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.

Multiple-qcurrent states in a multicomponent superconducting channel.

It is well-established that multicomponent superconductors can host different nonstandard phenomena such as broken-time reversal symmetry (BTRS) states, exotic Fulde-Ferrell-Larkin-Ovchinnikov phases, the fractional Josephson effect as well as plenty of topological defects like phase solitons, domain walls and unusual vortex structures. We show that in the case of a two-component superconducting quasi-one-dimensional channel this catalogue can be extended by a novel inhomogeneous current state, which we have termed as a multiple-qstate, characterized by the coexistence of two different interpenetrating Cooper pair condensates with different total momenta. Within the Ginzburg-Landau formalism for a dirty two-band superconductor with sizable impurity scattering treated in the Born-approximation we reveal that under certain conditions, the occurrence of multiple-qstates can induce a cascade of transitions involving switching between them and the homogeneous BTRS (non-BTRS) states and vice versa leading this way to a complex interplay of homogeneous and inhomogeneous current states. We find that hallmarks of such a multiple-qstate within a thin wire or channel can be a saw-like dependence of the depairing current and the existence of two distinct stable branches on it (a bistable current state).

Pattern Formation by Electric-Field Quench in a Mott Crystal.

The control of the Mott phase is intertwined with the spatial reorganization of the electronic states. Out-of-equilibrium driving forces typically lead to electronic patterns that are absent at equilibrium, whose nature is however often elusive. Here, we unveil a nanoscale pattern formation in the Ca2RuO4 Mott insulator. We demonstrate how an applied electric field spatially reconstructs the insulating phase that, uniquely after switching off the electric field, exhibits nanoscale stripe domains. The stripe pattern has regions with inequivalent octahedral distortions that we directly observe through high-resolution scanning transmission electron microscopy. The nanotexture depends on the orientation of the electric field; it is nonvolatile and rewritable. We theoretically simulate the charge and orbital reconstruction induced by a quench dynamics of the applied electric field providing clear-cut mechanisms for the stripe phase formation. Our results open the path for the design of nonvolatile electronics based on voltage-controlled nanometric phases.

Designing spin and orbital sources of Berry curvature at oxide interfaces.

Quantum materials can display physical phenomena rooted in the geometry of electronic wavefunctions. The corresponding geometric tensor is characterized by an emergent field known as the Berry curvature (BC). Large BCs typically arise when electronic states with different spin, orbital or sublattice quantum numbers hybridize at finite crystal momentum. In all the materials known to date, the BC is triggered by the hybridization of a single type of quantum number. Here we report the discovery of the first material system having both spin- and orbital-sourced BC: LaAlO3/SrTiO3 interfaces grown along the [111] direction. We independently detect these two sources and probe the BC associated to the spin quantum number through the measurements of an anomalous planar Hall effect. The observation of a nonlinear Hall effect with time-reversal symmetry signals large orbital-mediated BC dipoles. The coexistence of different forms of BC enables the combination of spintronic and optoelectronic functionalities in a single material.

Colossal Orbital Edelstein Effect in Noncentrosymmetric Superconductors.

In superconductors that lack inversion symmetry, the flow of supercurrent can induce a nonvanishing magnetization, a phenomenon which is at the heart of nondissipative magnetoelectric effects, also known as Edelstein effects. For electrons carrying spin and orbital moments, a question of fundamental relevance deals with the orbital nature of magnetoelectric effects in conventional spin-singlet superconductors with Rashba coupling. Remarkably, we find that the supercurrent-induced orbital magnetization is more than 1 order of magnitude greater than that due to the spin, giving rise to a colossal magnetoelectric effect. The induced orbital magnetization is shown to be sign tunable, with the sign change occurring for the Fermi level lying in proximity of avoiding crossing points in the Brillouin zone. In the presence of superconducting phase inhomogeneities, a modulation of the Edelstein signal on the scale of the superconducting coherence length appears, leading to domains with opposite orbital moment orientations. These hallmarks are robust to real-space self-consistent treatment of the superconducting order parameter. The orbital-dominated magnetoelectric phenomena, hence, have clear-cut marks for detection both in the bulk and at the edge of the system and are expected to be a general feature of multiorbital superconductors with inversion symmetry breaking.

Gate Control of the Current-Flux Relation of a Josephson Quantum Interferometer Based on Proximitized Metallic Nanojuntions.

We demonstrate an Al superconducting quantum interference device in which the Josephson junctions are implemented through gate-controlled proximity Cu mesoscopic weak links. This specific kind of metallic weak links behaves analogously to genuine superconducting metals in terms of the response to electrostatic gating and provides a good performance in terms of current-modulation visibility. We show that through the application of a static gate voltage we can modify the interferometer current-flux relation in a fashion that seems compatible with the introduction of π-channels within the gated weak link. Our results suggest that the microscopic mechanism at the origin of the suppression of the switching current in the interferometer is apparently phase coherent, resulting in an overall damping of the superconducting phase rigidity. We finally tackle the performance of the interferometer in terms of responsivity to magnetic flux variations in the dissipative regime and discuss the practical relevance of gated proximity-based all-metallic SQUIDs for magnetometry at the nanoscale.

Fermi surface and kink structures in [Formula: see text] revealed by synchrotron-based ARPES.

The low-energy electronic structure, including the Fermi surface topology, of the itinerant metamagnet [Formula: see text] is investigated for the first time by synchrotron-based angle-resolved photoemission. Well-defined quasiparticle band dispersions with matrix element dependencies on photon energy or photon polarization are presented. Four bands crossing the Fermi-level, giving rise to four Fermi surface sheets are resolved; and their complete topography, effective mass as well as their electron and hole character are determined. These data reveal the presence of kink structures in the near-Fermi-level band dispersion, with energies ranging from 30 to 69 meV. Together with previously reported Raman spectroscopy and lattice dynamic calculation studies, the data suggest that these kinks originate from strong electron-phonon coupling present in [Formula: see text]. Considering that the kink structures of [Formula: see text] are similar to those of the other three members of the Ruddlesden Popper structured ruthenates, the possible universality of strong coupling of electrons to oxygen-related phonons in [Formula: see text] compounds is proposed.

Synthetic Weyl Points and Chiral Anomaly in Majorana Devices with Nonstandard Andreev-Bound-State Spectra.

We demonstrate how to design various nonstandard types of Andreev-bound-state (ABS) dispersions, via a composite construction relying on Majorana bound states (MBSs). Here, the MBSs appear at the interface of a Josephson junction consisting of two topological superconductors (TSCs). Each TSC harbors multiple MBSs per edge by virtue of a chiral or unitary symmetry. We find that, while the ABS dispersions are 2π periodic, they still contain multiple crossings which are protected by the conservation of fermion parity. A single junction with four interface MBSs and all MBS couplings fully controllable, or networks of such coupled junctions with partial coupling tunability, open the door for topological band structures with Weyl points or nodes in synthetic dimensions, which in turn allow for fermion-parity (FP) pumping with a cycle set by the ABS-dispersion details. In fact, in the case of nodes, the FP pumping is a manifestation of chiral anomaly in 2D synthetic spacetime. The possible experimental demonstration of ABS engineering in these devices further promises to unveil new paths for the detection of MBSs and higher-dimensional chiral anomaly.

Independent Geometrical Control of Spin and Charge Resistances in Curved Spintronics.

Spintronic devices operating with pure spin currents represent a new paradigm in nanoelectronics, with a higher energy efficiency and lower dissipation as compared to charge currents. This technology, however, will be viable only if the amount of spin current diffusing in a nanochannel can be tuned on demand while guaranteeing electrical compatibility with other device elements, to which it should be integrated in high-density three-dimensional architectures. Here, we address these two crucial milestones and demonstrate that pure spin currents can effectively propagate in metallic nanochannels with a three-dimensional curved geometry. Remarkably, the geometric design of the nanochannels can be used to reach an independent tuning of spin transport and charge transport characteristics. These results laid the foundation for the design of efficient pure spin current-based electronics, which can be integrated in complex three-dimensional architectures.

Edge States and Topological Insulating Phases Generated by Curving a Nanowire with Rashba Spin-Orbit Coupling.

We prove that curvature effects in low-dimensional nanomaterials can promote the generation of topological states of matter by considering the paradigmatic example of quantum wires with Rashba spin-orbit coupling, which are bent in a nanoscale periodic serpentine structure. The effect of the periodic curvature generally results in the appearance of insulating phases with a corresponding novel butterfly spectrum characterized by the formation of finite measure complex regions of forbidden energies. When the Fermi energy lies in the gaps, the system displays localized end states protected by topology. We further show that for certain superstructure periods the system possesses topologically nontrivial insulating phases at half filling. Our results suggest that the local curvature and the topology of the electronic states are inextricably intertwined in geometrically deformed nanomaterials.

Spin-orbital coupling in a triplet superconductor-ferromagnet junction.

We study the interplay of spin and orbital degrees of freedom in a triplet superconductor-ferromagnet junction. Using a self-consistent spatially dependent mean-field theory, we show that increasing the angle between the ferromagnetic moment and the triplet vector order parameter enhances or suppresses the p-wave gap close to the interface, according to whether the gap antinodes are parallel or perpendicular to the boundary, respectively. The associated change in condensation energy establishes an orbitally dependent preferred orientation for the magnetization. When both gap components are present, as in a chiral superconductor, first-order transitions between different moment orientations are observed as a function of the exchange field strength.

Magnetic intragap states and mixed parity pairing at the edge of spin-triplet superconductors.

We show that a spontaneous magnetic moment may appear at the edge of a spin-triplet superconductor if the system allows for pairing in a subdominant channel. To unveil the microscopic mechanism behind such an effect, we combine numerical solution of the Bogoliubov-de Gennes equations for a tight-binding model with nearest-neighbor attraction, and the symmetry based Ginzburg-Landau approach. We find that a potential barrier modulating the electronic density near the edge of the system leads to a nonunitary superconducting state close to the boundary where spin-singlet pairing coexists with the dominant triplet superconducting order. We demonstrate that the spin polarization at the edge appears due to the inhomogeneity of the nonunitary state and originates in the lifting of the spin degeneracy of the Andreev bound states.

Neutron diffraction study of triple-layered Sr4Ru3O10.

The magnetic properties of the triple-layered Sr(4)Ru(3)O(10) have been investigated by means of neutron scattering diffraction. At zero field we find that the magnetic moments are ferromagnetically coupled and oriented along the c-axis with no signatures of either long-range antiferromagnetic order or ferromagnetic components in the ab-plane. The field dependence of the reflection intensity points to a metamagnetic response involving only the planar magnetic moments. The structural refinement indicates a distinct rearrangement of the unit cell as a function of both temperature and in-plane applied field. We show that at the temperature T* ~/= 50 K, below which the metamagnetic behavior is observed, the c-axis lattice parameter exhibits a rapid increase while the in-plane amplitude saturates. A similar upturn of the in-plane lattice parameter after the quench of the c-axis amplitude occurs above a critical magnetic field.

Angle-resolved photoemission spectroscopy at ultra-low temperatures.

The physical properties of a material are defined by its electronic structure. Electrons in solids are characterized by energy (ω) and momentum (k) and the probability to find them in a particular state with given ω and k is described by the spectral function A(k, ω). This function can be directly measured in an experiment based on the well-known photoelectric effect, for the explanation of which Albert Einstein received the Nobel Prize back in 1921. In the photoelectric effect the light shone on a surface ejects electrons from the material. According to Einstein, energy conservation allows one to determine the energy of an electron inside the sample, provided the energy of the light photon and kinetic energy of the outgoing photoelectron are known. Momentum conservation makes it also possible to estimate k relating it to the momentum of the photoelectron by measuring the angle at which the photoelectron left the surface. The modern version of this technique is called Angle-Resolved Photoemission Spectroscopy (ARPES) and exploits both conservation laws in order to determine the electronic structure, i.e. energy and momentum of electrons inside the solid. In order to resolve the details crucial for understanding the topical problems of condensed matter physics, three quantities need to be minimized: uncertainty* in photon energy, uncertainty in kinetic energy of photoelectrons and temperature of the sample. In our approach we combine three recent achievements in the field of synchrotron radiation, surface science and cryogenics. We use synchrotron radiation with tunable photon energy contributing an uncertainty of the order of 1 meV, an electron energy analyzer which detects the kinetic energies with a precision of the order of 1 meV and a He(3) cryostat which allows us to keep the temperature of the sample below 1 K. We discuss the exemplary results obtained on single crystals of Sr2RuO4 and some other materials. The electronic structure of this material can be determined with an unprecedented clarity.

Is the nature of itinerant ferromagnetism playing a role in the competition between spin polarization and singlet pair correlations?

We consider the competition between spin singlet pairing and itinerant ferromagnetism whose magnetization is yielded by a relative shift of the bands with opposite spin polarization or by asymmetric spin-dependent bandwidths. Within the framework of the exact solution of an extended version of the reduced BCS model, the structure of the coexisting state is shown to have general features that are not related to the character of the ferromagnetism. The role of different types of ferromagnet is then investigated for the proximity effect in a system made of a bilayer junction with a spin singlet superconductor interfaced with a ferromagnet in the clean limit. We show that the qualitative behaviour of the proximity effect does not depend on the nature of the ferromagnetism. Differences emerge at the borderline with the half-metallic regime. For the spin-dependent bandwidth type of ferromagnetism the pairing amplitude exhibits an oscillating behaviour until the density of the minority spin carrier becomes almost zero. The crossover from an oscillating to an exponentially damped profile occurs away from the half-metallic limit when a spin exchange type ferromagnet is considered.

Exact solution for a trapped Fermi gas with population imbalance and BCS pairing.

The problem of a two-component Fermi gas in a harmonic trap, with an imbalanced population and a pairing interaction of zero total momentum, is mapped onto the exactly solvable reduced BCS model. For a one-dimensional trap, the complete ground state diagram is determined with various topological features in ground state energy spectra. In addition to the conventional two-shell density profile of a paired core and polarized outer wings, a three-shell structure as well as a double-peak superfluid distribution are unveiled.

Coexistence of ferromagnetism and singlet superconductivity via kinetic exchange.

We propose a novel mechanism for the coexistence of metallic ferromagnetism and singlet superconductivity assuming that the magnetic instability is due to kinetic exchange. Within this scenario, the unpaired electrons which contribute to the magnetization have a positive feedback on the gain of the kinetic energy in the coexisting phase by undressing the effective mass of the carriers involved in the pairing. The evolution of the magnetization and pairing amplitude and the phase diagram are first analyzed for a generic kinetic exchange model and then are determined within a specific case with spin dependent bond-charge occupation.