In this work, we revisit the crystal field acting on the non-Kramers ${\mathrm{Pr}}^{3+}$ ion $\left(4f^2\right)$ in the quantum spin-ice candidate ${\mathrm{Pr}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ using both a standard calculation restricted to the ground spin-orbit multiplet and intermediate coupling states in the full basis of the $f^2$ configuration. Analysis of the thermal variation of the polycrystal magnetic susceptibility and of the local susceptibilities ${\chi }_{\perp }$ and ${\chi }_{\parallel }$ determined by means of polarized neutron diffraction experiments reveals that the effective antiferromagnetic exchange is strongly depleted at low temperature with respect to its high-temperature value. We then discuss the influence of crystal field imperfections arising from residual strains, which are especially important for a non-Kramers ion. We find that they are an essential ingredient to account for the very low temperature $M\left(H\right)$ magnetization curves, showing that the saturation is not achieved even at 8 T. Furthermore, as possible candidates to qualitatively understand the Curie-like behavior observed below 0.5 K, we discuss the influence of the magnetic hyperfine interaction.

Three closely related double perovskites (DP) based on the $5d^2$ ion, $\mathrm{O}{\mathrm{s}}^{6+},\mathrm{B}{\mathrm{a}}_{2}M\mathrm{Os}{\mathrm{O}}_6$, with $M=\mathrm{Mg}$, Zn, and Cd have been prepared and characterized using x-ray (XRD) and neutron diffraction (ND), dc magnetization, heat capacity, and muon spin relaxation $\left(\mu \mathrm{SR}\right)$ techniques. All three are cubic, Fm-$3m$, at ambient temperature from XRD with $\mathrm{\Delta }d/d\sim 5\times {10}^{-4}$ resolution. For both $M=\mathrm{Mg}$ and Zn, ND data at 3.5 K and lower, $\mathrm{\Delta }d/d=2\times {10}^{-3}$, resolution show no signs of a distortion. The results are compared with the known DP material, $\mathrm{B}{\mathrm{a}}_2\mathrm{CaOs}{\mathrm{O}}_6$, which shows antiferromagnetic (AF) order below $T_{\mathrm{N}}=49\mathrm{K}$ and a moderate frustration index, $f\sim 4$, $\left(f=|{\theta }_{\mathrm{CW}}|/T_{\mathrm{N}}\right)$, where ${\theta }_{\mathrm{CW}}$ is the Curie-Weiss temperature. $\mathrm{B}{\mathrm{a}}_2\mathrm{MgOs}{\mathrm{O}}_6$ with a unit cell constant $a_0=8.0757\left(1\right)\AA$, 3% smaller than for $\mathrm{B}{\mathrm{a}}_2\mathrm{CaOs}{\mathrm{O}}_6$, also shows Néel order below $T_{\mathrm{N}}=51\mathrm{K}$ with $f\sim 2$. However, $\mathrm{B}{\mathrm{a}}_2\mathrm{ZnOs}{\mathrm{O}}_6,a_0=8.0975\left(1\right)\AA$, 0.27% larger than $\mathrm{B}{\mathrm{a}}_2\mathrm{MgOs}{\mathrm{O}}_6$, does not show Néel order from either heat capacity or $\mu \mathrm{SR}$ data. A zero field cooled/field cooled (ZFC/FC) irreversibility occurs near 30 K and a broad heat capacity anomaly is detected at a similar temperature. The $\mu \mathrm{SR}$ data are consistent with a weak spin ordering with an onset below 28 K but with a coexisting dynamic component. $\mathrm{B}{\mathrm{a}}_2\mathrm{CdOs}{\mathrm{O}}_6$ with $a_0=8.3190\left(1\right)\AA$, 0.5% smaller than $\mathrm{B}{\mathrm{a}}_2\mathrm{CaOs}{\mathrm{O}}_6$, shows no evidence for any type of order/spin freezing to 0.47 K from any of the measurement techniques applied. The results for $M=\mathrm{Zn}$ and Cd appear to lie outside of the mean field theory of Chen and Balents [Phys. Rev. B 84, 094420 (2011)] for cubic $d^2$ DP with strong spin orbit coupling, but $\mathrm{B}{\mathrm{a}}_2\mathrm{MgOs}{\mathrm{O}}_6$, along with $\mathrm{B}{\mathrm{a}}_2\mathrm{CaOs}{\mathrm{O}}_6$, is likely one of the three predicted AF phases. The remarkable contrast between the doppelgänger pairs $M=\mathrm{Mg}$/Zn and $M=\mathrm{Ca}$/Cd may be traceable to differences in electronic structure of the diamagnetic $M$ ions. All of the super-super exchange pathways in these DP materials involve Os–O–$M$–O–Os linkages.

Local spectral functions and nuclear magnetic relaxation (NMR) rates, $1/T_1$, for the spin-half Heisenberg antiferromagnet on the Kagome lattice are calculated using the Moriyas Gaussian approximation, as well as through an extrapolation of multiple frequency moments. The temperature dependence of the calculated rates is compared with the oxygen $1/T_1$ NMR data in Herbertsmithite. We find that the Gaussian approximation for $1/T_1$ shows behavior qualitatively similar to experiments with a sharp drop in rates at low temperatures, consistent with a spin-gapped behavior. However, this approximation significantly underestimates the magnitude of $1/T_1$ even at room temperature. Rates obtained from extrapolation of multiple frequency moments give very good agreement with the room temperature NMR data with $J=195\pm 20$ K and hyperfine couplings determined independently from other measurements. The use of multiple frequency moments also leads to additional low-frequency weight in the local structure factors. The convergence of our calculations with higher-frequency moments breaks down at low temperatures, suggesting the existence of longer-range dynamic correlations in the system despite the very short range static correlations.

We report a simultaneous investigation of $3d$ and $4f$ magnetic moments by exploring the $\mathrm{Fe}-L_{2,3}$ and $\mathrm{Dy}-M_{4,5}$ electron energy-loss edges of a $\mathrm{DyF}{\mathrm{e}}_2/\mathrm{YF}{\mathrm{e}}_2$ superlattice using the energy-loss magnetic chiral dichroism (EMCD) technique. Specific EMCD sum rules for $M_{4,5}$ edges were established and carefully applied to the dichroic signal at $\mathrm{Dy}-M_{4,5}$ edges, giving an orbital to the effective spin moment ratio of $5.1\pm 1.8$. With dynamic diffraction effects considered, the opposite signs of $\mathrm{Fe}-L_3$ and $\mathrm{Dy}-M_5$ dichroic peaks unambiguously indicate the antiparallel alignment of net Fe $3d$ and Dy $4f$ moments. The EMCD technique is shown to be an effective tool to locally characterize the $4f$ moment of rare earth elements and study $3d-4f$ moment coupling.

We model a semiconductor wire with strong spin-orbit coupling which is proximity-coupled to a superconductor with chemical potential disorder. When tunneling at the semiconductor-superconductor interface is very weak, disorder in the superconductor does not affect the induced superconductivity nor, therefore, the effective topological superconductivity that emerges above a critical magnetic field. Here we demonstrate, nonperturbatively, how this result breaks down with stronger proximity coupling by obtaining the low-energy (i.e., subgap) excitation spectrum through direct numerical diagonalization of an appropriate Bogoliubov–de Gennes Hamiltonian. We find that the combination of strong proximity coupling and superconductor disorder suppresses the (nontopological) induced gap at zero magnetic field by disordering the induced pair potential. In the topological superconducting phase at large magnetic field, strong proximity coupling also reduces the localization length of Majorana bound states, such that the induced disorder eliminates the topological gap while bulk zero modes proliferate, even for short wires.

In the paper by Khomenko et al. [Phys. Rev. B 91, 180504 (2015)] the authors, numerically analyzing the steady counterflowing helium in an inhomogeneous channel flow, concluded that the production term $\mathcal{P}$ in the Vinen equation is proportional to $|{\mathbf{V}}_{\mathrm{ns}}{|}^3{\mathcal{L}}^{1/2}$ (where $\mathcal{L}$ is the vortex-line density and ${\mathbf{V}}_{\mathrm{ns}}$ is the counterflow velocity). In this Comment we demonstrated that the procedure, implemented by the authors, includes a number of questionable steps, such as a decomposition of velocity of line and interpretation of the flux term. Additionally, the overall strategy,—extracting information on the temporal behavior from the stationary solution also remains questionable. Because the method of determination of the explicit shape of the Vinen equation is very sensitive to the listed elements, the final conclusion of the authors cannot be considered as unambiguous.

This is a Reply to Nemirovskii's Comment [Phys. Rev. B 94, 146501 (2016)] on Khomenko et al. [Phys. Rev. B 91, 180504 (2015)] in which a new form of the production term in Vinen's equation for the evolution of the vortex-line density $\mathcal{L}$ in the thermal counterflow of superfluid ${}^4\mathrm{He}$ in a channel was suggested. To further substantiate the suggested form which was questioned in the Comment, we present a physical explanation for the improvement of the closure suggested in Khomenko et al. [Phys. Rev. B 91, 180504 (2015)] in comparison to the form proposed by Vinen. We also discuss the closure for the flux term, which agrees well with the numerical results without any fitting parameters.

The description of interacting quantum impurity models in steady-state nonequilibrium is an open challenge for computational many-particle methods: the numerical requirement of using a finite number of lead levels and the physical requirement of describing a truly open quantum system are seemingly incompatible. One possibility to bridge this gap is the use of Lindblad-driven discretized leads (LDDL): one couples auxiliary continuous reservoirs to the discretized lead levels and represents these additional reservoirs by Lindblad terms in the Liouville equation. For quadratic models governed by Lindbladian dynamics, we present an elementary approach for obtaining correlation functions analytically. In a second part, we use this approach to explicitly discuss the conditions under which the continuum limit of the LDDL approach recovers the correct representation of thermal reservoirs. As an analytically solvable example, the nonequilibrium resonant level model is studied in greater detail. Lastly, we present ideas towards a numerical evaluation of the suggested Lindblad equation for interacting impurities based on matrix product states. In particular, we present a reformulation of the Lindblad equation, which has the useful property that the leads can be mapped onto a chain where both the Hamiltonian dynamics and the Lindblad driving are local at the same time. Moreover, we discuss the possibility to combine the Lindblad approach with a logarithmic discretization needed for the exploration of exponentially small energy scales.

The recent nonempirical semilocal exchange functional of Armiento and Kümmel [Phys. Rev. Lett. 111, 036402 (2013)], AK13, incorporates a number of features reproduced by higher-order theory. The AK13 potential behaves analogously with the discontinuous jump associated with the derivative discontinuity at integer particle numbers. Recent works have established that AK13 gives a qualitatively improved orbital description compared to other semilocal methods, and reproduces a band structure closer to higher-order theory. However, its energies and energetics are inaccurate. The present work further investigates the deficiency in energetics. In addition to AK13 results, we find that applying the local-density approximation (LDA) non-self-consistently on the converged AK13 density gives very reasonable energetics with equilibrium lattice constants and bulk moduli well described across 13 systems. We also confirm that the attractive orbital features of AK13 are retained even after full structural relaxation. Hence, the deficient energetics cannot be a result of the AK13 orbitals having adversely affected the quality of the electron density compared to that of usual semilocal functionals; an improved orbital description and good energetics are not in opposition. This is also confirmed by direct calculation of the principal component of the electric field gradient. In addition, we prove that the non-self-consistent scheme is equivalent to using a single external-potential-dependent functional in an otherwise consistent, nonvariational Kohn-Sham density-functional theory (KS DFT) scheme. Furthermore, our results also demonstrate that, while an internally consistent KS functional is presently missing, non-self-consistent LDA on AK13 orbitals works as a practical nonempirical computational scheme to predict geometries, bulk moduli, while retaining the band structure features of AK13 at the computational cost of semi-local DFT.

An accurate and consistent theory of phonons in metals requires that all long-range Coulomb interactions between charged particles (electrons and ions) be treated on equal footing. So far, all attempts to deal with this nonperturbative system were relying on uncontrolled approximations in the absence of small parameters. In this paper, we develop the diagrammatic Monte Carlo approach for a two-component Coulomb system that obtains the solution to this fundamental problem in an approximation-free way by computing vertex corrections from higher-order skeleton graphs. The feasibility of the method is demonstrated by calculating the spectrum of longitudinal acoustic phonons in a simple cubic lattice, determining their sound velocity, and obtaining the phonon spectral densities by analytic continuation of the Matsubara-Green's functions. Final results are checked against the lowest-order fully self-consistent $GW$ approximation in both adiabatic and nonadiabatic regimes.

The nearest-neighbor superexchange-mediated mechanism for $d_{x^2-y^2}$ superconductivity in the one-band Hubbard model faces the challenge that nearest-neighbor Coulomb repulsion can be larger than superexchange. To answer this question, we use cellular dynamical mean-field theory (CDMFT) with a continuous-time quantum Monte Carlo solver to determine the superconducting phase diagram as a function of temperature and doping for on-site repulsion $U=9t$ and nearest-neighbor repulsion $V=0,2t,4t$. In the underdoped regime, $V$ increases the CDMFT superconducting transition temperature $T_c^d$ even though it decreases the superconducting order parameter at low temperature for all dopings. However, in the overdoped regime $V$ decreases $T_c^d$. We gain insight into these paradoxical results through a detailed study of the frequency dependence of the anomalous spectral function, extracted at finite temperature via the MaxEntAux method for analytic continuation. A systematic study of dynamical positive and negative contributions to pairing reveals that even though $V$ has a high-frequency depairing contribution, it also has a low frequency pairing contribution since it can reinforce superexchange through $J=4t^2/(U-V)$. Retardation is thus crucial to understanding pairing in doped Mott insulators, as suggested by previous zero-temperature studies. We also comment on the tendency to charge order for large $V$ and on the persistence of $d$-wave superconductivity over extended-$s$ or $s+d$ wave.

We present a first principles investigation into the electronic properties of an extended interface between rutile ${\mathrm{TiO}}_2$ and Cu. We show that owing to the highly polarizable nature of ${\mathrm{TiO}}_2$, the interface is unstable to the spontaneous formation of small electron polarons at the interface. The resulting dipole leads to an increase in the conduction band offset by 0.4 eV and the presence of a band of occupied states related to Ti $d$ states 1.4 eV below the Fermi energy. This effect should be expected more generally at interfaces between highly polarizable oxides and metals but is missed by standard first principles approaches. Given the ubiquitous nature of such interfaces, this previously overlooked effect may have important implications for diverse applications across science and technology.

Recently, a nonsymmorphic topological insulator was predicted, where the characteristic feature is the emergence of an “hourglass fermion” surface state protected by the nonsymmorphic symmetry. This prediction was supported soon after by the angle-resolved photoemission spectroscopy. We propose a simple model possessing the hourglass fermion surface state. The model is constructed by stacking the quantum spin Hall insulators with the interlayer coupling introduced so as to preserve the nonsymmorphic symmetry and the time-reversal symmetry. The Dirac theory is also derived, whose analytical results reproduce the hourglass fermion surface state remarkably well. Furthermore, we discuss how the hourglass state is destroyed by introducing perturbations based on the symmetry analysis. Our results show that the hourglass fermion surface state is universal in the helical edge system with the nonsymmorphic symmetry.

We applied terahertz (THz) time-domain spectroscopy to reveal the mechanism of the relativistic Doppler reflection of THz light from a photoinduced plasma front in a silicon wafer. The frequency upshift caused by the Doppler reflection was identified by measurement of the reflected THz waveforms and compared to the calculated results obtained using the one-dimensional finite-difference time-domain method. The relation between the energy density of the pump light and the frequency upshift was also explored. We found that the interaction time of the moving plasma front and the reflected THz pulse is a key factor in understanding the mechanism of the relativistic Doppler reflection.

The ability to fabricate 2D device architectures with desired properties, based on stacking of weakly (van der Waals) interacting atomically thin layers, is quickly becoming reality. In order to design ever more complex devices of this type, it is crucial to know the precise strain and composition dependence of the layers' electronic and optical properties. Here, we present a theoretical study of these dependences for monolayers with compositions varying from pure ${MX}_2$ to the mixed $MXY$, where $M=\text{Mo}$, W and $X,Y=\text{S}$, Se. We employ both density-functional-theory and GW calculations, as well as values of the exciton binding energies based on a self-consistent treatment of dielectric properties, to obtain the band gaps that correspond to optical or transport measurements; we find reasonable agreement with reported experimental values for the unstrained monolayers. Our predictions for the strain-dependent electronic properties should be a useful guide in the effort to design heterostructures composed of these layers on various substrates.

We show that time reversal can be achieved with a spatially uniform temporal modulation of the gauge potential. The method can be applied to the quantum wave function of electrons where there are natural gauge potentials, and to classical waves such as the acoustic and optical waves where effective gauge potentials have been demonstrated recently. This time-reversal process can provide a compensation of higher-order dispersion effects. Moreover, our approach can be used to time reverse the propagation of a wave packet in three dimensions, as well as a topologically protected one-way edge state where the underlying Hamiltonian does not have time-reversal symmetry. Our work shows that modulation of gauge potentials provides a versatile approach for dynamically controlling wave propagation.

We develop a self-consistent theory describing the spin and spatial electron diffusion in the impurity band of doped semiconductors under the effect of a weak spin-orbit coupling. The resulting low-temperature spin-relaxation time and diffusion coefficient are calculated within different schemes of the self-consistent framework. The simplest of these schemes qualitatively reproduces previous phenomenological developments, while more elaborate calculations provide corrections that approach the values obtained in numerical simulations. The results are universal for zinc-blende semiconductors with electron conductance in the impurity band, and thus they are able to account for the measured spin-relaxation times of materials with very different physical parameters. From a general point of view, our theory opens a new perspective for describing the hopping dynamics in random quantum networks.

We investigated temperature- and fluence-dependent dynamics of the time-resolved optical reflectivity in undoped spin-density-wave (SDW) and doped superconducting (SC) ${\mathrm{EuFe}}_2{(\mathrm{As},\mathrm{P})}_2$ with emphasis on the ordered ${\mathrm{Eu}}^{2+}$ spin temperature region. The data indicate that in ${\mathrm{EuFe}}_2{(\mathrm{As},\mathrm{P})}_2$ the SDW order coexists at low temperature with the SC and ${\mathrm{Eu}}^{2+}$-ferromagnetic order. Increasing the excitation fluence leads to a slow thermal suppression of the ${\mathrm{Eu}}^{2+}$ spin order due to the crystal-lattice heating on a nanosecond time scale while the SDW order is suppressed nonthermally on a subpicosecond time scale at a higher fluence.