Spin-Orbit-Coupled Correlated Metal Phase in Kondo Lattices: An Implementation with Alkaline-Earth Atoms.

We show that an interplay between quantum effects, strong on-site ferromagnetic exchange interaction, and antiferromagnetic correlations in Kondo lattices can give rise to an exotic spin-orbit coupled metallic state in regimes where classical treatments predict a trivial insulating behavior. This phenomenon can be simulated with ultracold alkaline-earth fermionic atoms subject to a laser-induced magnetic field by observing dynamics of spin-charge excitations in quench experiments.

Heavy-Fermion Valence-Bond Liquids in Ultracold Atoms: Cooperation of the Kondo Effect and Geometric Frustration.

We analyze a microscopic mechanism behind the coexistence of a heavy Fermi liquid and geometric frustration in Kondo lattices. We consider a geometrically frustrated periodic Anderson model and demonstrate how orbital fluctuations lead to a Kondo-screened phase in the limit of extreme strong frustration when only local singlet states participate in the low-energy physics. We also propose a setup to realize and study this exotic state with SU(3)-symmetric alkaline-earth cold atoms.

Orbital order and Hund's rule frustration in Kondo lattices.

We analyze a microscopic origin of the Kondo effect-assisted orbital order in heavy-fermion materials. By studying the periodic two-orbital Anderson model with two local electrons, we show that frustration of Hund's rule coupling due to the Kondo effect leads to an incommensurate spiral orbital and magnetic order, which exists only inside the Kondo screened (heavy-electron) phase. This spiral state can be observed in neutron and resonant x-ray scattering measurements in U- and Pr-based heavy-fermion compounds, and realized in cold atomic gases, e.

Heavy antiferromagnetic phases in Kondo lattices.

We propose a microscopic physical mechanism that stabilizes the coexistence of the Kondo effect and antiferromagnetism in heavy-fermion systems. We consider a two-dimensional quantum Kondo-Heisenberg lattice model and show that long-range electron hopping leads to a robust antiferromagnetic Kondo state. By using a modified slave-boson mean-field approach we analyze the stability of the heavy antiferromagnetic phase across a range of parameters, and discuss transitions between different phases.

Superconductivity in strongly repulsive fermions: the role of kinetic-energy frustration.

We discuss a physical mechanism of a non-BCS nature which can stabilize a superconducting state in a strongly repulsive electronic system. By considering the two-dimensional Hubbard model with spatially modulated electron hoppings, we demonstrate how kinetic-energy frustration can lead to robust d-wave superconductivity at arbitrarily large on-site repulsion. This phenomenon should be observable in experiments using fermionic atoms, e.