Spinel MnV${}_2$O${}_4$ exhibits orbital ordering at $T_c=57$ K accompanied by a structural phase transition from cubic to tetragonal and ferrimagnetic ordering. We measured the temperature dependence of the optical reflectivity spectra on the cleaved surface of a MnV${}_2$O${}_4$ single crystal with controlled twin structures below $T_c$. We found that there are two peaks at 1.6 and 2.3 eV, corresponding to the Mott excitations, in the optical conductivity spectra obtained by the Kramers-Kronig transformation of the reflectivity, and that the two peaks exhibit a similar anisotropic change below $T_c$. Furthermore, we found that these two peaks exhibit a different temperature dependence above $T_c$. We analyzed these results by a model in which the multiplet structures of the $d$ state for the Mott excitation are fully taken into account, and discussed the occupation of the triply degenerate $t_{2g}$ orbitals both below and above $T_c$.

In the theory of electron-phonon superconductivity both the magnitude of the electron-phonon coupling $\lambda$ and the Coulomb pseudopotential ${\mu }^{*}$ are important to determine the transition temperature $T_c$ and other properties. We calculate corrections to the conventional result for the Coulomb pseudopotential. Our calculations are based on the Hubbard-Holstein model, where electron-electron and electron-phonon interactions are local. We develop a perturbation expansion, which accounts for the important renormalization effects for the electrons, the phonons, and the electron-phonon vertex. We show that retardation effects are still operative for higher order corrections, but less efficient due to a reduction of the effective bandwidth. This can lead to larger values of the pseudopotential and reduced values of $T_c$. The conclusions from the perturbative calculations are corroborated up to intermediate couplings by comparison with nonperturbative dynamical mean-field results.

It is shown that the magnetization rounding measured by L. Li and coworkers above the superconducting transition in optimally doped YBa${}_2$Cu${}_3$O${}_{7-\delta }$ crystals under magnetic fields up to 14 T [Phys. Rev. B 81, 054510 (2010)] may be explained at a phenomenological level in terms of the mean-field Gaussian-Ginzburg-Landau (GGL) approach for layered superconductors. This result challenges the claims of Li and coworkers, who write “$[\cdots ]$ we are observing the phase-disordering mechanism, rather than Gaussian mean-field fluctuations,” but it is in full agreement with earlier magnetization measurements by different authors in optimally doped YBa${}_2$Cu${}_3$O${}_{7-\delta }$ under lower magnetic fields. The adequacy of the mean-field Ginzburg-Landau descriptions is further confirmed when analyzing the magnetization data reported below $T_c$ by Li and coworkers.

We analyze recent torque measurements of the magnetization $M_d$ vs magnetic field $H$ in optimally doped YBa${}_2$Cu${}_3$O${}_{7-y}$ (OPT YBCO) to argue against a recent proposal by R. I. Rey et al. [Phys. Rev. B 87, 056501 (2013)] that the magnetization results above $T_c$ are consistent with Gaussian fluctuations. We find that despite its strong interlayer coupling, OPT YBCO displays an anomalous nonmonotonic dependence of $M_d$ on $H$ which represents direct evidence for the locking of the pair wave function phase ${\theta }_n$ at $T_c$ and the subsequent unlocking by a relatively weak $H$. These unusual features characterize the unusual nature of the transition to the Meissner state in cuprate superconductors. They are absent in low-$T_c$ superconductors to our knowledge. We also stress the importance of the vortex liquid state, as well as the profiles of the melting field $H_m\left(T\right)$ and the upper critical field curve $H_{c2}\left(T\right)$ in the $T$-$H$ plane. Contrary to the claims of Rey et al., we show that the curves of the magnetization and the Nernst signal illustrate the inaccessibility of the $H_{c2}$ line near $T_c$. The prediction of the $H_{c2}$ line by Rey et al. is shown to be invalid in OPT YBCO.

The present study applies high-resolution transmission electron microscopy with a combination of geometric phase analysis to characterize atomic structures of a twist grain boundary in gold, illuminating the presence of misfit dislocations with a stand-off distance from the grain boundary. The formation of the stand-off misfit dislocations is attributed to a difference in shear modulus between the two grains bordering the grain boundary, which originates in elastic anisotropy of Au.

Quasilongitudinal and quasitransverse picosecond strain pulses injected into a ferromagnetic (311) (Ga,Mn)As film induce dynamical shear strain in the film, thereby modulating the magnetic anisotropy and inducing resonant precession of the magnetization at a frequency ∼10 GHz. The modulation of the out-of-plane magnetization component by the quasitransverse strain reaches amplitudes as large as 10$\%$ of the equilibrium magnetization. Our theoretical analysis is in good agreement with the observed results, thus providing a strategy for ultrafast magnetization control in ferromagnetic films by strain pulses.

Motivated by an intriguing report, in some frustrated quantum antiferromagnets, of magnetization plateaus whose simple collinear structure is not stabilized by an external magnetic field in the classical limit, we develop a semiclassical method to estimate the zero-point energy of collinear configurations even when they do not correspond to a local minimum of the classical energy. For the spin-$1/2$ frustrated square-lattice antiferromagnet, this approach leads to the stabilization of a large 1/2 plateau with “up-up-up-down” structure for $J_2/J_1>1/2$, in agreement with exact diagonalization results, while for the spin-$1/2$ anisotropic triangular antiferromagnet, it predicts that the 1/3 plateau with “up-up-down” structure is stable far from the isotropic point, in agreement with the properties of Cs${}_2$CuBr${}_4$.

We use the tomographic density of states (TDOS), which is a measure of the density of states for a single slice through the band structure of a solid, to study the temperature evolution of the superconducting gap in the cuprates. The TDOS provides accuracy in determining both the superconducting pair-forming strength $\Delta$ and the pair-breaking rate $\Gamma$. In both optimally and underdoped Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$, we find the near-nodal $\Delta$ smoothly evolves through the superconducting transition temperature—clear evidence for the existence of preformed pairs. Additionally, we find the long-observed “filling” of the superconducting gap in the cuprates is due to the strongly temperature-dependent $\Gamma$.

Piezoelectric and ex situ electric-field induced structural studies were carried out on closely spaced compositions in the morphotropic phase boundary region of ($1-x$) PbTiO${}_3$-($x$)BiScO${}_3$. While the common approach of zero field structural analysis failed to provide a unique relationship between the anomalous piezoresponse of $x$ = 0.3725 and structural factor(s), ex situ study of electric-field induced structural changes revealed that the composition exhibiting the highest piezoelectric response is the one which also exhibits significantly enhanced polarizability of the lattices of both coexisting (monoclinic and tetragonal) phases. The enhanced lattice polarizability manifests as a significant fraction of the monoclinic phase transforming irreversibly to the tetragonal phase after electric poling.

We report a method to reliably count the number of atoms from high-angle annular dark field scanning transmission electron microscopy images. A model-based analysis of the experimental images is used to measure scattering cross sections at the atomic level. The high sensitivity of these measurements in combination with a thorough statistical analysis enables us to count atoms with single-atom sensitivity. The validity of the results is confirmed by means of detailed image simulations. We will show that the method can be applied to nanocrystals of arbitrary shape, size, and atom type without the need for a priori knowledge about the atomic structure.

We provide a detailed derivation of the low-energy model for Zn-diluted La${}_2$CuO${}_4$ in the limit of low doping together with a study of the ground-state properties of that model. We consider Zn-doped La${}_2$CuO${}_4$ within a framework of the three-band Hubbard model, which closely describes high-$T_c$ cuprates on the energy scale of the most relevant atomic orbitals. To obtain the low-energy effective model, we first determine hybridized electronic states of CuO${}_4$ and ZnO${}_4$ plaquettes within the CuO${}_2$ planes. Qualitatively, we find that the hybridization of zinc and oxygen orbitals can result in an impurity state with the energy $\varepsilon$, which is lower than the effective Hubbard gap $U$. In the limit of the effective hopping integral $t\ll \varepsilon$, $U$, the low-energy, spin-only Hamiltonian includes terms of the order $t^2/U$ and $t^4/{\varepsilon }^3$. That is, besides the usual nearest-neighbor superexchange $J$ terms of order $t^2/U$, the low-energy model contains impurity-mediated, further-neighbor frustrating interactions among the Cu spins surrounding Zn sites in an otherwise unfrustrated antiferromagnetic background. These terms, denoted as $J_{\mathrm{Zn}}^{\prime }$ and $J_{\mathrm{Zn}}^{\prime \prime }$, are of order $t^4/{\varepsilon }^3$ and can be substantial when $\varepsilon \sim U/2$, the latter value corresponding to the realistic CuO${}_2$ parameters. In order to verify this spin-only model, we subsequently apply the $T$-matrix approach to study the effect of impurities on the antiferromagnetic order parameter. Previous theoretical studies, which include only the dilution effect of impurities, show a large discrepancy with experimental data in the doping dependence of the staggered magnetization at low doping. We demonstrate that this discrepancy is eliminated by including impurity-induced frustrations into the effective spin model with realistic CuO${}_2$ parameters. Recent experimental study shows a significantly stronger suppression of spin stiffness in the case of Zn-doped La${}_2$CuO${}_4$ compared to the Mg-doped case and thus gives strong support to our theory. We argue that the proposed impurity-induced frustrations should be important in other strongly correlated oxides and charge-transfer insulators.

We study phase slips in one-dimensional topological superconducting wires. These wires have been proposed as building blocks for topologically protected qubits in which the quantum information is distributed over the length of the device and thus is immune to local sources of decoherence. However, phase slips are nonlocal events that can result in decoherence. Phase slips in topological superconductors are peculiar for the reason that they occur in multiples of $4\pi$ (instead of $2\pi$ in conventional superconductors). We reestablish this fact via a beautiful analogy to the particle physics concept of dynamic symmetry breaking by explicitly finding a “hidden” zero mode in the fermion spectrum computed in the background of a $2\pi$ phase slip. Armed with the understanding of phase slips in topological superconductors, we propose a simple experimental setup with which the predictions can be tested by monitoring the tunneling rate of a superconducting flux quantum through a topological superconducting wire.

In order to study the interplay between Kondo and Ruderman-Kittel-Kasuya-Yosida interaction, we calculate the spin-spin correlation functions between two Kondo impurities coupled to different sites of a half-filled open Hubbard chain. Using the density-matrix renormalization group (DMRG), we reexamine the exponents for the power-law decay of the correlation function between the two impurity spins as a function of the antiferromagnetic coupling $J$, the Hubbard interaction $U$, and the distance $R$ between the impurities. The exponents for finite systems obtained in this work deviate from previously published DMRG calculations. We furthermore show that the long-distance behavior of the exponents is the same for impurities coupled to the bulk or to both ends of the chain. We note that a universal exponent for the asymptotic behavior can not be extracted from these finite-size systems with open boundary conditions.

Many theoretical approaches find $d$-wave superconductivity in the prototypical one-band Hubbard model for high-temperature superconductors. At strong coupling ($U\ge W$, where $U$ is the on-site repulsion and $W=8t$ the bandwidth) pairing is controlled by the exchange energy $J=4t^2/U$. One may then surmise, ignoring retardation effects, that near-neighbor Coulomb repulsion $V$ will destroy superconductivity when it becomes larger than $J$, a condition that is easily satisfied in cuprates, for example. Using cellular dynamical mean-field theory with an exact diagonalization solver for the extended Hubbard model, we show that pairing at strong coupling is preserved, even when $V\gg J$, as long as $V\lesssim U/2$. While at weak coupling $V$ always reduces the spin fluctuations and hence $d$-wave pairing, at strong coupling, in the underdoped regime, the increase of $J=4t^2/(U-V)$ caused by $V$ increases binding at low frequency while the pair-breaking effect of $V$ is pushed to high frequency. These two effects compensate in the underdoped regime, in the presence of a pseudogap. While the pseudogap competes with superconductivity, the proximity to the Mott transition that leads to the pseudogap, and retardation effects, protect $d$-wave superconductivity from $V$.

We show that for multiorbital quantum impurity models the noncrossing approximation and one-crossing approximation versions of the self-consistent hybridization expansions violate the sum rules relating the coefficients of the high-frequency expansion of the self-energy and the product of the self-energy and Green's function to thermodynamic expectation values. Comparison of noncrossing/one-crossing results to numerically exact quantum Monte Carlo calculations shows that the consistency with sum rules provides a useful estimate of the reliability of the approximations. The sum rule violations are more pronounced, and therefore the quality of the noncrossing/one-crossing approximation is poorer, in situations with multiple orbitals and away from particle-hole symmetry but becomes less severe as the correlation strength increases. The one-crossing approximation is markedly superior to the noncrossing approximation.

Magnetic molecules adsorbed on a superconductor give rise to a local competition of Cooper pair and Kondo singlet formation inducing subgap bound states. For manganese-phthalocyanine molecules on a Pb(111) substrate, scanning tunneling spectroscopy resolves pairs of subgap bound states and two Kondo screening channels. We show in a combined approach of scaling and numerical renormalization group calculations that the intriguing relation between Kondo screening and superconducting pairing is solely determined by the hybridization strength with the substrate. We demonstrate that an effective one-channel Anderson impurity model with a sizable particle-hole asymmetry captures universal and nonuniversal observations in the system quantitatively. The model parameters and disentanglement of the two screening channels are elucidated by scaling arguments.

This paper studies the quantum properties of lattice vacancies in topological band insulators and topological superconductors (TSCs) on a honeycomb lattice with particle-hole symmetry. Each vacancy exhibits one “gauge-invariant” zero mode for the spinless Haldane model and two “gauge-invariant” zero modes for the Kane-Mele model. In addition, there exist Majorana zero modes around the vacancies in TSCs on honeycomb lattices with particle-hole symmetry. These zero-energy modes are protected by the particle-hole symmetry of these topological states.

The magnetic properties and the origins of ferroelectric polarization in recently discovered multiferroics material CaMn${}_7$O${}_{12}$ have been investigated on the basis of model analysis and first-principles calculations. We find the noncollinear-type exchange-striction mechanism and the p-d hybridization with spin-orbit coupling coexist in the origins of polarization. The induced giant ferroelectricity can be mainly attributed to the former, related to two kinds of charge-order chains combined with the same spiral spin chirality as Mn ions. Our results confirm that the polarization induced by the two mechanisms follows the $S_i·S_j$ and $S_i\times S_j$ laws, respectively.

We analyze the phase diagram for a system of weakly coupled electrons having an electron- and a hole-band with imperfect nesting. Namely, both bands have spherical Fermi surfaces, but their radii are slightly different, with a mismatch proportional to the doping. Such a model is used to describe the antiferromagnetism of chromium and its alloys, pnictides, AA-stacked graphene bilayers, as well as other systems. Here we show that the uniform ground state of this model is unstable with respect to electronic phase separation in a wide range of model parameters. Physically, this instability occurs due to the competition between commensurate and incommensurate antiferromagnetic states and could be of importance for other models with imperfect nesting.

Using atomically resolved electron energy-loss spectroscopy, the atomic-plane-by-atomic-plane, unit-cell-by-unit-cell stoichiometry, and charge characteristics of the oxide interface (Nd${}_{0.35}$Sr${}_{0.65}$)MnO${}_3$/SrTiO${}_3$, with a primitive polar discontinuity of (Nd${}_{0.35}$Sr${}_{0.65}$O)${}^{0.35+}$-(TiO${}_2$)${}^0$, were thoroughly investigated. (Nd${}_{0.35}$Sr${}_{0.65}$)MnO${}_3$ is a strongly correlated insulator and the interface was characterized to be insulating. The cell-specific stoichiometric evaluation unveiled an extensive interdiffusion across the interface. The plane-specific charge characterization revealed that the interdiffusion grades the primitive polar discontinuity. Despite the graded polar discontinuity, a charge transfer inversely into (Nd${}_{0.35}$Sr${}_{0.65}$)MnO${}_3$ was firmly resolved with a length scale of ∼2 nm and a charge density on the order of ∼10${}^{13}$/cm${}^2$ and is effectively mediated by an asymmetric Ti interdiffusion. The intricate electronic correlations of the interfacial (Nd${}_{0.35}$Sr${}_{0.65}$)MnO${}_3$ unit cells and the interdiffusion-induced chemical disorder tend to render the charges localized, resulting in a localized two-dimensional electron density and thus the insulating interface, in distinct contrast to the conventional understanding of a vanishing charge density for an insulating interface and the metallic two-dimensional electron gas found at other classical polar-discontinuous interface systems. A potential strain manipulation on the electronic localization of the electron density was also proposed.