Local electronic nematicity in the two-dimensional one-band Hubbard model.

Nematicity is a well-known property of liquid crystals and has been recently discussed in the context of strongly interacting electrons. An electronic nematic phase has been seen in many experiments in certain strongly correlated materials, in particular, in the pseudogap phase generic to many hole-doped cuprate superconductors. Recent measurements in high Tc superconductors have shown that even if the lattice is perfectly rotationally symmetric, the ground state can still have strongly nematic local properties. Our study of the two-dimensional one-band Hubbard model provides strong support for the recent experimental results on local rotational C4 symmetry breaking. The variational cluster approach is used here to show the possibility of an electronic nematic state and the proximity of the underlying symmetry-breaking ground state within the Hubbard model. We identify this nematic phase in the overdoped region and show that the local nematicity decreases with increasing electron filling. Our results also indicate that strong Coulomb interaction may drive the nematic phase into a phase similar to the stripe structure. The calculated spin (magnetic) correlation function in momentum space shows the effects resulting from real-space nematicity.

Spin-charge separation and electron pairing instabilities in Hubbard nanoclusters.

Electron charge and spin pairing instabilities in various cluster geometries for attractive and repulsive electrons are studied exactly under variation of interaction strength, electron doping and temperature. The exact diagonalization, level crossing degeneracies, spin-charge separation and separate condensation of paired electron charge and opposite spins yield intriguing insights into the origin of magnetism, ferroelectricity and superconductivity seen in inhomogeneous bulk nanomaterials and various phenomena in cold fermionic atoms in optical lattices. Phase diagrams resemble a number of inhomogeneous, coherent and incoherent nanoscale phases found recently in high-T(c) cuprates, manganites and multiferroic nanomaterials probed by scanning tunneling microscopy. Separate condensation of electron charge and spin degrees at various crossover temperatures offers a new route for superconductivity, different from the BCS scenario. The calculated phase diagrams resemble a number of inhomogeneous paired phases, superconductivity, ferromagnetism and ferroelectricity found in Nb and Co nanoparticles. The phase separation and electron pairing, monitored by electron doping and magnetic field surprisingly resemble incoherent electron pairing in the family of doped high-T(c) cuprates, ruthenocuprates, iron pnictides and spontaneous ferroelectricity in multiferroic materials.