We investigate the rotation effect of the RuO$_6$ octahedron around the $c$ axis on the topological and transport properties near the surface of the spin-triplet superconductor Sr$_2$RuO$_4$. While the Fermi level of bulk Sr$_2$RuO$_4$ is near the Li
fshitz transition, the RuO$_6$ rotation realized near the surface leads to the change of the Fermi surface topology. The edge current resulting from the time-reversal symmetry breaking in the chiral $p$-wave phase with fully opened excitation gap is less affected around Lifshitz transition. The topological property and the edge state are sensitive to the rotation angle and the amplitude of the nearest neighbor interaction, and the superconducting gap is strongly reduced in the larger next nearest neighbor interaction region. Although the edge state in Sr$_2$RuO$_4$ is topologically protected, it is not robust to the disorder such as impurity or defect.
Modeling the spin-triplet superconductor Sr2RuO4 through a three-orbital tight-binding model we investigate topological properties and edge states assuming chiral p-wave pairing. In concordance with experiments the three Fermi surfaces consist of two
electron-like and one hole-like one corresponding to the alpha-, beta- and gamma-band on the level of a two-dimensional system. The quasi-particle spectra and other physical quantities of the superconducting phase are calculated by means of a self-consistent Bogoliubov-de Gennes approach for a ribbon shaped system. While a full quasiparticle excitation gap is realized in the bulk system, at the edges gapless states appear some of which have linear and others nearly flat dispersion around zero energy. This study shows the interplay between spin-orbit coupling induced spin currents, chiral edge currents and correlation driven surface magnetism. The topological nature of the chiral p-wave state manifests itself in the gamma-band characterized by an integer Chern number. As the gamma-band is close to a Lifshitz transition in Sr2RuO4, changing the sign of the Chern number, the topological nature may be rather fragile.
Motivated by Sr2RuO4 the magnetic properties of edge states in a two-band spin-triplet superconductor with electron- and hole-like Fermi surfaces are investigated assuming chiral p-wave pairing symmetry. The two bands correspond to the alpha-beta-ban
ds of Sr2RuO4 and are modeled within a tight-binding model including inter-orbital hybridization and spin-orbit coupling effects. Including superconductivity the quasiparticle spectrum is determined by means of a self-consistent Bogolyubov-de Gennes calculation. While a full quasiparticle excitation gap appears in the bulk, gapless states form at the edges which produce spontaneous spin and/or charge currents. The spin current is the result of the specific band structure while the charge current originates from the superconducting condensate. Together they induce a small spin polarization at the edge. Furthermore onsite Coulomb repulsion is included to show that the edge states are unstable against the formation of a Stoner-like spin polarization of the edge states. Through spin-orbit coupling the current- and the correlation-induced magnetism are coupled to the orientation of the chirality of the superconducting condensate. We speculate that this type of phenomenon could yield a compensation of the magnetic fields induced by currents and also explain the negative result in the recent experimental search for chiral edge currents.
The wavefunction of a massless fermion consists of two chiralities, left-handed and right-handed, which are eigenstates of the chiral operator. The theory of weak interactions of elementally particle physics is not symmetric about the two chiralities
, and such a symmetry breaking theory is referred to as a chiral gauge theory. The chiral gauge theory can be applied to the massless Dirac particles of graphene. In this paper we show within the framework of the chiral gauge theory for graphene that a topological soliton exists near the boundary of a graphene nanoribbon in the presence of a strain. This soliton is a zero-energy state connecting two chiralities and is an elementally excitation transporting a pseudospin. The soliton should be observable by means of a scanning tunneling microscopy experiment.
