Coexistence of superconductivity and ferromagnetism in two dimensions

Ferromagnetism is usually considered to be incompatible with conventional superconductivity, as it destroys the singlet correlations responsible for the pairing interaction. Superconductivity and ferromagnetism are known to coexist in only a few bulk rare-earth materials. Here we report evidence for their coexistence in a two-dimensional system: the interface between two bulk insulators, LaAlO(3) (LAO) and SrTiO(3) (STO), a system that has been studied intensively recently. Magnetoresistance, Hall, and electric-field dependence measurements suggest that there are two distinct bands of charge carriers that contribute to the interface conductivity. The sensitivity of properties of the interface to an electric field makes this a fascinating system for the study of the interplay between superconductivity and magnetism.     

Supersymmetric skyrmions in four dimensions

Possible topological solitons (skyrmions) of four-dimensional supersymmetric nonlinear σ-models are investigated. The requirements of supersymmetry limit our study to the CP¹ model. A stable soliton seems possible, but in the absence of a demonstrated lower-bound for the mass, the stability of the soliton is unproved. The semi-classical spectrum of the CP¹ skyrmion, as well as its supersymmetric extension, is studied.     

Non-translation-invariant states in two dimensions

We construct a class of models with translation-invariant interaction for which in dimension two there already exist non-periodic Gibbs states at low temperatures.     

Topological charge from thermodynamics in two dimensions

It is shown that in the weak coupling limit the partition function of massless (QED)₂ in a finite volume is identical to that of a bose field if the boson topological charge is identified with the fermion number. Generalizations to theories with U(N) gauge symmetry, fractional fermion number, and the Schwinger model for any coupling are also discussed.     

Topological order and semions in a strongly correlated quantum spin Hall insulator

We provide a self-consistent mean-field framework to study the effect of strong interactions in a quantum spin Hall insulator on the honeycomb lattice. We identify an exotic phase for large spin-orbit coupling and intermediate Hubbard interaction. This phase is gapped and does not break any symmetry. Instead, we find a fourfold topological degeneracy of the ground state on the torus and fractionalized excitations with semionic mutual braiding statistics. Moreover, we argue that it has gapless edge modes protected by time-reversal symmetry but a trivial Z(2) topological invariant. Finally, we discuss the experimental signatures of this exotic phase. Our work highlights the important theme that interesting phases arise in the regime of strong spin-orbit coupling and interactions.     

Electrical manipulation and measurement of spin properties of quantum spin Hall edge states

We study the effects of a gate-controlled Rashba spin-orbit coupling to quantum spin Hall edge states in HgTe quantum wells. A uniform Rashba coupling can be employed in tuning the spin orientation of the edge states while preserving the time-reversal symmetry. We introduce a sample geometry where the Rashba coupling can be used in probing helicity by purely electrical means without requiring spin detection, application of magnetic materials or magnetic fields. In the considered setup a tilt of the spin orientation with respect to the normal of the sample leads to a reduction in the two-terminal conductance with current-voltage characteristics and temperature dependence typical of Luttinger liquid constrictions.     

Topological Hall effect in pyrochlore lattice with varying density of spin chirality

The three-site spin correlation, S(i)·(S(j)×S(k)) on the neighboring triangular sites i, j and k, termed scalar spin chirality, can endow the conduction electron with a quantum Berry phase and resultant transverse (Hall) transport. The paramagnetic barely metallic state was prepared in hole-doped Y2Mo2O7 with pyrochlore lattice using a high-pressure synthesis method, which is further endowed with the spin chirality by partially replacing Y site with Tb (content x). The local spin chirality formed by the adjacent three Tb Ising moments on the pyrochlore lattice can couple to the conduction electrons to give rise to the topological Hall effect whose magnitude increases in proportion to x3 or the density of the Tb-moment triangular clusters.     

Collective spin states in the electron gas in different dimensions and geometries

We study spin longitudinal and transverse linear response of the 3-dimensional electron gas, metal clusters and quantum dots. When the systems are spin unpolarized in the ground state, a low energy collective state emerges in finite size systems due to the discrete shell structure, whereas it is absent in the bulk due to the Landau damping. In the case of spin polarization of the ground state a collective state is present also in the bulk and a family of new collective states appears in finite size systems. Presented by E. Lipparini at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997.     

Enhanced photonic spin Hall effect with subwavelength topological edge states

Photonic structures offer unique opportunities for controlling light‐matter interaction, including the photonic spin Hall effect associated with the transverse spin‐dependent displacement of a light beam that propagates in specially designed optical media. However, due to small spin‐orbit coupling, the photonic spin Hall effect is usually weak at the nanoscale. Here we suggest theoretically and demonstrate experimentally, in both optics and microwave experiments, the photonic spin Hall effect enhanced by topologically protected edge states in subwavelength arrays of resonant dielectric particles. Based on direct near‐field measurements, we observe the selective excitation of the topological edge states controlled by the handedness of the incident light. Additionally, we reveal the main requirements to the symmetry of photonic structures to achieve the topology‐enhanced spin Hall effect, and also analyse the robustness of the photonic edge states against the long‐range coupling.

     

Vortex states in soft magnets in two and three dimensions

The magnetization curves of arrays of near-spherical soft ferromagnetic particles are compared with those of quasi-two-dimensional dots with similar radius prepared by a rapid e-beam lithographic technique. Curves for the three-dimensional particles are anhysteretic and fit a M(H)/M_s=tanh(cμ₀H) law, whereas the two-dimensional arrays show irreversible segments in the first and third quadrants where the planar vortex state transforms to a collinear state by discontinuous rotation of magnetization about an axis perpendicular to the vortex axis. The additional symmetry of the spherical particle allows this rotation to occur continuously, without energy barriers due to the demagnetizing field.     

Topological superconductivity in bilayer Rashba system

We theoretically study a possible topological superconductivity in the interacting two layers of Rashba systems, which can be fabricated by the heterostructures of semiconductors and oxides. The hybridization, which induces the gap in the single particle dispersion, and the electron-electron interaction between the two layers leads to the novel phase diagram of the superconductivity. It is found that the topological superconductivity without breaking time-reversal symmetry is realized when (i) the Fermi energy is within the hybridization gap, and (ii) the interlayer interaction is repulsive, both of which can be satisfied in realistic systems. Edge channels are studied in a tight-binding model numerically, and the several predictions on experiments are also given.     

Edge states for quantum Hall droplets in higher dimensions and a generalized WZW model

We consider quantum Hall droplets on complex projective spaces with a combination of Abelian and non-Abelian background magnetic fields. Carrying out an analysis similar to what was done for Abelian backgrounds, we show that the effective action for the edge excitations is given by a chiral, gauged Wess–Zumino–Witten (WZW) theory generalized to higher dimensions.     

Renormalization group approach to three-state spin models in two dimensions

The real space renormalization group approach is used to study spin one anisotropic models with dipolar and quadrupolar interactions on the triangular lattice. The method is tested for the three state Potts model and the Blume-Emery-Griffiths model leading to results which are basically in agreement with other treatments of these models. The phase diagram for a quadrupolar model (anisotropic Potts model) is obtained and the influence of an external magnetic field on the transition temperature to the quadrupolar phase is determined. The fixed point which controls a transition to the phase with Ising dipolar order andXY-type quadrupolar order is found.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich