Spin-triplet excitonic states and electron-electron correlations on the Topological Insulator surface

Topological insulators are novel states of matter that host Dirac-dispersion on its surface. The spectrum also supports helical spin texture and unscreened Coulomb potential as a result of the 2D geometry. We investigate the electron-electron correlations on the surface of a topological Insulators that produce a gap in the spectrum and discuss the enhancement of spin-triplet excitonic states as a result of this spin texture. Using Green’s function technique and numerical diagonalization of the equation we find the possible order parameters that describe the systems that retain their topological structure. We discuss realistic mechanisms that enhance this state taking into account spin and charge fluctuations.