The interplay between spin-orbit coupling (SOC) and electron correlation ($U$) is considered for many exotic phenomena in iridium oxides. We have investigated the evolution of structural, magnetic, and electronic properties in the pyrochlore iridate ${\mathrm{Y}}_2{\mathrm{Ir}}_{2-x}{\mathrm{Ru}}_x{\mathrm{O}}_7$ where the substitution of Ru has been aimed to tune this interplay. The Ru substitution does not introduce any structural phase transition, however, we do observe an evolution of lattice parameters with the doping level $x$. X-ray photoemission spectroscopy (XPS) study indicates Ru adopts the charge state of ${\mathrm{Ru}}^{4+}$ and replaces the ${\mathrm{Ir}}^{4+}$ accordingly. Magnetization data reveal both the onset of magnetic irreversibility and the magnetic moment decreases with progressive substitution of Ru. These materials show a nonequilibrium low temperature magnetic state as revealed by magnetic relaxation data. Interestingly, we find the magnetic relaxation rate increases with substitution of Ru. The electrical resistivity shows an insulating behavior in the whole temperature range, however, resistivity decreases with the substitution of Ru. The nature of electronic conduction has been found to follow power-law behavior for all the materials.

We present an exhaustive theoretical analysis of a double-loop Josephson proximity interferometer, such as the one recently realized by Strambini et al. for control of the Andreev spectrum via an external magnetic field. This system, called $\omega$-SQUIPT, consists of a T-shaped diffusive normal metal ($N$) attached to three superconductors ($S$) forming a double-loop configuration. By using the quasiclassical Green-function formalism, we calculate the local normalized density of states, the Josephson currents through the device, and the dependence of the former on the length of the junction arms, the applied magnetic field, and the $S/N$ interface transparencies. We show that by tuning the fluxes through the double loop, the system undergoes transitions from a gapped to a gapless state. We also evaluate the Josephson currents flowing in the different arms as a function of magnetic fluxes, and we explore the quasiparticle transport by considering a metallic probe tunnel-coupled to the Josephson junction and calculating its $I-V$ characteristics. Finally, we study the performances of the $\omega$-SQUIPT and its potential applications by investigating its electrical and magnetometric properties.

A semiclassical theory is provided for the metastability regime diagram of atomtronic superfluid circuits. Such circuits typically exhibit high-dimensional chaos, and nonlinear resonances that couple the Bogoliubov excitations manifest. Contrary to the expectation, these resonances do not originate from the familiar Beliaev and Landau damping terms. Rather, they are described by a variant of the Cherry Hamiltonian of celestial mechanics. Consequently, we study the induced decay process and its dependence on the number of sites and condensed particles.

Systems where all energy eigenstates are localized are known to display an emergent local integrability, in the sense that one can construct an extensive number of operators that commute with the Hamiltonian and are localized in real space. Here we show that emergent local integrability does not require a set of localized eigenstates to be complete. Given a set of localized eigenstates comprising a nonzero fraction $(1-p_f)$ of the full many-body spectrum, one can construct an extensive number of integrals of motion which are local in the sense that they have nonzero weight in a compact region of real space, in the thermodynamic limit. However, these modified integrals of motion have a “global dressing” whose weight vanishes as $\sim p_f$ as $p_f\to 0$. In this sense, the existence of a nonzero fraction of localized eigenstates is sufficient for emergent local integrability. We discuss the implications of our findings for systems where the spectrum contains delocalized states, for systems with projected Hilbert spaces, and for the robustness of quantum integrability.

The effect of a slow noise in nondiagonal matrix element $J\left(t\right)$ that describes the diabatic level coupling on the probability of the Landau-Zener transition is studied. For slow noise, the correlation time ${\tau }_c$ of $J\left(t\right)$ is much longer than the characteristic time of the transition. Existing theory for this case suggests that the average transition probability is the result of averaging of the conventional Landau-Zener probability, calculated for a given constant $J$, over the distribution of $J$. We calculate a finite-${\tau }_c$ correction for this classical result. Our main finding is that this correction is dominated by sparse realizations of noise for which $J\left(t\right)$ passes through zero within a narrow time interval near the level crossing. Two models of noise, random telegraph noise and Gaussian noise, are considered. Naturally, in both models the average probability of transition decreases upon decreasing ${\tau }_c$. For Gaussian noise we identify two domains of this falloff with specific dependencies of average transition probability on ${\tau }_c$.

We study the magnetic and lattice contributions to the thermal conductivity of electrically insulating strongly spin-orbit coupled magnetically ordered phases on a two-dimensional honeycomb lattice using the Kitaev-Heisenberg model. Depending on model parameters, such as the relative strength of the spin-orbit induced anisotropic coupling, a number of magnetically ordered phases are possible. In this work, we study two distinct regimes of thermal transport depending on whether the characteristic energy of the phonons or the magnons dominates, and focus on two different relaxation mechanisms, boundary scattering and magnon-phonon scattering. For spatially anisotropic magnetic phases, the thermal conductivity tensor can be highly anisotropic when the magnetic energy scale dominates, since the magnetic degrees of freedom dominate the thermal transport for temperatures well below the magnetic transition temperature. In the opposite limit in which the phonon energy scale dominates, the thermal conductivity will be nearly isotropic, reflecting the isotropic (at low temperatures) phonon dispersion assumed for the honeycomb lattice. We further discuss the extent to which thermal transport properties are influenced by strong spin-orbit induced anisotropic coupling in the local moment regime of insulating magnetic phases. The developed methodology can be applied to any 2D magnon-phonon system, and more importantly to systems where an analytical Bogoliubov transformation cannot be found and magnon bands are not necessarily isotropic.

Definitive determination of first-order character of the magnetocaloric magnetic transition remains elusive. Here we use a microcalorimetry technique in two modes of operation to determine the contributions to entropy change from latent heat and heat capacity separately in an engineered set of $\mathrm{La}{\left(\mathrm{Fe},\mathrm{Mn},\mathrm{Si}\right)}_{13}$ samples. We compare the properties extracted by this method with those determined using magnetometry and propose a model-independent parameter that would allow the degree of first-order character to be defined across different families of materials. The microcalorimetry method is sufficiently sensitive to allow observation at temperatures just above the main magnetic transition of an additional peak feature in the low field heat capacity associated with the presence of Mn in these samples. The feature is of magnetic origin but is insensitive to magnetic field, explicable in terms of inhomogeneous occupancy of Mn within the lattice resulting in antiferromagnetic ordered Mn clusters.

We successfully synthesized single crystals of the verdazyl radical $2\text{−}\mathrm{Cl}\text{−}3,6\text{−}{\mathrm{F}}_2\text{−}\mathrm{V}$ [=3-(2-chloro-3,6-difluorophenyl)-1,5-diphenylverdazyl], which is a rare model compound with an $S=\frac{1}{2}$ Heisenberg antiferromagnetic (HAF) honeycomb lattice. Ab initio molecular orbital calculations indicate two dominant AF interactions, forming a slightly distorted honeycomb lattice. We explain the magnetic susceptibility and the magnetization curve up to the saturation field based on the expected spin model using the quantum Monte Carlo method. In the low-temperature regions, we found a phase transition to an AF ordered state at about 0.77 K for the zero field and obtained the magnetic field-temperature phase diagram from the magnetic susceptibility and the specific heat for various magnetic fields. Through the analysis considering the effect of lattice distortion on magnetic behavior, we confirm that the lattice distortion of the present model is small enough that it does not affect the intrinsic behavior of the uniform $S=\frac{1}{2}$ HAF honeycomb lattice.

We study the intrinsic electronic anisotropy and fermiology of the quasi-one-dimensional superconductor ${\mathrm{Ta}}_4{\mathrm{Pd}}_3{\mathrm{Te}}_{16}$. Below $T^{*}=20$ K, we detect a thermodynamic phase transition that predominantly affects the conductivity perpendicular to the quasi-one-dimensional chains. The transition relates to the presence of charge order that precedes superconductivity. Remarkably, the Fermi surface pockets detected by de Haas–van Alphen oscillations are unaffected by this transition, suggesting that the ordered state does not break any translational symmetries but rather alters the scattering of the quasiparticles themselves.

The nonequilibrium evolution of the system of two kinds of fermions under the action of a pulse of the external field has been studied. The number of fermions of each kind oscillates (with beats and decaying) as a function of the duration of the pulse about the value determined by the magnitude of the pulse, and as a function of the magnitude of the pulse. For low-dimensional systems those oscillations can serve as a non-zero-temperature manifestation of dynamical quantum phase transitions. The response of a Fermi gas or liquid in a tilted magnetic field, an edge state of a topological insulator, a quantum wire with spin-orbit coupling, and a dimerized spin-1/2 chain to the pulse can manifest such dynamical oscillations, which can be observed in experiments.

We investigate the local electronic structure of a Sinai-like, quadrilateral graphene quantum billiard with zigzag and armchair edges using scanning tunneling microscopy (STM) at room temperature. It is revealed that besides the $(\sqrt{3}\times \sqrt{3})R{30}^{\circ }$ superstructure, which is caused by the intervalley scattering, its overtones also appear in the STM measurements, which are attributed to the Umklapp processes. We point out that these results can be well understood by taking into account the Coulomb interaction in the quantum billiard, accounting for both the measured density of state values and the experimentally observed topography patterns. The analysis of the level-spacing distribution substantiates the experimental findings as well. We also reveal the magnetic properties of our system which should be relevant in future graphene based electronic and spintronic applications.

The variational cluster approximation is used to study the isotropic triangular-lattice Hubbard model at half filling, taking into account the nearest-neighbor $\left(t_1\right)$ and next-nearest-neighbor $\left(t_2\right)$ hopping parameters for magnetic frustrations. We determine the ground-state phase diagram of the model. In the strong-correlation regime, the ${120}^{\circ }$ Néel- and stripe-ordered phases appear, and a nonmagnetic insulating phase emerges in between. In the intermediate correlation regime, the nonmagnetic insulating phase expands to a wider parameter region, which goes into a paramagnetic metallic phase in the weak-correlation regime. The critical phase boundary of the Mott metal-insulator transition is discussed in terms of the van Hove singularity evident in the calculated density of states and single-particle spectral function.

We investigate the process of coarsening via annihilation of vortex-antivortex pairs, following the quench to the condensate phase in a nonresonantly pumped polariton system. We find that the late-time dynamics is an example of universal phase-ordering kinetics, characterized by scaling of correlation functions in time. Depending on the parameters of the system, the evolution of the characteristic length scale $L\left(t\right)$ can be the same as for the two-dimensional $XY$ model, described by a power law with the dynamical exponent $z\approx 2$ and a logarithmic correction, or $z\approx 1$ which agrees with previous studies of conservative superfluids.

We show that implementations for quantum sensing with exceptional sensitivity and spatial resolution can be made using spin-$\frac{3}{2}$ semiconductor defect states. We illustrate this using the silicon monovacancy deep center in hexagonal SiC based on our rigorous derivation of this defect's ground state and of its electronic and optical properties. For a single ${\mathrm{V}}_{\mathrm{Si}}^{-}$ defect, we obtain magnetic field sensitivities capable of detecting individual nuclear magnetic moments. We also show that its zero-field splitting has an exceptional strain and temperature sensitivity within the technologically desirable near-infrared window of biological systems. The concepts and sensing schemes developed here are applicable to other point defects with half spin multiplet ($S\ge \frac{3}{2}$) configurations.

The interplay of charge, spin, and lattice correlations strongly influence the insulator-metal (I-M) transition and magnetic ordering in rare earth nickelates. In this context, we explored the low-energy charge dynamics in structurally modulated $\mathrm{PrNi}{\mathrm{O}}_3$ (PNO) thin films to unravel the complexity of ground state across I-M transition using terahertz (THz) spectroscopy. The THz optical constants of compressive film on $\mathrm{LaAl}{\mathrm{O}}_3$ (100) substrate and the tensile films on $\mathrm{NdGa}{\mathrm{O}}_3$ (100), (001), (110), and (111) substrates with varying orthorhombic distortion exhibit remarkably distinct features as a function of frequency and temperature. The THz conductivity of compressive film sans any I-M transition follows the Drude model. In contrast, the tensile strained films exhibit non-Drude THz conductivity, a giant positive dielectric permittivity, and negative imaginary conductivity, all of which can be explained by the Drude-Smith model. This rich variety of low-energy dynamics manifests as a function of temperature, strain, and crystal orientation. Such distinct THz spectral features, as induced by a subtle variation in strain while crossing over from tensile to compressive strain and with varying degree of orthorhombicity coupled with oxygen vacancies, reveal a novel facet of structure-property relationship of PNO.

Hybrid semiconductor-superconductor quantum dot devices are tunable physical realizations of quantum impurity models for a magnetic impurity in a superconducting host. The binding energy of the localized subgap Shiba states is set by the gate voltages and external magnetic field. In this work we discuss the effects of the Zeeman spin splitting, which is generically present both in the quantum dot and in the (thin-film) superconductor. The unequal $g$ factors in semiconductor and superconductor materials result in respective Zeeman splittings of different magnitude. We consider both classical and quantum impurities. In the first case we analytically study the spectral function and the subgap states. The energy of bound states depends on the spin-splitting of the Bogoliubov quasiparticle bands as a simple rigid shift. For the case of collinear magnetization of impurity and host, the Shiba resonance of a given spin polarization remains unperturbed when it overlaps with the branch of the quasiparticle excitations of the opposite spin polarization. In the quantum case, we employ numerical renormalization group calculations to study the effect of the Zeeman field for different values of the $g$ factors of the impurity and of the superconductor. We find that in general the critical magnetic field for the singlet-doublet transition changes nonmonotonically as a function of the superconducting gap, demonstrating the existence of two different transition mechanisms: Zeeman splitting of Shiba states or gap closure due to Zeeman splitting of Bogoliubov states. We also study how in the presence of spin-orbit coupling, modeled as an additional noncollinear component of the magnetic field at the impurity site, the Shiba resonance overlapping with the quasiparticle continuum of the opposite spin gradually broadens and then merges with the continuum.

We formulate and solve the perhaps simplest two-body bound-state problem for interacting Dirac fermions in two spatial dimensions. A two-body bound state is predicted for gapped graphene monolayers in the presence of weakly repulsive electron-electron interactions and a Coulomb impurity with charge $Ze>0$, where the most interesting case corresponds to $Z=1$. We introduce a variational Chandrasekhar-Dirac spinor wave function and show the existence of at least one bound state. This state leaves clear signatures accessible by scanning tunneling microscopy. One may thereby obtain direct information about the strength of electron-electron interactions in graphene.

The plasmonic character of monolayer silicene is investigated by time-dependent density functional theory in the random phase approximation. Both the intrinsic (undoped) and several extrinsic (carrier doped or gated) conditions are explored by simulating injection of a probe particle (i.e., an electron or a photon) of energy below 20 eV and in-plane momentum smaller than $1.1\AA {}^{-1}$. The energy-loss function of the system is analyzed, with particular reference to its induced charge-density fluctuations, i.e., plasmon resonances and corresponding dispersions, occurring in the investigated energy-momentum region. At energies larger than 1.5 eV, two intrinsic interband modes are detected and characterized. The first one is a hybridized $\pi$-like plasmon, which is assisted by competing one-electron processes involving $s{p}^2$ and $s{p}^3$ states, and depends on the slightest changes in specific geometric parameters, such as nearest-neighbor atomic distance and buckling constant. The second one is a more conventional $\pi -\sigma$ plasmon, which is more intense than the $\pi$-like plasmon and more affected by one-electron processes involving the $\sigma$ bands with respect to the analogous collective oscillation in monolayer graphene. At energies below 1 eV, two extrinsic intraband modes are predicted to occur, which are generated by distinct types of Dirac electrons (associated with different Fermi velocities at the so-called Dirac points). The most intense of them is a two-dimensional plasmon, having an energy-momentum dispersion that resembles that of a two-dimensional electron gas. The other is an acoustic plasmon that occurs for specific momentum directions and competes with the two-dimensional plasmon at mid-infrared energies. The strong anisotropic character of this mode cannot be explained in terms of the widely used Dirac-cone approximation. As in mono-, bi-, and few-layer graphene, the extrinsic oscillations of silicene are highly sensitive to the concentration of injected or ejected charge carriers. More importantly, the two-dimensional and acoustic plasmons appear to be a signature of the honeycomb lattice, independently of the chemistry of the group-IV elements and the details of the unit-cell geometry.

Acoustic metamaterials have exhibited extraordinary potential for manipulating the propagation of sound waves. To date, it has been a challenge to control the propagation of a sound wave through arbitrary pathways in a network. Here, we design a symmetry-breaking, cross-shaped metamaterial comprising Helmholtz resonant cells and a square column. The square column is eccentrically arranged. The sound wave can be transmitted in a quasilossless manner through the channels along the eccentric direction with compressed spaces, which breaks through the general transmission phenomenon. This exotic propagation characteristic is verified by the band structure and the mode of the metamaterial. Two acoustic networks, including a $2\times 2$ network and an $8\times 8$ network, demonstrate the quasilossless propagation of the sound wave along various arbitrarily shaped pathways, which include a Great Wall shape, a stairway shape, and a serpentine shape, by reconfiguring the eccentric directions. This ability opens up a new method for routing sound waves and exhibits promising applications ranging from acoustic communication to energy transmission.