We observe thermal Hall conductivity for ${\left({\mathrm{Tb}}_{0.3}{\mathrm{Y}}_{0.7}\right)}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, which is even larger than the previously observed thermal Hall conductivity for ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ [Science 348, 106 (2015)]. The robustness against the dilution of the Tb magnetic moment indicates the Hall effect of phonons is the origin of thermal Hall conductivity in Tb pyrochlore oxide. The temperature and magnetic field dependences are observed to follow the empirical relation that the Hall angle is proportional to the magnetization. We also investigate thermal Hall conductivity for ${\left({\mathrm{Tb}}_{0.3}{\mathrm{Y}}_{0.7}\right)}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$. We observe barely finite thermal conductivity at low temperatures. This confirms the thermal Hall conductivity in Tb-garnet oxide. The origins of the empirical relation in the pyrochlore system and the magnitude difference between the two systems are discussed comparatively with previously proposed theories of the phonon Hall effect.

The noncentrosymmetric superconductor BeAu has been investigated using magnetization, resistivity, specific heat, and muon-spin relaxation/rotation. BeAu crystallizes in a cubic FeSi-type B20 structure with a superconducting transition temperature $T_c=3.2\pm 0.1\mathrm{K}$. The low-temperature specific heat data, $C_{\mathrm{el}}$(T), indicates a weakly-coupled fully gapped BCS superconductivity with an isotropic energy gap $2\mathrm{\Delta }\left(0\right)/k_B{T}_c=3.76$, close to the BCS value of 3.52. Interestingly, type-I superconductivity is inferred from the $\mu \mathrm{SR}$ measurements, in contrast to the earlier reports of type-II superconductivity in BeAu. The Ginzburg-Landau parameter is ${\kappa }_{\mathrm{GL}}=0.4<1/\sqrt{2}$. The frequency domain transverse-field $\mu \mathrm{SR}$ spectra, depicting the internal magnetic field probability distribution, P(B), also confirms the absence of the mixed state in BeAu. The thermodynamic critical field, $H_c$, is calculated to be around 259 Oe. The zero-field $\mu \mathrm{SR}$ results indicate that time-reversal symmetry is preserved and supports a spin-singlet pairing in the superconducting ground state.

We present muon spin rotation and relaxation $\left(\mu \mathrm{SR}\right)$ measurements as well as demagnetizing-field-corrected magnetization measurements on polycrystalline samples of the noncentrosymmetric superconductor BeAu. From $\mu \mathrm{SR}$ measurements in a transverse field, we determine that BeAu is a type-I superconductor with H${}_c=$ 258 Oe, amending the previous understanding of the compound as a type-II superconductor. To account for demagnetizing effects in magnetization measurements, we produce an ellipsoidal sample, for which a demagnetization factor can be calculated. After correcting for demagnetizing effects, our magnetization results are in agreement with our $\mu \mathrm{SR}$ measurements. Using both types of measurements, we construct a phase diagram from $T=30$ mK to $T_c\approx 3.25$ K. We then study the effect of hydrostatic pressure and find that 450 MPa decreases T${}_c$ by 35 mK, comparable to the change seen in the type-I elemental superconductors Sn, In, and Ta. This suggests BeAu is far from a quantum critical point accessible by the application of pressure.

We use a state-of-the-art $GW$ Bethe-Salpeter equation (BSE) formalism to study electronic structure and optical properties of oxygen vacancies ($F$ centers) in $\alpha$-alumina. The density functional theory (DFT) + $GW$ formalism has been employed to compute the charge transition levels (CTLs) for oxygen vacancies. We propose a reformulation of the DFT+GW approach to calculate these CTLs. Our new approach allows for transparent application of electrostatic corrections required in finite supercell calculations using periodic boundary conditions. We find that $F$ centers in this material introduce deep donor levels, (+2/+1) at 2.4 eV, and a (+1/0) level at 3.9 eV above the valence band maximum. We also study $F$-center absorption and emission processes using constrained DFT and BSE. Our calculated absorption and emission energies are in excellent agreement with experiments and provide an unambiguous interpretation of the same.

The exotic phenomenon of time-translation-symmetry breaking under periodic driving—one of the main features of the so-called time crystals—has been shown to occur in many-body systems even in clean setups where disorder is absent. In this work, we propose a realization of this effect in few-body systems, both in the context of trapped cold atoms with strong interactions and of a circuit of superconducting qubits. We show how these two models can be treated in a fairly similar way by adopting an effective spin-chain description, to which we apply a simple driving protocol. We focus on the response of the magnetization in the presence of imperfect pulses and interactions, and show how the results can be interpreted, in the cold atomic case, in the context of experiments with trapped bosons and fermions. Furthermore, we provide a set of realistic parameters for the implementation of the superconducting circuit.

The pressure dependencies of the magnetic and superconducting transitions, as well as that of the superconducting upper critical field, are reported for single crystalline ${\mathrm{EuRbFe}}_4{\mathrm{As}}_4$. Resistance measurements were performed under hydrostatic pressures up to 6.21 GPa and in magnetic fields up to 9 T. Zero-field-cooled magnetization measurements were performed under hydrostatic pressures up to 1.24 GPa under 20 mT applied field. Superconducting transition temperature, $T_{\text{c}}$, up to 6.21 GPa and magnetic transition temperature, $T_{\text{M}}$, up to 1.24 GPa were obtained and a pressure-temperature phase diagram was constructed. Our results show that $T_{\text{c}}$ is monotonically suppressed upon increasing pressure. $T_{\text{M}}$ is linearly increased up to 1.24 GPa. For the studied pressure range, no signs of the crossing of $T_{\text{M}}$ and $T_{\text{c}}$ lines are observed. The normalized slope of the superconducting upper critical field is gradually suppressed with increasing pressure, which may be due to the continuous change of Fermi velocity $v_F$ with pressure.

We study the fractal properties of single-particle eigenmodes of an entanglement Hamiltonian in free-fermion models. One of these modes that has the highest entanglement information and is thus called the maximally entangled mode (MEM) is especially considered. In free-fermion models with Anderson localization, the fractality of the MEM is obtained numerically and compared with the fractality of the Hamiltonian eigenmode at the Fermi level. We show that both eigenmodes have similar fractal properties: both have the same single-fractal dimension in the delocalized phase which equals the dimension of the system, and both show multifractality at the phase transition point. Therefore, we conclude that fractal behavior of the MEM, in addition to the fractal behavior of the Hamiltonian eigenmode, can be used as a quantum phase transition characterization.

We present a detailed study of the imaginary and real parts of the spin susceptibility of silicene which can be generalized to other buckled honeycomb structures. We find that while the off-diagonal components are nonzero in individual valleys, they add up to zero upon including contributions from both the valleys. We investigate the interplay of the spin-orbit interaction and an external electric field applied perpendicular to the substrate and find that although the $xx$ and $yy$ components of the susceptibility are identical, they differ from the $zz$ component. The external electric field plays an important role in modifying the allowed intersubband regions. In the dynamic limit, the real part of the susceptibility exhibits log divergence, the position of which can be tuned by the electric field and therefore has implications for spin-collective excitations. The effect of the electric field on the static part of the susceptibility and its consequence for the long distance decay of the spin susceptibility have been explored.

Strong electron-electron interaction in ultraflat edge states can be responsible for correlated phases of matter, such as magnetism, charge-density wave, or superconductivity. Here we consider the diamond (111) surface that, after Pandey reconstruction, presents zigzag carbon chains, generating a flat surface band. By performing full structural optimization with hybrid functionals and neglecting spin polarization, we find that a substantial dimerization ($0.090\AA /0.076\AA$ bond disproportionation in the PBE0/HSE06) occurs on the chains; a structural effect absent in calculations with functionals based on the local density/generalized gradient approximation. This dimerization is the primary mechanism for the opening of an insulating gap in the absence of spin polarization. The single-particle direct gap is $1.7\mathrm{eV}$ ($1.0\mathrm{eV}$) in the PBE0 (HSE06), comparable with the experimental optical gap of $1.47\mathrm{eV}$, and on the larger (smaller) side of the estimated experimental single-particle gap window of 1.57–1.87 eV, after inclusion of excitonic effects. However, by including spin polarization in the calculation, we find that the exchange interaction stabilizes a different ground state, undimerized, with no net magnetization and ferrimagnetic along the Pandey $\pi$ chains with magnetic moments as large as $0.2–0.3{\mu }_B$ in the PBE0. The direct single-particle band gap in the equal spin channel is approximately $2.2\mathrm{eV}$ ($1.5\mathrm{eV}$) with the PBE0 (HSE06) functional. Our work is relevant for systems with flat bands in general and wherever the interplay between structural, electronic, and magnetic degrees of freedom is crucial, as in twisted bilayer graphene, IVB atoms on IVB(111) surfaces such as Pb/Si(111), or molecular crystals.

Using Hall photovoltage measurements, we demonstrate that a linear transverse Hall voltage can be induced in few-layer ${\mathrm{WTe}}_2$ under circularly polarized light illumination. By applying a bias voltage along different crystal axes, we find that the photon-helicity induced Hall effect coincides with a particular crystal axis. Our results are consistent with the underlying Berry curvature exhibiting a dipolar distribution due to the breaking of crystal inversion symmetry. Using time-resolved optoelectronic autocorrelation spectroscopy, we find that the decay time of the detected Hall voltage exceeds the electron-phonon scattering time by orders of magnitude but is consistent with the comparatively long spin lifetime of carriers in the momentum-indirect electron and hole pockets in ${\mathrm{WTe}}_2$. Our observation suggests that a helicity induced nonequilibrium spin density on the Fermi surface after the initial charge carrier relaxation gives rise to a linear Hall effect.

Gallium phosphide is an important indirect band gap material with a variety of applications in optics ranging from LEDs to applications in GaP/Si based solar cells. We investigated GaP using ultrafast, pump-probe coherent acoustic phonon spectroscopy (time-domain Brillouin scattering). We measured the dependence of the amplitude of the differential reflectivity as modulated by coherent acoustic phonons (CAPs) as a function of laser probe energy and found that the amplitude of the coherent phonon oscillations varies nonmonotonically near the direct gap transition at the $\mathrm{\Gamma }$ point. A theoretical model is developed which quantitatively explains the experimental data and shows that one can use coherent phonon spectroscopy to provide detailed information about the electronic structure, the dielectric function, and optical transitions in indirect band gap materials. Our calculations show that the modeling of experimental results is extremely sensitive to the wavelength dependent dielectric function and its derivatives.

In principle the stacking of different two-dimensional (2D) materials allows the construction of 3D systems with entirely new electronic properties. Here we propose to realize topological crystalline insulators (TCI) protected by mirror symmetry in heterostructures consisting of graphene monolayers separated by two-dimensional polar spacers. The polar spacers are arranged such that they can induce an alternating doping and/or spin-orbit coupling in the adjacent graphene sheets. When spin-orbit coupling dominates, the nontrivial phase arises due to the fact that each graphene sheet enters a quantum spin-Hall phase. Instead, when the graphene layers are electron and hole doped in an alternating fashion, a uniform magnetic field leads to the formation of quantum Hall phases with opposite Chern numbers. It thus has the remarkable property that unlike previously proposed and observed TCIs, the nontrivial topology is generated by an external time-reversal breaking perturbation.

We study time-dependent subgap properties of a quantum dot (QD) embedded between two superconductors and another metallic lead, solving the Heisenberg equations of motion by the Laplace transform technique subject to the initial conditions. Focusing on the response of the system induced by a sudden coupling of the QD to external reservoirs, we analyze the transient currents and their differential conductance. We also derive analytical expressions for measurable quantities and find that they oscillate in time with the frequency governed by the QD coupling to superconducting reservoirs. Such quantum oscillations are damped due to relaxation processes caused by the normal lead, whereas their period is controlled by the phase difference $\varphi$ between the order parameters of superconducting leads (except the case $\varphi =\pi$, when all observables evolve to their stationary values without any oscillations). We also explore time-dependent development of the subgap quasiparticles and find their signatures measurable in the differential conductance. We evaluate (numerically and analytically) three typical time scales, characterizing the initial and large-time stages of the transient dynamics which in the asymptotic limit ($t\to \infty$) drives these subgap quasiparticles to the true Andreev states.

The inevitable and random impurities or defects can significantly influence the lattice-vibrational properties of materials and devices. Thus, the capability of effectively treating disorder effects is indispensable for theoretical simulations. In this paper, we report an auxiliary coherent medium theory, in the framework of multiple scattering theory, to simulate disordered vibrational systems containing both mass and force-constant disorders. In this method, the physical Green's function is related to an auxiliary Green's function by introducing a separable force-constant model to describe disordered systems. As an important result, the force-constant disorder can be transformed to a diagonal-like disorder in the auxiliary Hamiltonian while maintaining the important force-constant sum rule. In combination with the single-site and cluster coherent potential approximation, the configurational average over the auxiliary Green's function can be performed to obtain the configuration-averaged physical properties. To demonstrate the effectiveness of this method, we apply it to a one-dimensional harmonic chain with atomic disorders and find our calculations agree very well with the exact results for a wide range of mass and force constants. Moreover, we show that the phonon transport property of disordered devices can be derived based on the auxiliary Green's function formalism in combination with vertex corrections. The auxiliary coherent medium theory features easy implementation and feasible incorporation with diagrammatic technique in many-body perturbation and various cluster approximations, providing an important approach to analyze disorder effects on the vibrational properties. Moreover, it is also straightforward to apply the present formalism to treat the general atomic disorder in electronic systems.

We report the development and application of a method for carrying out computational investigations of the effects of mass and force-constant (FC) disorder on phonon spectra. The method is based on the recently developed typical medium dynamical cluster approach, which is a Green's function approach. Excellent quantitative agreement with previous exact diagonalization results establishes the veracity of the method. Application of the method to a model system of binary mass and an FC-disordered system leads to several findings. A narrow resonance, significantly below the van Hove singularity, that has been termed the boson peak, is seen to emerge for low soft particle concentrations. We show, using the typical phonon spectrum, that the states constituting the boson peak cross over from being completely localized to being extended as a function of increasing soft particle concentration. In general, an interplay of mass and FC disorder is found to be cooperative in nature, enhancing phonon localization over all frequencies. However, for a certain range of frequencies, and depending on material parameters, FC disorder can delocalize the states that were localized by mass disorder, and vice versa. Modeling vacancies as weakly bonded sites with vanishing mass, we find that vacancies, even at very low concentrations, are extremely effective in localizing phonons. Thus, inducing vacancies is proposed as a promising route for efficient thermoelectrics. Finally, we use model parameters corresponding to the alloy system, ${\mathrm{Ni}}_{1-x}{\mathrm{Pt}}_x$, and we show that mass disorder alone is insufficient to explain the pseudogap in the phonon spectrum; the concomitant presence of FC disorder is necessary.

We present bulk and neutron scattering measurements performed on the isotopically enriched ${}^{154}{\mathrm{Sm}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ and ${}^{154}{\mathrm{Sm}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ samples. Both compounds display sharp heat capacity anomalies, at 350 and 440 mK, respectively. Inelastic neutron scattering measurements are employed to determine the crystalline electric field (CEF) level scheme, which includes transitions between the ground-state and first excited $J$ multiplets of the ${\mathrm{Sm}}^{3+}$ ion. To further validate those results, the single-ion magnetic susceptibility of the compounds is calculated and compared with the experimental dc-susceptibility measured in low applied magnetic fields. It is demonstrated that the inclusion of intermultiplet transitions in the CEF analysis is fundamental to the understanding of the intermediate and, more importantly, low-temperature magnetic behavior of the Sm-based pyrochlores. Finally, the heat capacity anomaly is shown to correspond to the onset of an all-in-all-out long-range order in the stannate sample, while in the titanate a dipolar long-range order can be only indirectly inferred.

In this paper, we investigate a linear chain of qubits and determine that it can be configured into a conditional two-qubit swapping gate, where the first and last qubits of the chain are the swapped qubits, and the remaining middle ancilla qubits are controlling the state of the gate. The swapping gate introduces different phases on the final states depending on the initial states. In particular, we focus on a chain of four qubits and show the swapping gate it implements. We simulate the chain with realistic parameters, and decoherence noise and leakage to higher excited states, and find an average fidelity of around 0.99. We propose a superconducting circuit which implements this chain of qubits and present a circuit design of the circuit. We also discuss how to operate the superconducting circuit such that the state of the gate can be controlled. Lastly, we discuss how the circuit can be straightforwardly altered and may be used to simulate Hamiltonians with nontrivial topological properties.

The scalability of quantum networks based on solid-state spin qubits is hampered by the short range of natural spin-spin interactions. Here, we propose a scheme to entangle distant spin qubits via the soft modes of an antiferromagnetic domain wall (DW). As spin qubits, we focus on quantum impurities (QIs) placed in the vicinity of an insulating antiferromagnetic thin film. The low-energy modes harbored by the DW are embedded in the antiferromagnetic bulk, whose intrinsic spin-wave dynamics have a gap that can exceed the THz range. By setting the QI frequency and the temperature well within the bulk gap, we focus on the dipolar interaction between the QI and two soft modes localized at the DW. One is a stringlike mode associated with transverse displacements of the DW position, while the dynamics of the other, corresponding to planar rotations of the Néel order parameter, constitute a spin superfluid. By choosing the geometry in which the QI does not couple to the string mode, we use an external magnetic field to control the gap of the spin superfluid and the qubit-qubit coupling it engenders. We suggest that a tunable micron-range coherent coupling between qubits can be established using common antiferromagnetic materials.