The hidden order phase in URu$_2$Si$_2$: Remarkable nesting and spin-orbital hybridization

Aspects of Fermi surface (FS) nesting properties of URu$_2$Si$_2$ are analyzed with particular focus on their implication for the mysterious hidden order phase which occurs at 17.5~K. We show that there exist two Fermi surfaces that exhibit unusually strong nesting at the antiferromagnetic wavevector, $\mathbf{Q}_0$=(0,\,0,\,1). The corresponding energy dispersions fulfill the relation $\epsilon_{1}(\mathbf{k})$=$- \epsilon_{2} (\mathbf{k}\pm \mathbf{Q}_0)$ at eight FS hotspot lines on the surfaces. Notably, the spin-orbital characters of the involved $5f$ states are {\it different}: $j_z$=$\pm$5/2 {\it vs.} $\pm$3/2, and hence the occurring degenerate Dirac crossings are symmetry protected in the nonmagnetic normal state. Pairing of electrons in these two FSs can commence through interaction with a quasiparticle with wavevector $\mathbf{Q}_0$ and exchange of longitudinal angular momentum $\Delta j_z$. Dynamical symmetry breaking through an Ising-like spin-orbital excitation mode at $\mathbf{Q}_0$ with $\Delta j_z$=$\pm$1 induces a hybridization of the two states, causing substantial FS gapping. Concomitant spin and orbital currents in the uranium planes can give rise to a rotational symmetry breaking. The existence of such specifically nested FSs in URu$_2$Si$_2$ is confirmed in recent experiments.\\[4pt] This work has been performed with S. Elgazzar, J. Rusz, Q. Feng, T. Durakiewicz and J.A. Mydosh.