Signatures of a surface spin-orbital chiral metal.

The relation between crystal symmetries, electron correlations and electronic structure steers the formation of a large array of unconventional phases of matter, including magneto-electric loop currents and chiral magnetism1-6. The detection of such hidden orders is an important goal in condensed-matter physics. However, until now, non-standard forms of magnetism with chiral electronic ordering have been difficult to detect experimentally7. Here we develop a theory for symmetry-broken chiral ground states and propose a methodology based on circularly polarized, spin-selective, angular-resolved photoelectron spectroscopy to study them. We use the archetypal quantum material Sr2RuO4 and reveal spectroscopic signatures that, despite being subtle, can be reconciled with the formation of spin-orbital chiral currents at the surface of the material8-10. As we shed light on these chiral regimes, our findings pave the way for a deeper understanding of ordering phenomena and unconventional magnetism.

Topological order in an entangled SU(2) ⊗ XY spin-orbital ring.

We present rigorous topological order which emerges in a one-dimensional spin-orbital model due to the ring topology. Although this model with SU(2) spin and XY orbital interactions is known to exactly separate spins from orbitals by means of a unitary transformation on the open chain, we find that they are not quite independent when the chain is closed, and the spins form two half-rings carrying opposite quasimomenta. We show that on changing the topology from an open to a periodic chain, the degeneracy of the ground state is partially lifted while the low-energy excitations have a quadratic dispersion as a function of the total quasimomentum. This novel type of topological order which emerges from changing the topology from an open to a periodic chain is reminiscent of the infinite-U Hubbard chain.

Pentagonal nanowires from topological crystalline insulators: a platform for intrinsic core-shell nanowires and higher-order topology.

We report on the experimental realization of Pb1-xSnx Te pentagonal nanowires (NWs) with [110] orientation using molecular beam epitaxy techniques. Using first-principles calculations, we investigate the structural stability of NWs of SnTe and PbTe in three different structural phases: cubic, pentagonal with [001] orientation and pentagonal with [110] orientation. Within a semiclassical approach, we show that the interplay between ionic and covalent bonds favors the formation of pentagonal NWs. Additionally, we find that this pentagonal structure is more likely to occur in tellurides than in selenides. The disclination and twin boundary cause the electronic states originating from the NW core region to generate a conducting band connecting the valence and conduction bands, creating a symmetry-enforced metallic phase. The metallic core band has opposite slopes in the cases of Sn and Te twin boundaries, while the bands from the shell are insulating. We finally study the electronic and topological properties of pentagonal NWs unveiling their potential as a new platform for higher-order topology and fractional charge. These pentagonal NWs represent a unique case of intrinsic core-shell one-dimensional nanostructures with distinct structural, electronic and topological properties between the core and the shell region.

Noncollinear magnetic order stabilized by entangled spin-orbital fluctuations.

Quantum phase transitions in the two-dimensional Kugel-Khomskii model on a square lattice are studied using the plaquette mean field theory and the entanglement renormalization Ansatz. When 3z(2)-r(2) orbitals are favored by the crystal field and Hund's exchange is finite, both methods give a noncollinear exotic magnetic order that consists of four sublattices with mutually orthogonal nearest-neighbor and antiferromagnetic second-neighbor spins. We derive an effective frustrated spin model with second- and third-neighbor spin interactions which stabilize this phase and follow from spin-orbital quantum fluctuations involving spin singlets entangled with orbital excitations.

Spin, orbital and topological order in models of strongly correlated electrons.

Different types of order are discussed in the context of strongly correlated transition metal oxides, involving pure compounds and [Formula: see text] and [Formula: see text] hybrids. Apart from standard, long-range spin and orbital orders we observe also exotic noncollinear spin patterns. Such patters can arise in presence of atomic spin-orbit coupling, which is a typical case, or due to spin-orbital entanglement at the bonds in its absence, being much less trivial. Within a special interacting one-dimensional spin-orbital model it is also possible to find a rigorous topological magnetic order in a gapless phase that goes beyond any classification tables of topological states of matter. This is an exotic example of a strongly correlated topological state. Finally, in the less correlated limit of 4d 4 oxides, when orbital selective Mott localization can occur it is possible to stabilize by a 3d 3 doping one-dimensional zigzag antiferromagnetic phases. Such phases have exhibit nonsymmorphic spatial symmetries that can lead to various topological phenomena, like single and multiple Dirac points that can turn into nodal rings or multiple topological charges protecting single Dirac points. Finally, by creating a one-dimensional [Formula: see text] hybrid system that involves orbital pairing terms, it is possible to obtain an insulating spin-orbital model where the orbital part after fermionization maps to a non-uniform Kitaev model. Such model is proved to have topological phases in a wide parameter range even in the case of completely disordered 3d 2 impurities. What more, it exhibits hidden Lorentz-like symmetries of the topological phase, that live in the parameters space of the model.