrons the perturbations that correspond to unequal couplings between the three wires are always irrelevant, we find that, when the electron spin is included, there are small regions in the phase diagram where a current flows only between two of the wires and the third wire is decoupled.

The dependence of the optical band gap of $\mathrm{In}{\mathrm{N}}_x{\mathrm{Sb}}_{1-x}$ and $\mathrm{Ga}{\mathrm{N}}_x{\mathrm{Sb}}_{1-x}$ on nitrogen content has been calculated using an $s{p}^3{s}^{*}$ tight-binding Hamiltonian in large supercell calculations that explicitly include the effects of allowing a random distribution of nitrogen atoms. We calculate for InNSb that the energy levels associated with nitrogen complexes consisting of two or three atoms mostly lie above the InNSb conduction band edge (CBE). The steady reduction in the band gap of InNSb with increasing N composition is then well described using a two-level band-anticrossing model. The calculated effective mass of electrons in InNSb also smoothly decreases with composition, as predicted by the band-anticrossing model, due to the steady closure of the band gap and weak mixing with the N states. For GaNSb the situation is dramatic: the band gap and optical properties are shown to be strongly affected and highly sensitive to the distribution of the nitrogen atoms. We find that there is a wide distribution of N levels lying close to and below the CBE. The higher-lying N states push the CBE down in energy, as in GaAs, but the large number of lower-energy N states mix in strongly with the conduction band edge states, severely disrupting the band edge dispersion in GaNSb.

Bosonization predicts that the specific heat $C\left(T\right)$ of a one-dimensional interacting Fermi system is a sum of the specific heats of free collective charge and spin excitations, plus the term with the running backscattering amplitude which flows to zero logarithmically with decreasing $T$. We verify whether this result is reproduced in the $g$-ology model. Of specific interest are the anomalous terms in $C\left(T\right)$ that depend on the bare backscattering amplitude. We show that these terms can be incorporated into a renormalized spin velocity. We do this by proving the equivalence of the results for $C\left(T\right)$ obtained within the $g$-ology model and by bosonization with velocities obtained by the numerical solution of the Bethe-ansatz equations for the Hubbard model.