We report on the spin properties of individual Mn atoms in strain-free quantum dots. The quantum dots are formed by width fluctuations in a thin CdTe/(Cd,Mg)Te quantum-well lattice matched on a CdTe substrate. This approach is complementary to the incorporation of Mn atoms in self-assembled CdTe/ZnTe quantum dots where the magnetic atom spin is split by the large biaxial strain in the quantum dot plane. We first demonstrate that the exciton-Mn exchange interaction is strong enough in these strain-free quantum dots to allow for the optical probing and addressing of any spin state of a Mn atom. We show that, at zero magnetic field, the absence of strain prevents the preparation of the Mn spin by optical pumping. As a result of this weak optical pumping efficiency, a large photoluminescence intensity is obtained under resonant optical excitation of the exciton-Mn complex. An efficient optical pumping of the Mn spin is restored under a weak magnetic field. The observed reduction of the resonant photoluminescence intensity under magnetic field is described by a model including the fine and hyperfine structure of the Mn atom. Finally, we show that the second-order correlation function of the resonant photoluminescence presents a large photon bunching at short delays which is a probe of the dynamics of the Mn spin.

We introduce and study three-dimensional quantum dimer models with positive resonance terms. We demonstrate that their ground state wave functions exhibit a nonlocal sign structure that can be exactly formulated in terms of loops, and as a direct consequence, monomer excitations obey Fermi statistics. The sign structure and Fermi statistics in these “signful” quantum dimer models can be naturally described by a parton construction, which becomes exact at the solvable point.

We prepare single-unit-cell FeSe films on insulating ${\text{SrTiO}}_3$ substrates by molecular beam epitaxy and investigate the evolution of their superconducting properties with annealing by in situ scanning tunneling microscopy and scanning tunneling spectroscopy and ex situ transport measurements. We find that through an annealing process, the superconductivity of 1-uc FeSe films on ${\text{SrTiO}}_3$ substrates develops with the formation of stoichiometric FeSe films and is further enhanced by charge transfer from ${\text{SrTiO}}_3$ substrates to FeSe films. Moreover, the superconductivity is independent of the bulk property of the ${\text{SrTiO}}_3$ substrate, regardless of whether it is insulating or conductive. Our results reveal that the high-temperature superconductivity of 1-uc FeSe films on ${\text{SrTiO}}_3$ substrates indeed occurs at the FeSe/${\text{SrTiO}}_3$ interface, where the electron doping at FeSe films plays an important role in this interfacial superconductivity.

We report a dc magnetization study of the critical phenomenon around the ferromagnetic transition temperature $T_{\mathrm{C}}$ in high-quality single crystals of uranium ferromagnetic superconductors ${\text{UGe}}_2$ and URhGe. The critical exponents, $\beta$ for the temperature dependence of the magnetization below $T_{\mathrm{C}}$, $\gamma$ for the magnetic susceptibility, and $\delta$ for the magnetic isothermal at $T_{\mathrm{C}}$, have been determined with a modified Arrott plot, a Kouvel-Fisher plot, and the scaling analysis. Magnetization in the ferromagnetic state has strong uniaxial magnetic anisotropy in the two compounds. However, the universality class of the critical phenomena do not belong to the 3D Ising system. Although the values of $\beta$ in ${\text{UGe}}_2$ and URhGe are close to those in the 3D magnets, the values of $\gamma$ are close to unity, that expected from the mean-field theory. Similar critical exponents have been reported previously for the 3D Ising ferromagnet UIr where superconductivity appears under high pressure. The critical behavior may be limited to a very narrow Ginzburg critical region of $\Delta T_{\mathrm{G}}\sim$ 1 mK because of the strong itinerant character of the $5f$ electrons in the ferromagnetic superconductor UCoGe where the mean-field behavior of the magnetization has been reported. The unconventional critical scaling of magnetization in ${\text{UGe}}_2$, URhGe, and UIr cannot be explained via previous approaches to critical phenomena. The ferromagnetic correlation between the $5f$ electrons differs from that in the 3D Ising system and this difference may be a key point for the understanding of the ferromagnetism where superconductivity emerges.

We report results of a muon spin rotation and relaxation ($\mu$SR) study of dilute ${\mathrm{Pd}}_{1-x}$${\mathrm{Ni}}_x$ alloys, with emphasis on Ni concentrations $x=0.0243$ and 0.025. These are close to the critical value $x_{\mathrm{cr}}$ for the onset of ferromagnetic long-range order (LRO), which is a candidate for a quantum critical point. Additional control data were taken for pure nonmagnetic Pd, and for an alloy where ferromagnetism is well established ($x=0.05$). The 2.43 and 2.5 at.% Ni alloys exhibit similar $\mu$SR properties. Both samples are fully magnetic, with average zero-temperature muon local fields $\langle B^{\mathrm{loc}}(T=0)\rangle =2.0$ and 3.8 mT and Curie temperatures $T_C=1.0$ and 2.03 K for 2.43 and 2.5 at.% Ni, respectively. The temperature dependence of $\langle B^{\mathrm{loc}}\rangle$ suggests ordering of Ni spin clusters rather than isolated spins. Just above $T_C$, the temperature where LRO vanishes, a two-phase region is found with coexisting separate volume fractions of quasistatic short-range order (SRO) and paramagnetism. The SRO fraction decreases to zero with increasing temperature a few kelvin above $T_C$. This mixture of SRO and paramagnetism is consistent with the notion of an inhomogeneous alloy with Ni clustering. The measured values of $T_C$ extrapolate to $x_{\mathrm{cr}}=0.0236\pm 0.0027$. The dynamic muon spin relaxation in the vicinity of $T_C$ differs for the two samples: a relaxation-rate maximum at $T_C$ is observed for $x=0.0243$, reminiscent of critical slowing down, whereas for $x=0.025$ no dynamic relaxation is observed within the $\mu$SR time window. The data suggest a mean-field-like transition in this alloy.

We present first-principles calculations for quasiparticle excitations in sodium and lithium, including the effects of charge and spin fluctuations. We employ the Overhauser-Kukkonen form for the electron self-energy arising from spin fluctuations and demonstrate that the coupling of electrons to spin fluctuations gives an important contribution to the quasiparticle lifetime but does not significantly reduce the occupied bandwidth. Including correlation effects beyond the random-phase approximation in the screening from charge fluctuations yields good agreement with experiment.

We report experimental evidence for the observation of the superconducting amplitude mode, the so-called ‘‘Higgs” mode, in the charge density wave superconductor $2H-{\text{NbSe}}_2$ using Raman scattering. By comparing $2H-{\text{NbSe}}_2$ and its isostructural partner 2H-NbS${}_2$ which shows superconductivity but lacks the charge density wave order, we demonstrate that the superconducting mode in $2H-{\text{NbSe}}_2$ owes its spectral weight to the presence of the coexisting charge density wave order. In addition, temperature dependent measurements in $2H-{\text{NbSe}}_2$ show a full spectral weight transfer from the charge density wave mode to the superconducting mode upon entering the superconducting phase. Both observations are fully consistent with a superconducting amplitude mode or Higgs mode.

The time-dependent numerical renormalization group (TDNRG) method [Anders et al., Phys. Rev. Lett. 95, 196801 (2005)] offers the prospect of investigating in a nonperturbative manner the time dependence of local observables of interacting quantum impurity models at all time scales following a quantum quench. Here, we present a generalization of this method to arbitrary finite temperature by making use of the full density matrix approach [Weichselbaum et al., Phys. Rev. Lett. 99, 076402 (2007)]. We show that all terms in the projected full density matrix ${\rho }^{i\to f}={\rho }^{++}+{\rho }^{--}+{\rho }^{+-}+{\rho }^{-+}$ appearing in the time evolution of a local observable may be evaluated in closed form at finite temperature, with ${\rho }^{+-}={\rho }^{-+}=0$. The expression for ${\rho }^{--}$ is shown to be finite at finite temperature, becoming negligible only in the limit of vanishing temperatures. We prove that this approach recovers the short-time limit for the expectation value of a local observable exactly at arbitrary temperatures. In contrast, the corresponding long-time limit is recovered exactly only for a continuous bath, i.e., when the logarithmic discretization parameter $\Lambda \to 1^{+}$. Since the numerical renormalization group approach breaks down in this limit, and calculations have to be carried out at $\Lambda >1$, the long-time behavior following an arbitrary quantum quench has a finite error, which poses an obstacle for the method, e.g., in its application to the scattering-states numerical renormalization group method for describing steady-state nonequilibrium transport through correlated impurities [Anders, Phys. Rev. Lett. 101, 066804 (2008)]. We suggest a way to overcome this problem by noting that the time dependence, in general, and the long-time limit, in particular, become increasingly more accurate on reducing the size of the quantum quench. This suggests an improved generalized TDNRG approach in which the system is time evolved between the initial and final states via a sequence of small quantum quenches within a finite time interval instead of by a single large and instantaneous quantum quench. The formalism for this is provided, thus generalizing the TDNRG method to multiple quantum quenches, periodic switching, and general pulses. This formalism, like our finite-temperature generalization of the single-quench case, rests on no other approximation than the NRG approximation. The results are illustrated numerically by application to the Anderson impurity model.

We present time-resolved measurements of spin-flip photon-assisted tunneling and spin-flip relaxation in a doubly occupied double quantum dot. The photon-assisted excitation rate as a function of magnetic field indicates that spin-orbit coupling is the dominant mechanism behind the spin-flip under the present conditions. We are able to extract the resulting effective “spin-flip tunneling” energy, which is found to be three orders of magnitude smaller than the regular spin-conserving tunneling energy. We also measure the relaxation and dephasing times of a qubit formed out of two two-electron states with different spin and charge configurations.

We present a theoretical analysis of the relaxation cascade of a photoexcited electron in graphene in the presence of screened electron-electron interaction in the random phase approximation. We calculate the relaxation rate of high energy electrons and the jump-size distribution of the random walk constituting the cascade which exhibits fat tails. We find that the statistics of the entire cascade are described by Lévy flights with constant drift instead of standard drift diffusion in energy space. The Lévy flight manifests nontrivial scaling relations of the fluctuations in the cascade time, which is related to the problem of the first passage time of Lévy processes. Furthermore we determine the transient differential transmission of graphene after an excitation by a laser pulse taking into account the fractional kinetics of the relaxation dynamics.

Accurate values for absolute surface energies are required to understand bulk and thin-film growth. Using first-principles calculations based on hybrid density functional theory we determine energies for bare and hydrogenated surfaces of wurtzite GaN in polar and nonpolar orientations. We find that the energies of the nonpolar $m$ and $a$ planes are similar and constant over the range of Ga, N, and H chemical potentials studied. In contrast, the energies of the polar planes are strongly condition dependent. We find that the $+c$ polar plane is systematically lower in energy than the $-c$ plane.

We study the effect of the Chern-Simons gauge fields on the possible transition from two decoupled composite fermion metals to the interlayer coherent composite fermion state proposed by Alicea et al. [Phys. Rev. Lett. 103, 256403 (2009)] in a symmetrically doped quantum Hall bilayer with total Landau level filling fraction ${\nu }_{\text{tot}}=1$. In this transition, interlayer Coulomb repulsion leads to excitonic condensation of composite fermions which are then free to tunnel coherently between layers. We find that this coherent tunneling is strongly suppressed by the layer-dependent Aharonov-Bohm phases experienced by composite fermions as they propagate through the fluctuating gauge fields in the system. This suppression is analyzed by treating these gauge fluctuations within the random-phase approximation and calculating their contribution to the energy cost for forming an exciton condensate of composite fermions. This energy cost leads to (1) an increase in the critical interlayer repulsion needed to drive the transition; and (2) a discontinuous jump in the energy gaps to out-of-phase excitations (i.e., excitations involving currents with opposite signs in the two layers) at the transition.

We report on an experimental observation of spin noise in a single semiconductor quantum well embedded into a microcavity. The great cavity-enhanced sensitivity to fluctuations of optical anisotropy has allowed us to measure the Kerr rotation and ellipticity noise spectra in the strong-coupling regime. The spin noise spectra clearly show two resonant features: a conventional magnetoresonant component shifting towards higher frequencies with a magnetic field and an unusual “nonmagnetic” component centered at zero frequency and getting suppressed with an increasing magnetic field. We attribute the first of them to the Larmor precession of free electron spins, whereas, the second one is presumably due to hyperfine electron-nuclei spin interactions.

Magnetoelectric (ME) materials are of fundamental interest and have been investigated for their broad potential for technological applications. The search for, and eventually the theoretical design of, materials with large ME couplings present challenging issues. First-principles methods have only recently been developed to calculate the full ME response tensor $\alpha$ including both electronic and ionic (i.e., lattice-mediated) contributions. The latter is proportional to both the Born dynamical electric charge $Z^{\mathrm{e}}$ and its analog, the dynamical magnetic charge $Z^{\mathrm{m}}$. Here we present a theoretical study of the magnetic charge $Z^{\mathrm{m}}$ and the mechanisms that could enhance it. Using first-principles density functional methods, we calculate the atomic $Z^{\mathrm{m}}$ tensors in ${\mathrm{Cr}}_2{\mathrm{O}}_3$, a prototypical magnetoelectric, and in KITPite, a fictitious material that has previously been reported to show a strong ME response arising from exchange striction effects. Our results confirm that in ${\mathrm{Cr}}_2{\mathrm{O}}_3$, the $Z^{\mathrm{m}}$ values and resulting ME responses arise only from spin-orbit coupling (SOC) and are therefore rather weak. In KITPite, by contrast, the exchange striction acting on the noncollinear spin structure induces large $Z^{\mathrm{m}}$ values that persist even when SOC is completely absent.

We formulate a theory of non-Abelian fractional quantum Hall states by considering an anisotropic system consisting of coupled, interacting one-dimensional wires. We show that Abelian bosonization provides a simple framework for characterizing the Moore-Read state, as well as the more general Read-Rezayi sequence. This coupled wire construction provides a solvable Hamiltonian formulated in terms of electronic degrees of freedom, and provides a direct route to characterizing the quasiparticles and edge states in terms of conformal field theory. This construction leads to a simple interpretation of the coset construction of conformal field theory, which is a powerful method for describing non-Abelian states. In the present context, the coset construction arises when the original chiral modes are fractionalized into coset sectors, and the different sectors acquire energy gaps due to coupling in “different directions.” The coupled wire construction can also can be used to describe anisotropic lattice systems, and provides a starting point for models of fractional and non-Abelian Chern insulators. This paper also includes an extended introduction to the coupled wire construction for Abelian quantum Hall states, which was introduced earlier.