Mie's theory of light scattering on spherical particles is being increasingly used in nanophotonics, and these demanding applications have laid bare some shortcomings of Mie theory in its standard formulation. One problem that deserves special attention is the electron spill-out in small metallic nanoparticles, which invalidates the assumption of an abrupt interface. Here we present an alternative derivation of Mie theory without this assumption. To avoid the usual electromagnetic boundary conditions suitable for a hard-wall interface, we set up equations for the electromagnetic potentials instead of the electric and magnetic field. We show that in the limit of a hard-wall interface, the results of the standard Mie theory are recovered. Additionally, a numerical solution scheme is proposed for the equations for the vector potential and the scalar potential. Analysis of the optical cross sections of soft-interface nanospheres shows that the absorption increases and occurs at lower frequencies as compared to hard-walled nanospheres. This effect is rather dramatic in large spheres with large spill-out, due to the disappearance of high-frequency resonance peaks.

We generalize the $K$ matrix formulation to nontrivial non-Abelian families of ($2+1$)-dimensional topological orders. Given a topological order $\mathcal{C}$, any topological order in the same non-Abelian family as $\mathcal{C}$ can be efficiently described by $\mathit{a}=\left(a_I\right)$, where $a_I$ are Abelian anyons in $\mathcal{C}$, together with a symmetric invertible matrix $K,K_{IJ}=k_{IJ}-t_{a_I,a_J}$, where $k_{IJ}$ are integers, $k_{II}$ are even, and $t_{a_I,a_J}$ are the mutual statistics between $a_I,a_J$. In particular, when $\mathcal{C}$ is a root whose rank is the smallest in the family, $K$ becomes an integer matrix. Our results make it possible to generate the data of large numbers of topological orders instantly, thus providing a large reservoir of potentially useful topological materials.

We show that model states of fractional quantum Hall fluids at all experimentally detected plateaus can be uniquely determined by imposing translational invariance with a particular scheme of Hilbert space truncation. The truncation is based on classical local exclusion conditions, motivated by constraints on physical measurements. The scheme allows us to identify filling factors, topological shifts, and clustering of topological quantum fluids universally without resorting to microscopic Hamiltonians. This prompts us to propose the notion of emergent commensurability as a fundamental property for many known fractional quantum Hall (FQH) states, which allows us to predict families of new FQH states that can be realized in principle. We also discuss the implications of certain missing states proposed from other phenomenological approaches, and suggest that the physics of the FQH effect could fundamentally arise from the algebraic structure of the Hilbert space in a single Landau level.

Two-dimensional (2D) generalization of the Su-Schriffer-Heeger (SSH) model serves as a platform for exploring higher-order topological insulators (HOTI). We investigate this model in a magnetic field which interpolates two models studied so far with zero flux and $\pi$ flux per plaquette. We show that in the Hofstadter butterfly there appears a wide gap around the $\pi$ flux, which belongs to the same HOTI discovered by Benalcazar-Bernevig-Hughes (BBH). It turns out that in a weak field regime HOTI could exist even within a small gap disconnected from the wider gap around $\pi$ flux. To characterize HOTI, we employ the entanglement polarization (eP) technique which is useful even if the basic four bands split into many Landau levels under a magnetic field.

Using the ab initio embedded dynamical mean-field theory (eDMFT) approach, we study the effect of long-range magnetic ordering on the spectral properties in the binary transition metal oxides, and find that the most significant changes appear in the momentum resolved spectral functions, which sharpen into quite well-defined bands in the antiferromagnetic (AFM) phase. The strongest change across the transition is found at the topmost valence-band edge (VBE), which is commonly associated with the Zhang-Rice bound state. This VBE state strengthens in the AFM phase, but only for the minority spin component, which is subject to stronger fluctuations. A similar hybridized VBE state also appears in the DFT single-particle description of the AFM phase, but gets much stronger and acquires a well-defined energy in the eDMFT description.

Motivated by the recent interest in nonequilibrium phenomena in quantum many-body systems, we study strongly interacting fermions on a lattice by deriving and numerically solving quantum Boltzmann equations that describe their relaxation to thermodynamic equilibrium. The derivation is carried out by inspecting the hierarchy of correlations within the framework of the $1/Z$ expansion. Applying the Markov approximation, we obtain the dynamic equations for the distribution functions. Interestingly, we find that in the strong-coupling limit, collisions between particles and holes dominate over particle-particle and hole-hole collisions—in stark contrast to weakly interacting systems. As a consequence, our numerical simulations show that the relaxation timescales strongly depend on the type of excitations (particles or holes or both) that are initially present.

We study a model of a quantum dot coupled to a quantum Hall edge of the Laughlin state, taking into account short-range interactions between the dot and the edge. This system has been studied experimentally in electron quantum optics in the context of single particle sources. We consider driving the dot out of equilibrium by a time-dependent bias voltage. We calculate the resulting current on the edge by applying the Kubo formula to the bosonized Hamiltonian. The Hamiltonian of this system can also be mapped to the spin-boson model and, in this picture, the current can be perturbatively calculated using the noninteracting blip approximation. We show that both methods of solution are in fact equivalent. We present numerics demonstrating that the perturbative approaches capture the essential physics at early times, although they fail to capture the charge quantization (or lack thereof) in the current pulses integrated over long times.

The electronic dispersions of the quasi-one-dimensional organic conductor TTF-TCNQ are studied by angle-resolved photoelectron spectroscopy (ARPES) with higher angular resolution and accordingly smaller step width than in previous studies. Our experimental results suggest that a refinement of the single-band 1D Hubbard model that includes finite-range interactions is needed to explain these photoemission data. To account for the effects of these finite-range interactions we employ a mobile quantum impurity scheme that describes the scattering of fractionalized particles at energies above the standard Tomonaga-Luttinger liquid limit. Our theoretical predictions agree quantitatively with the location in the $(k,\omega )$ plane of the experimentally observed ARPES structures at these higher energies. The nonperturbative microscopic mechanisms that control the spectral properties are found to simplify in terms of the exotic scattering of the charge fractionalized particles. We find that the scattering occurs in the unitary limit of (minus) infinite scattering length, which limit occurs within neutron-neutron interactions in shells of neutron stars and in the scattering of ultracold atoms but not in perturbative electronic condensed-matter systems. Our results provide important physical information on the exotic processes involved in the finite-range electron interactions that control the high-energy spectral properties of TTF-TCNQ. Our results also apply to a wider class of 1D and quasi-1D materials and systems that are of theoretical and potential technological interest.

Low energy ion scattering (LEIS) and direct recoil spectroscopy (DRS) are among the few experimental techniques that allow for the direct detection of hydrogen on a surface. The interpretation of LEIS and DRS measurements, however, is often made difficult by complexities that can arise from complicated scattering processes. Previously, these complexities were successfully navigated to identify the exact binding configurations of hydrogen on a few surfaces using a simple channeling model for the projectile ion along the surface. For the W(111) surface structure, this simple channeling model breaks down due to the large lateral atomic spacing on the surface and small interlayer spacing. Instead, our observed hydrogen recoil signal can only be explained by considering not just channeling along the surface but also scattering from subsurface atoms. Using this more complete model, together with molecular dynamics (MD) simulations, we determine that hydrogen adsorbs to the bond-centered site for the W(111)$+\text{H}$(ads) system. Additional MD simulations were performed to further constrain the adsorption site to a height $h=1.0\pm 0.1\AA$ and a position $d_{\mathrm{BC}}=1.6\pm 0.1\AA$ along the bond between neighbors in first and second layers. Our determination of the hydrogen adsorption site is consistent with density functional theory simulation results in the literature.

We study the high-pressure structures of ${\mathrm{SrB}}_6$ up to 200 GPa using first-principles structure prediction calculations and high-pressure x-ray diffraction experiments. The computations show that the ambient-pressure cubic phase transforms to an orthorhombic structure $\left(Cmmm\right)$ at 48 GPa, and then to a tetragonal structure $\left(I4/mmm\right)$ at 60 GPa. The high-pressure experiments are consistent with the theoretically predicted tetragonal structure, which was quenched successfully to ambient conditions. Pressure induces simple boron octahedra to form complex networks in which the electrons are delocalized, leading to metallic ground states with large density of states at the Fermi level. Calculated stress-strain relations for the $I4/mmm$ structure of ${\mathrm{SrB}}_6$ demonstrate its intrinsic hard nature with an estimated Vickers hardness of 15 GPa, and reveal a novel deformation mechanism with transient multicenter bonding that results in the combination of high strength and high ductility. Our findings offer valuable insights for understanding the rich and complex crystal structures of ${\mathrm{SrB}}_6$, which have broad implications for further explorations of hexaboride materials.

Practical quantum information technique requires a large scalable quantum network. We proposed a hybrid system for deterministic scalable spin entanglement network based on nitrogen-vacancy (NV) centers in diamond coupling with carbon nanotube. The fault-tolerant entangled gate between two remote NV centers can be realized with vibrating nanotube assisted spin-spin interaction with current experimental technology. This interaction can be directly generalized to multi-NV-center entanglement architecture. Moreover, the effects of the single spin dephasing (SSD) and spin cross relaxation (SCR) on this state generation process were analyzed in detail. We found that the decay rate scales as $N^2$, corresponding to the number of independent decoherence channels. However, by employing dressed state protection and independent tunable interaction method, SSD and SCR can be mitigated efficiently and the decay rate of the generated multi-NV-center entanglement scales as $N$, which boosts the size of the entanglement network up to hundreds of qubits. Such a hybrid quantum system compatible with current topological protection provides a useful platform for the investigation of quantum computation.

Germanium oxide is a prototype network-forming oxide with pressure-induced structural changes similar to those found in crystals and amorphous silicate oxides at high pressure. Studying density and coordination changes in amorphous $\mathrm{Ge}{\mathrm{O}}_2$ allows for insight into structural changes in silicate oxides at very high pressure, with implications for the properties of planetary magmas. Here, we report the density of germanium oxide glass up to 133 GPa using the x-ray absorption technique, with very good agreement with previous experimental data at pressure below 40 GPa and recent calculation up to 140 GPa. Our data highlight four distinct compressibility domains, corresponding to changes of the local structure of $\mathrm{Ge}{\mathrm{O}}_2$. Above 80 GPa, our density data show a compressibility and bulk modulus similar to the counterpart crystal phase, and we propose that a compact distorted sixfold coordination, similar to the structural motif of the pyritelike crystalline $\mathrm{Ge}{\mathrm{O}}_2$ polymorph, is likely to be stable in that pressure range. Our density data point to a smooth continuous evolution of the average coordination for pressure above 20 GPa with persistent sixfold coordination, without sharp density or density slope discontinuities. These observations are in very good agreement with theoretical calculations and spectroscopic measurements, and our results indicate that glasses and melts may behave similarly to their high-pressure solid counterparts with comparable densities, compressibility, and possibly average coordination.

High magnetic field x-ray diffraction experiments of solid oxygen have been performed at 10 K using DC magnetic fields of up to 5 T as well as pulsed magnetic fields of up to 25 T. The $\alpha$ phase of oxygen exhibits no magnetostriction greater than $\mathrm{\Delta }d/d={10}^{-4}$ at 5 T, where $d$ and $\mathrm{\Delta }d$ denote a lattice plane spacing and its magnetic field variation, respectively. The $\mathrm{\Delta }d/d$ at higher fields of up to 25 T is found to be smaller than $2\times {10}^{-3}$. These results contradict the previously reported giant magnetostriction in the $\alpha$ phase where the volume magnetostriction $\mathrm{\Delta }V/V$ reaches ${10}^{-2}$ at 7.5 T [K. Katsumata et al., J. Phys.: Condens. Matter 17, L235 (2005)].

We introduce quantum circuits in two and three spatial dimensions which are classically simulable, despite producing a high degree of operator entanglement. We provide a partial characterization of these “automaton” quantum circuits and use them to study operator growth, information spreading, and local charge relaxation in quantum dynamics with subsystem symmetries, which we define as overlapping symmetries that act on lower-dimensional submanifolds. With these symmetries, we discover the anomalous subdiffusion of conserved charges; that is, the charges spread slower than diffusion in the dimension of the subsystem symmetry. By studying an effective operator hydrodynamics in the presence of these symmetries, we predict the charge autocorrelator to decay (i) as $ln\left(t\right)/\sqrt{t}$ in two dimensions with a conserved U(1) charge along intersecting lines and (ii) as $1/t^{3/4}$ in three spatial dimensions with intersecting planar U(1) symmetries. Through large-scale studies of automaton dynamics with these symmetries, we numerically observe charge relaxation that is consistent with these predictions. In both cases, the spatial charge distribution is distinctly non-Gaussian and reminiscent of the diffusion of charges along a fractal surface. We numerically study the onset of quantum chaos in the spreading of local operators under these automaton dynamics and observe power-law broadening of the ballistically propagating fronts of evolving operators in two and three dimensions and the saturation of out-of-time-ordered correlations to values consistent with quantum chaotic behavior.

We investigate an interfacial spin-transfer torque and $\beta$-term torque with alternating current (AC) parallel to a magnetic interface. We find that both torques are resonantly enhanced as the AC frequency approaches the exchange splitting energy. We show that this resonance allows us to estimate directly the interfacial exchange interaction strength from the domain wall motion. We also find that the $\beta$ term includes an unconventional contribution which is proportional to the time derivative of the current and exists even in the absence of any spin relaxation processes.

We study nonlinear optical responses in superconducting systems with inversion- $\left(\mathcal{I}\right)$ symmetry-breaking order parameters. We first show that any superconducting system with $\mathcal{I}$ and time-reversal $\left(\mathcal{T}\right)$ symmetries requires an $\mathcal{I}$-breaking order parameter to support optical transitions between particle-hole pair bands. We then use a one-dimensional (1D) toy model of an $\mathcal{I}$-breaking superconductor to numerically calculate linear and nonlinear conductivities, including shift current and second-harmonic generation (SHG) responses. We find that the magnitude of the signal is significantly larger in shift current/SHG response than in the linear response due to the matrix element effect. We also present various scaling behaviors of the SHG signal, which may be relevant to the recent experimental observation of SHG in cuprates [L. Zhao, C. A. Belvin, R. Liang, D. A. Bonn, W. N. Hardy, N. P. Armitage, and D. Hsieh, Nat. Phys. 13, 250 (2016)]. Finally, we confirm the generality of our observations regarding nonlinear responses of $\mathcal{I}$-breaking superconductors, by analyzing other models including a 1D three-band model and 2D square lattice model.

Sustained external forces acting on a material provide additional mechanisms to evolve the state of the system, and these mechanisms do not necessarily obey the microscopic detailed balance. Therefore standard methods to compute the thermodynamic and kinetic properties do not apply in such driven systems. The competition between these mechanisms and the standard thermally activated jumps leads to nonequilibrium steady states. We extend the self-consistent mean-field theory to take into account forced atomic relocations (FARs) as a model of these additional kinetic mechanisms. The theory is applied to the atomic-scale modeling of radiation damage. Using a first-shell approximation of the theory, we highlight the violation of Onsager reciprocal relations in driven systems. An implementation of the extended theory into the kineclue code yields calculations of the effective Onsager coefficients in agreement with Monte Carlo simulations. A systematic parametric study is performed to emphasize the effect of FAR distances and the solute-defect interaction on the diffusion properties. The effect of FAR on the vacancy-solute flux coupling and the solute tracer diffusivity is non-negligible when (i) the solute-vacancy thermodynamic attraction is large, (ii) the magnitude of the thermal jump frequencies is lower or comparable to the frequencies of FAR, and (iii) the range of interactions between vacancies and solute atoms is close to FAR distances.

Nonreciprocal transport, which refers to directional transport, is known to occur in noncentrosymmetric systems with broken time-reversal symmetry. In this paper, we study the nonreciprocal motion of a super-Ohmic dissipative particle—with a quadratic spectral density function of the environment ($s=2$)—in an asymmetric periodic potential. Using the Keldysh formalism, we derive general expressions for the perturbative corrections to finite-frequency mobility up to third order in potential strength. We find from numerical integration that as a function of temperature, second-order mobility in the low-frequency limit scales exponentially in the low-temperature region, ${\mu }_2^{\left(3\right)}(T;{\omega }_1,{\omega }_2)\sim exp(-b/T),(b>0)$ and scales as a power law in the high-temperature region, ${\mu }_2^{\left(3\right)}(T;{\omega }_1,{\omega }_2)\sim T^{-3}$. As a function of frequency, we show that second-order mobility scales according to ${\mu }_2^{\left(3\right)}({\omega }_1,{\omega }_2;T)\sim i(\omega log(\omega /{\omega }_c){)}^{-3}$ for the $s=2$ case, but scales as a power law, ${\mu }_2^{\left(3\right)}({\omega }_1,{\omega }_2;T)\sim i{\omega }^{-3}$, for $s\ge 3,(s\in {\mathbb{Z}}^{+})$.

We study the magnetic short range order (MSRO) in ${\mathrm{Fe}}_{1-x}{\mathrm{Cr}}_x\left(0\le x\le 0.15\right)$ where an inversion of atomic short range order (ASRO) occurs at $x_C=0.11\left(1\right)$. Our combination of neutron diffuse scattering and bulk magnetization measurements offers a comprehensive description of these local orders at a microscopic level. In the dilute alloys $\left(x<0.04\right)$, the Cr atoms bear a large moment ${\mu }_{\mathrm{Cr}}=-1.0\left(1\right){\mu }_{\mathrm{B}}$, antiparallel to the Fe ones $\left({\mu }_{\mathrm{Fe}}\right)$. They fully repel their Cr first and second neighbors, and perturb the surrounding Fe moments. With increasing $x$, near neighbor Cr-Cr pairs start to appear and the Cr moment magnitude decreases, while ${\mu }_{\mathrm{Fe}}$ shows a rounded maximum for $x_1=0.06\left(1\right)<x_C$. Above $x_C$, ASRO turns to local Cr segregation, thereby increasing magnetic frustration. First-principles calculations reproduce the observed moment variations but overestimate the magnitude of the Cr moment. In order to reconcile theory with experiment quantitatively, we propose that the magnetic moments start canting locally, already above $x_1$. This picture actually anticipates the spin glasslike behavior of Cr-rich alloys. The whole study points out the subtle interplay of MSRO and ASRO, yielding an increasing frustration as $x$ increases, due to competing Fe-Cr and Cr-Cr interactions and Cr clustering tendency.