The Josephson effect in a superconductor/triple-quantum-dot ring/superconductor structure is theoretically investigated. We find that in this structure, interdot spin correlation can be driven, which contributes to the occurrence of new 0 and $\pi$ phases of the Josephson current. Moreover, in the 0-$\pi$ phase-transition process, an intermediate bistable phase appears in which the Josephson current is completely suppressed. By analyzing the interdot spin correlation, the electron motion mechanism is clarified. We then attribute the disappearance of the Josephson current to the occurrence of the Josephson-Fano effect. What is interesting is that the disappearing Josephson current is accompanied by the apparent persistent current in the ring whose direction is determined by the superconducting phase difference. With the calculated results, we consider such a structure to be a candidate for the realization of the persistent current bit.

We report the first numerical observation of composite fermion (CF) states in fractional Chern insulators (FCI) using exact diagonalization. The ruby lattice Chern insulator model for both fermions and bosons exhibits a clear signature of CF states at filling factors $2/5$ and $3/7$ ($2/3$ and $3/4$ for bosons). The topological properties of these states are studied through several approaches. Quasihole and quasielectron excitations in FCI display similar features as their fractional quantum hall (FQH) counterparts. The entanglement spectrum of FCI ground states shows an identical fingerprint to its FQH partner. We show that the correspondence between FCI and FQH obeys the emergent symmetry already established, proving the validity of this approach beyond the clustered states. We investigate other Chern insulator models and find similar signatures of CF states. However, some of these systems exhibit strong finite size effects.

We report the observation of a series of Abelian and non-Abelian topological states in fractional Chern insulators (FCIs). The states appear at bosonic filling $\nu =k/(C+1)$ ($k,C$ integers) in several lattice models, in fractionally filled bands of Chern numbers $C\ge 1$ subject to on-site Hubbard interactions. We show strong evidence that the $k=1$ series is Abelian while the $k>1$ series is non-Abelian. The energy spectrum at both ground-state filling and upon the addition of quasiholes shows a low-lying manifold of states whose total degeneracy and counting matches, at the appropriate size, that of the fractional quantum Hall (FQH) SU$\left(C\right)$ (color) singlet $k$-clustered states (including Halperin, non-Abelian spin singlet states and their generalizations). The ground-state momenta are correctly predicted by the FQH to FCI lattice folding. However, the counting of FCI states also matches that of a spinless FQH series, preventing a clear identification just from the energy spectrum. The entanglement spectrum lends support to the identification of our states as SU$\left(C\right)$ color singlets, but offers anomalies in the counting for $C>1$, possibly related to dislocations that call for the development of alternative counting rules of these topological states.

We study the effect of a magnetic field in the Kondo regime of a double-quantum-dot system consisting of a strongly correlated dot (the “side dot”) coupled to a second, noninteracting dot that also connects two external leads. We show, using the numerical renormalization group, that application of an in-plane magnetic field sets up a subtle interplay between electronic interference, Kondo physics, and Zeeman splitting with nontrivial consequences for spectral and transport properties. The value of the side-dot spectral function at the Fermi level exhibits a nonuniversal field dependence that can be understood using a form of the Friedel sum rule that appropriately accounts for the presence of an energy- and spin-dependent hybridization function. The applied field also accentuates the exchange-mediated interdot coupling, which dominates the ground state at intermediate fields leading to the formation of antiparallel magnetic moments on the dots. By tuning gate voltages and the magnetic field, one can achieve complete spin polarization of the linear conductance between the leads, raising the prospect of applications of the device as a highly tunable spin filter. The system's low-energy properties are qualitatively unchanged by the presence of weak on-site Coulomb repulsion within the second dot.

We report on the magnetic and the electronic properties of the prototype dilute magnetic semiconductor Ga${}_{1-x}$Mn${}_x$As using infrared (IR) spectroscopy. Trends in the ferromagnetic transition temperature $T_C$ with respect to the IR spectral weight are examined using a sum-rule analysis of IR conductivity spectra. We find nonmonotonic behavior of trends in $T_C$ with the spectral weight to effective Mn ratio, which suggest a strong double-exchange component to the FM mechanism, and highlights the important role of impurity states and localization at the Fermi level. Spectroscopic features of the IR conductivity are tracked as they evolve with temperature, doping, annealing, As-antisite compensation, and are found only to be consistent with a Mn-induced IB scenario. Furthermore, our detailed exploration of these spectral features demonstrates that seemingly conflicting trends reported in the literature regarding a broad mid-IR resonance with respect to carrier density in Ga${}_{1-x}$Mn${}_x$As are in fact not contradictory. Our study thus provides a consistent experimental picture of the magnetic and electronic properties of Ga${}_{1-x}$Mn${}_x$As.

The phase structure of two-dimensional topological insulators under a sufficiently strong electron-electron interaction is investigated. The effective theory is constructed by extending the idea of the Kane-Melé model on the graphenelike honeycomb lattice, in terms of U(1) lattice gauge theory (quantum electrodynamics). We analyze the phase structure by the techniques of strong-coupling expansion of lattice gauge theory. As a result, we find that the topological phase structure of the system is modified by the electron-electron interaction. There evolves a new phase with the antiferromagnetism not parallel to the direction pointed by the spin-orbit coupling, in-between the conventional and the topological insulator phases. We also discuss the physical implication of the new phase structure found here, in analogy to the parity-broken phase in lattice quantum chromodynamics, known as the “Aoki phase.”

We theoretically study atomic friction experiments in the stick-slip regime within the framework of the Prandtl-Tomlinson model. We derive a differential equation describing the force probability distribution. Approximate analytical solutions of this equation are found for the asymptotic cases of high and low effective spring constant, but for arbitrary pulling velocities. Excellent accuracy of these approximate expressions is demonstrated numerically. In particular, the result for the mean force, although obtained for small spring constants, is shown to be accurate also somewhat outside of its expected validity range.

Cluster expansions are simplified, Ising-like models for binary alloys in which vibrational and electronic degrees of freedom are coarse grained. The usual practice is to learn the parameters of the cluster expansion by fitting the energy they predict to a finite set of ab initio calculations. In some cases, experiments suggest that such approaches may lead to overestimation of the phase transition temperature. In this work, we present a novel approach to fitting the parameters based on the relative entropy framework which, instead of energies, attempts to fit the Boltzmann distribution of the configurational degrees of freedom. We show how this leads to $T$-dependent parameters.

The static and dynamic magnetic properties of magnetic nanowire arrays with high packing density (>0.4) and wire diameter much greater than the exchange length have been studied by static and time-resolved magneto-optical Kerr effect measurements and micromagnetic simulations. The nanowires were formed by electrodeposition within a nanoporous template such that their symmetry axes lay normal to the plane of the substrate. A quantitative and systematic investigation has been made of the static and dynamic properties of the array, which lie between the limiting cases of a single wire and a continuous ferromagnetic thin film. In particular, the competition between anisotropies associated with the shape of the individual nanowires and that of the array as a whole has been studied. Measured and simulated hysteresis loops are largely anhysteretic with zero remanence, and the micromagnetic configuration is such that the net magnetization vanishes in directions orthogonal to the applied field. Simulations of the remanent state reveal antiferromagnetic alignment of the magnetization in adjacent nanowires and the formation of vortex flux closure structures at the ends of each nanowire. The excitation spectra obtained from experiment and micromagnetic simulations are in qualitative agreement for magnetic fields applied both parallel and perpendicular to the axes of the nanowires. For the field parallel to the nanowire axes, there is also good quantitative agreement between experiment and simulation. The resonant frequencies are initially found to decrease as the applied field is increased from remanence. This is the result of a change of mode profile within the plane of the array from nonuniform to uniform as the ground state evolves with increasing applied field. Quantitative differences between experimental and simulated spectra are observed when the field is applied perpendicular to the nanowire axes. The dependence of the magnetic excitation spectra upon the array packing density is explored, and dispersion curves for spin waves propagating within the array parallel to the nanowire axis are presented. Finally, a tunneling of end modes through the middle region of the nanowires was observed. The tunneling is more efficient for wires forming densely packed arrays, as a result of the extended penetration of the dynamic demagnetizing fields into the middle of the wires and due to the lowering of the tunneling barrier by the static demagnetizing field of the array.

The formation and evolution of dark spin-wave envelope solitons have been studied in a yttrium iron garnet (YIG) film. The Brillouin light scattering (BLS) technique has been used to map the propagation and evolution of the excited dark solitons. Experiments have been carried out using (1) a YIG-film delay-line structure supporting propagation of backward volume spin waves, (2) time- and space-resolved forward-scattering BLS, (3) a fixed magnetic field of 1000 Oe applied along the propagation direction, and (4) a soliton excitation technique based on the nonlinear interaction of two large amplitude cw input signals with fixed frequency enabling an induced modulation instability. Theoretical interpretation of the experiments based on numerical solution of the Ginzburg-Landau equation taking into account the conditions of nonlinear spin-wave dissipation is given. It is found that the dark soliton formation process involves competition between effects of nonlinearity and dispersion, and that nonlinear damping effects play an important role.

Recent studies show that the magnetization of nanoparticles with uniaxial anisotropy can be reversed by rotating magnetic fields applied perpendicular to the easy axis. In this contribution the details of this switching process is worked out in detail by solving the Fokker-Planck equation describing the dynamics of the magnetic moment at finite temperatures numerically. The dependence of the induced magnetization due to the rotating field on temperature as well as on frequency and amplitude of the driving field is studied. Of particular interest is the time for switching the magnetization between metastable states. This time is analyzed in detail and it is shown in particular that it increases dramatically with driving frequency. The numerical method developed in this paper is applicable to many other problems in magnetism on the nanoscale.

We report a combined experimental and theoretical study of the quasistatic hysteresis and dynamic excitations in large-area arrays of NiFe nanodisks forming a hexagonal lattice with the lattice constant of 390 nm. Arrays were fabricated by patterning a 20-nm-thick NiFe film using the etched nanosphere lithography. We have studied a close-packed (edge-to-edge separation between disks $d_{\mathrm{cp}}$ $=$ 65 nm) and an ultraclosed packed ($d_{\mathrm{ucp}}$ $=$ 20 nm) array. Hysteresis loops for both arrays were qualitatively similar and nearly isotropic, i.e., independent on the in-plane external field orientation. The shape of these loops revealed that magnetization reversal is governed by the formation and expulsion of vortices inside the nanodisks. When we assumed that the nanodisks’ magnetization significantly decreases near their edges, micromagnetic simulations with material parameters deter-mined independently from continuous film measu-rements could satisfactorily reproduce the hysteresis. Despite the isotropic hysteresis, significant in-plane anisotropy of the dynamic response of the ultraclose-packed array was found experimentally by the all-electrical spin-wave spectroscopy and Brillouin light scattering. Dynamical simulations could successfully reproduce the difference between excitation spectra for fields directed along the two main symmetry axes of the hexagonal lattice. Simulations revealed that this difference is caused by the magnetodipolar interaction between nanodisks, which leads to a strong variation of the spatial distribution of the oscillation power both for bulk and edge modes as a function of the bias field orientation. Comparison of simulated and measured frequencies enabled the unambiguous identification of experimentally observed modes. Results of this systematic research are relevant both for fundamental studies of spin-wave modes in patterned magnetic structures and for the design of magnonic crystals for potential applications as, e.g., spin-wave guides and filters.

We present a theory of magnetization dynamics driven by spin-polarized current in terms of the quantum master equation. In the spin coherent state representation, the master equation becomes a Fokker-Planck equation, which naturally includes the spin transfer and quantum fluctuation. The current electron scattering state is correlated to the magnet quantum states, giving rise to quantum correction to the electron transport properties in the usual semiclassical theory. In the large-spin limit, the magnetization dynamics is shown to obey the Hamilton-Jacobi equation or the Hamiltonian canonical equations.

We investigated the annealing effects on the physical properties of ${\mathrm{SrFe}}_2{\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right)}_2(x=0.35)$. The superconducting transition temperature ($T_c$) increased from 26 to 33 K by annealing. The x-ray diffraction measurement suggested that the annealed crystals have the shorter/longer $a/c$ axes and the larger pnictogen height $h_{\mathrm{Pn}}$. This must be linked to the $T_c$ enhancement by annealing. Moreover, it was found that the postannealing decreased the electronic specific heat coefficient at $T=0\mathrm{K},{\gamma }_r$, and changed the magnetic field ($H$) dependence from sublinear ${\gamma }_r\propto H^{0.7}$ to $H$ linear ${\gamma }_r\propto H$. This can be attributed the electronic change from dirty to clean superconductors with a $s_{\pm }$ gap.

We consider the linear and nonlinear electromagnetic responses of a nanowire connecting two bulk superconductors. The Andreev states appearing at a finite phase bias substantially affect the finite-frequency admittance of such a wire junction. Electron transitions involving the Andreev levels are easily saturated, leading to the nonlinear effects in photon absorption for the subgap photon energies. We evaluate the complex admittance analytically at an arbitrary frequency and arbitrary, possibly nonequilibrium, occupation of the Andreev levels. Special care is given to the limits of a single-channel contact and a disordered metallic weak link. We also evaluate the quasistatic fluctuations of admittance induced by fluctuations of the occupation factors of the Andreev levels. In view of possible qubit applications, we compare properties of a weak link with those of a tunnel Josephson junction. Compared to the latter, a weak link has smaller low-frequency dissipation. However, because of the deeper Andreev levels, the low-temperature quasistatic fluctuations of the inductance of a weak link are exponentially larger than of a tunnel junction. These fluctuations limit the applicability of nanowire junctions in superconducting qubits.

We report on the quadrupling of the transition spectrum of an Al/AlO${}_x$/Al Cooper-pair box (CPB) charge qubit in the $4.0–7.3$ GHz frequency range. The qubit was coupled to a quasilumped-element Al superconducting resonator and measured at a temperature of 25 mK. We obtained good matches between the observed spectrum and the spectra calculated from a model Hamiltonian containing two distinct low-excitation energy two-level systems (TLS) coupled to the CPB. In our model, each TLS has a charge that tunnels between two sites in a local potential and induces a change in the CPB critical current. By fitting the model to the spectrum, we have extracted microscopic parameters of the fluctuators including the well asymmetry, tunneling rate, and a surprisingly large fractional change ($30\%–40\%$) in the critical current (12 nA). This large change is consistent with a Josephson junction with a nonuniform tunnel barrier containing a few dominant conduction channels and a TLS that modulates one of them.

We derive and evaluate one-loop functional flow equations for the effective interactions, self-energy, and gap function in spin-singlet superfluids. The flow is generated by a fermionic frequency cutoff, which is supplemented by an external pairing field to treat divergencies associated with the Goldstone boson. To parametrize the singular momentum and frequency dependencies of the effective interactions, the Nambu interaction vertex is decomposed in charge, magnetic, and normal and anomalous pairing channels. The one-loop flow solves reduced (mean-field) models for superfluidity exactly, and captures also important fluctuation effects. The Ward identity from charge conservation is generally violated, but can be enforced by projecting the flow. Applying the general formalism to the two-dimensional attractive Hubbard model, we obtain detailed results on the momentum and frequency dependencies of the effective interactions for weak and moderate bare interactions. The gap is reduced by fluctuations, with a stronger reduction at weaker interactions, as expected.

We revisit the room-temperature linear magnetoelectric effect in Cr${}_2$O${}_3$ single crystals. It was found that the temperature dependence of dielectric constants in a magnetic field $H$ shows a λ-shaped peak at the Néel temperature (≈307 K) and that electric polarization induced by applying $H$ is reversed with a hysteresis by sweeping an electric field $E$. Similar reversal and hysteretic behaviors were also observed in the $H$ dependence of magnetization induced by applying $E$. These results imply that Cr${}_2$O${}_3$ behaves as a typical ferroelectric (ferromagnet) in finite $H$ ($E$) even at room temperature. We discuss the ferroic behaviors observed in the linear magnetoelectric system in the context of recent studies on multiferroics.

From the measurement and analysis of the specific heat of high-quality K${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$ single crystals we establish the presence of large $T^2$ contributions with coefficients ${\alpha }_{\mathrm{sc}}\approx 30$ mJ/mol K${}^3$ at low $T$ for both $x=0$ and $x=0.1$. Together with the observed $\sqrt{B}$ behavior of the specific heat in the superconducting state both findings give evidence of $d$-wave superconductivity on almost all Fermi-surface sheets with an average gap amplitude of ${\Delta }_0$ in the range of 0.4–0.8 meV. The derived ${\Delta }_0$ and observed $T_c$ agree well with the values calculated within Eliashberg theory, adopting a spin-fluctuation mediated pairing in the intermediate coupling regime.

The Li-Si materials system holds promise for use as an anode in Li-ion battery applications. For this system, we determine the charge capacity, voltage profiles, and energy storage density solely by ab initio methods without any experimental input. We determine the energetics of the stable and metastable Li-Si phases likely to form during the charging and discharging of a battery. Ab initio molecular dynamics simulations are used to model the structure of amorphous Li-Si as a function of composition, and a genetic algorithm coupled to density-functional theory searches the Li-Si binary phase diagram for small-cell, metastable crystal structures. Calculations of the phonon densities of states using density-functional perturbation theory for selected structures determine the importance of vibrational, including zero-point, contributions to the free energies. The energetics and local structural motifs of these metastable Li-Si phases closely resemble those of the amorphous phases, making these small unit cell crystal phases good approximants of the amorphous phase for use in further studies. The charge capacity is estimated, and the electrical potential profiles and the energy density of Li-Si anodes are predicted. We find, in good agreement with experimental measurements, that the formation of amorphous Li-Si only slightly increases the anode potential. Additionally, the genetic algorithm identifies a previously unreported member of the Li-Si binary phase diagram with composition Li${}_5$Si${}_2$ which is stable at 0 K with respect to previously known phases. We discuss its relationship to the partially occupied Li${}_7$Si${}_3$ phase.