In recent years, diamond magnetometers based on the nitrogen-vacancy (NV) center have been of considerable interest for applications at the nanoscale. An interesting application which is well suited for NV centers is the study of nanoscale magnetic phenomena in superconducting materials. We employ NV centers to interrogate magnetic properties of a thin-layer yttrium barium copper oxide (YBCO) superconductor. Using fluorescence-microscopy methods and samples integrated with an NV sensor on a microchip, we measure the temperature of phase transition in the layer to be $70.0\left(2\right)$ K and the penetration field of vortices to be $46\left(4\right)$ G. We observe pinning of the vortices in the layer at 65 K and estimate their density after cooling the sample in a $\sim 10$-G field to be $0.45\left(1\right)$ $\mu$${\text{m}}^{-2}$. These measurements are done with a 10-nm-thick NV layer, so that high spatial resolution may be enabled in the future. Based on these results, we anticipate that this magnetometer could be useful for imaging the structure and dynamics of vortices. As an outlook, we present a fabrication method for a superconductor chip designed for this purpose.

Superfluidity in electron-hole bilayers in graphene and GaAs has been predicted theoretically many times but not yet definitively observed. A key controversy is the correct approximation for the screening of the Coulomb interaction for the pairing. Mean-field theories using different approximations for the screening lead to diametrically contradictory predictions for superfluidity. We test these different approximations against diffusion quantum Monte Carlo results and find good agreement with the mean-field theory that uses screening in the superfluid state, but large discrepancies with other approximations for screening. This mean-field theory predicts no superfluidity in existing devices, provides pointers for new devices to generate the superfluidity, and, very importantly, it permits calculations for complicated lattices at finite temperatures, impractical in Monte Carlo.

An argument that relaxor ferroelectricity in the isovalent alloy $\mathrm{Ba}\left({\mathrm{Zr}}_{1-x}{\mathrm{Ti}}_x\right){\mathrm{O}}_3$ can be understood as an induced-moment soft pseudospin glass on the $B$ ions of the $AB{\mathrm{O}}_3$ matrix [Sherrington, Phys. Rev. Lett. 111, 227601 (2013)] is extended to the experimentally paradigmatic but theoretically more complex heterovalent relaxor $\mathrm{Pb}\left({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}\right){\mathrm{O}}_3$. It is argued that interesting behavior of the onset of nonergodicity, frequency-dependent permittivity peaks, and precursor nanodomains can be understood from analogous considerations of the $B$ ions, with the displacements of the Pb ions a largely independent, but distracting, side feature. This contrasts with conventional conceptualizations.

The skyrmion magnetic bubble in a ferromagnetic disk exhibits hypocycloidal gyrations contrary to the vortex gyration, showing a simple circular trajectory. To describe the hypocycloidal bubble gyration, a mass term is needed in Thiele's equation. In this study, we analytically derived both mass and spring constant term, which are crucial parameters for describing the bubble gyration. Values obtained by these analytic expressions were consistent with those obtained by simulations. We could find the dependences of these two terms on several external parameters, including the bubble radius. Especially using the radius's dependence, we could obtain regular polygonlike trajectories such as a square and a triangle confirmed by the numerical simulations. Based on this effective method to control the bubble gyration, the regular polygonlike trajectories of this skyrmion magnetic bubble make it possible to study the bubble gyration without time-resolved experiments.

The random-field Ising model (RFIM) is central to the study of disordered systems. Yet, for a long time it eluded realization in ferromagnetic systems because of the difficulty to produce locally random magnetic fields. Recently, it was shown that in anisotropic dipolar magnetic insulators, the archetype of which is the ${\text{LiHo}}_x{\text{Y}}_{1-x}{\text{F}}_4$ system, the RFIM can be realized in both ferromagnetic and spin-glass phases. The interplay between an applied transverse field and the off-diagonal terms of the dipolar interaction produce effective longitudinal fields, which are random in sign and magnitude as a result of spatial dilution. In this paper, we use exact numerical diagonalization of the full Hamiltonian of Ho pairs in ${\text{LiHo}}_x{\text{Y}}_{1-x}{\text{F}}_4$ to calculate the effective longitudinal field beyond the perturbative regime. In particular, we find that nearby spins can experience an effective field larger than the intrinsic dipolar broadening (of quantum states in zero field) which can therefore be evidenced in experiments. We then calculate the magnetization and susceptibility under several experimental protocols, and show how these protocols can produce direct measurement of the effective longitudinal field.

By combining genetic algorithm optimizations, first-principles calculations and the double-exchange model studies, we have revealed that the exotic insulating ferromagnetism in ${\text{LaMnO}}_3$ thin film originates from the previously unreported G-type $d_{3z^2-r^2}/d_{x^2-y^2}$ orbital ordering. An insulating gap opens as a result of both the orbital ordering and the strong electron-phonon coupling. Therefore, there exist two strain-induced phase transitions in the ${\text{LaMnO}}_3$ thin film, from the insulating A-type antiferromagnetic phase to the insulating ferromagnetic phase and then to the metallic ferromagnetic phase. These phase transitions may be exploited in tunneling magnetoresistance- and tunneling electroresistance-related devices.

It has been shown that a bubble in liquid helium containing two electrons is unstable against fission. In this paper, we consider the stability of electron bubbles containing 4, 6, or 12 electrons. We find that a bubble with four electrons is unstable at zero pressure and presumably breaks up into single electron bubbles. Our calculation is not accurate enough to determine whether a bubble with six electrons is stable at zero pressure. We find that in liquid ${}^4\mathrm{He}$ a bubble with 12 electrons is stable over a pressure range from $-0.32$ to 0.5 bar.

Multiband effects on Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states of a Pauli-limiting two-band superconductor are studied theoretically in the wide range of parameters, based on the Bogoliubov-de Gennes equation. First, we examine the phase diagrams of two-band systems with a passive band in which the intraband pairing interaction is absent and superconductivity is induced by a Cooper pair tunneling from an active band. The critical field of Bardeen-Cooper-Schrieffer to FFLO states becomes lower than the Lifshitz point with increasing the interband tunneling strength. We also study the thermodynamics of Pauli-limiting two-band superconductors with nonzero intraband pairing interactions. As a consequence of a competing effect between two bands, the FFLO phase is divided into two phases: $Q_1$- and $Q_2$-FFLO phases. In a particular case, the latter is further subdivided into a family of FFLO states with rational modulation lengths, where the spatial structure of the pair potential is approximately describable with sinusoidal functions with multiple modulation wave numbers. The resultant phase diagram is qualitatively different from that in a single-band superconductor and gives rise to a devil's staircase structure in the field dependence of physical quantities.

We study a Bose-Hubbard model having on-site repulsion, nearest-neighbor tunneling, and ferromagneticlike coupling between occupation parities of nearest-neighbor sites. For a uniform system in any dimension at zero tunneling, we obtain an exact phase diagram characterized by Mott-insulator (MI) and pair liquid phases and regions of phase separation of two MIs. For a general trapped system in one and two dimensions with finite tunneling, we perform quantum Monte Carlo and Gutzwiller mean-field calculations, both of which show the evolution of the system, as the parity coupling increases, from a superfluid to wedding-cake-structure MIs with their occupations jumping by 2. We also identify an exotic pair superfluid at relatively large tunneling strength. Our model ought to effectively describe recent findings in imbalanced Fermi gases in two-dimensional optical lattices and also potentially apply to an anisotropic version of bilinear-biquadratic spin systems.

Recent measurements of fluctuation diamagnetism in high-temperature superconductors show distinct features above and below $T_c$, which can not be explained by simple Gaussian fluctuation theory. Self-consistent calculation of magnetization in layered high-temperature superconductors, based on the Ginzburg-Landau-Lawrence-Doniach model and including all Landau levels is presented. The results agree well with the experimental data in a wide region around $T_c$, including both the vortex liquid below $T_c$ and the normal state above $T_c$. The Gaussian fluctuation theory significantly overestimates the diamagnetism for strong fluctuations. It is demonstrated that the intersection point of magnetization curves appears in the region where the lowest Landau level contribution dominates and magnetization just below $T_c$ is nonmonotonic. Our calculation supports the phase disordering picture of fluctuations above $T_c$.

Recent experimental advances in surface science have made it possible to track the evolution of superconductivity in films as the thickness enters the nanoscale region where it is expected that the substrate plays an important role. Here, we put forward a mean-field, analytically tractable, model that describes size effects in ultrathin films coupled to the substrate. We restrict our study to one-band, crystalline, weakly coupled superconductors with no impurities. The thin-film substrate/vacuum interfaces are described by a simple asymmetric potential well and a finite quasiparticle lifetime. Boundary conditions are chosen to comply with the charge neutrality condition. This model provides a fair description of experimental results in ultrathin lead films: on average, the superconducting gap decreases with thickness and it is always below the bulk value. Clear oscillations, remnants of the shape resonances, are still observed for intermediate thicknesses. For materials with a weaker electron-phonon coupling and negligible disorder, a modest enhancement of superconductivity seems to be feasible. The relaxation of the charge neutrality condition, which is in principle justified in complex oxide heterostructures and other materials, would lead to a much stronger enhancement of superconductivity by size effects.

The nature of the lattice instability connected to the structural transition and superconductivity of ${(\text{Sr},\text{Ca})}_3$${\text{Ir}}_4$${\text{Sn}}_{13}$ is not yet fully understood. In this work density functional theory (DFT) calculations of the phonon instabilities as a function of chemical and hydrostatic pressure show that the primary lattice instabilities in ${\text{Sr}}_3$${\text{Ir}}_4$${\text{Sn}}_{13}$ lie at phonon modes of wave vectors $\mathbf{q}=(0.5,0,0)$ and $\mathbf{q}=(0.5,0.5,0)$. Following these modes by calculating the energy of supercells incorporating the mode distortion results in an energy advantage of $-14.1$ and $-9.0$ meV per formula unit, respectively. However, the application of chemical pressure to form ${\text{Ca}}_3$${\text{Ir}}_4$${\text{Sn}}_{13}$ reduces the energetic advantage of these instabilities, which is completely removed by the application of a hydrostatic pressure of 35 kbar to ${\text{Ca}}_3$${\text{Ir}}_4$${\text{Sn}}_{13}$. The evolution of these lattice instabilities is consistent with the experimental phase diagram. The structural distortion associated with the mode at $\mathbf{q}=(0.5,0.5,0)$ produces a distorted cell with the same space-group symmetry as the experimentally refined low-temperature structure. Furthermore, calculation of the deformation potential due to these modes quantitatively demonstrates a strong electron-phonon coupling. Therefore, these modes are likely to be implicated in the structural transition and superconductivity of this system.

We study entanglement renormalization group transformations for the ground states of a spin model, called cubic code model $H_A$ in three dimensions, in order to understand long-range entanglement structure. The cubic code model has degenerate and locally indistinguishable ground states under periodic boundary conditions. In the entanglement renormalization, one applies local unitary transformations on a state, called disentangling transformations, after which some of the spins are completely disentangled from the rest and then discarded. We find a disentangling unitary to establish equivalence of the ground state of $H_A$ on a lattice of lattice spacing $a$ to the tensor product of ground spaces of two independent Hamiltonians $H_A$ and $H_B$ on lattices of lattice spacing $2a$. We further find a disentangling unitary for the ground space of $H_B$ with the lattice spacing $a$ to show that it decomposes into two copies of itself on the lattice of the lattice spacing $2a$. The disentangling transformations yield a tensor network description for the ground state of the cubic code model. Using exact formulas for the degeneracy as a function of system size, we show that the two Hamiltonians $H_A$ and $H_B$ represent distinct phases of matter.

We theoretically and numerically investigate metamaterials composed of coupled resonators with indirect coupling. First, we theoretically analyze a mechanical model of coupled resonators with indirect coupling. The theoretical analysis shows that an electromagnetically induced transparency (EIT)-like phenomenon with a transparency bandwidth narrower than the resonance linewidths of the constitutive resonators can occur in the metamaterial with strong indirect coupling. We then numerically examine the characteristics of the metamaterial composed of coupled cut-wire pairs using a finite-difference time-domain (FDTD) method. The FDTD simulation confirms that an EIT-like transparency phenomenon occurs in the metamaterial owing to indirect coupling. Finally, we compare the results of the theoretical and numerical analyses. The behavior of the EIT-like metamaterial is found to be well described by the mechanical model of the coupled resonators.

We perform first-principles calculations of the quasiparticle defect states, charge transition levels, and formation energies of oxygen vacancies in rutile titanium dioxide. The calculations are done within the recently developed combined $\mathrm{DFT}+GW$ formalism, including the necessary electrostatic corrections for the supercells with charged defects. We find the oxygen vacancy to be a negative $U$ defect, where $U$ is the defect electron addition energy. For Fermi level values below $\sim 2.8$ eV (relative to the valence-band maximum), we find the $+2$ charge state of the vacancy to be the most stable, while above $2.8$ eV we find that the neutral charge state is the most stable.

Torque magnetometry at low temperature and in high magnetic fields $B$ is performed on MgZnO/ZnO heterostructures incorporating high-mobility two-dimensional electron systems. We find a sawtoothlike quantum oscillatory magnetization $M\left(B\right)$, i.e., the de Haas-van Alphen (dHvA) effect. At the same time, nonequilibrium currents and unexpected spikelike overshoots in $M$ are observed which allow us to identify the microscopic nature and density of the residual disorder. The acceptorlike scatterers give rise to a magnetic thaw down effect which enhances the dHvA amplitude beyond the electron-electron interaction effects being present in the MgZnO/ZnO heterostructures.

The wave-packet evolution in graphene quantum dots in magnetic fields has been theoretically studied. By analyzing an effective Hamiltonian model we show the wave-packet dynamics exhibits three types of periodicities (Zitterbewegung, classical, and revival times). The influence of the size of the quantum dot and the strength of the external magnetic field in these periodicities has been considered. In addition, we have found that valley degeneracy breaking is shown by both classical and revival times.