Using a tight-binding approach we study theoretically the nature of surface states in Pb0.4Sn0.6Te -the newly discovered topological-crystalline-insulator. Apart from the studied before (001) surface states, two other surface families, {011} and {111}, in which the mirror symmetry of the crystal's rock-salt structure plays the same role in topological protection, are considered. Our calculations show that while in (111) surface states of (Pb,Sn)Te four single topologically protected Dirac-cones should appear, for the (110) surface states the protection is lifted for two L points. In this case, instead of the Dirac points energy gaps occur in the surface states, due to the interaction between the two L valleys. In all studied cases a chiral spin texture is obtained.

We study the nature of (001) surface states in Pb0.73Sn0.27Se in the newly discovered topologicalcrystalline-insulator (TCI) phase as well as the corresponding topologically trivial state above the band-gap-inversion temperature. Our calculations predict not only metallic surface states with a nontrivial chiral spin structure for the TCI case, but also nonmetallic (gapped) surface states with nonzero spin polarization when the system is a normal insulator. For both phases, angle-and spinresolved photoelectron spectroscopy measurements provide conclusive evidence for the formation of these (001) surface states in Pb0.73Sn0.27Se, as well as for their chiral spin structure.

We present angle resolved photoemission spectroscopy measurements of the surface states on in-situ grown (111) oriented films of Pb1−xSnxSe, a three dimensional topological crystalline insulator. We observe surface states with Dirac-like dispersion atΓ andM in the surface Brillouin zone, supporting recent theoretical predictions for this family of materials. We study the parallel dispersion isotropy and Dirac-point binding energy of the surface states, and perform tight-binding calculations to support our findings. The relative simplicity of the growth technique is encouraging, and suggests a clear path for future investigations into the role of strain, vicinality and alternative surface orientations in (Pb,Sn)Se compounds.

We envision that the quantum spin Hall effect should be observed in (111)-oriented thin films of SnSe and SnTe topological crystalline insulators. Using a tight-binding approach supported by firstprinciples calculations of the band structures, we demonstrate that in these films the energy gaps in the two-dimensional band spectrum depend in an oscillatory fashion on the layer thickness. These results as well as the calculated topological invariant indexes and edge state spin polarizations show that for films ∼20-40 monolayers thick a two-dimensional topological insulator phase appears. In this range of thicknesses in both SnSe and SnTe, (111)-oriented films edge states with Dirac cones with opposite spin polarization in their two branches are obtained. While in the SnTe layers a single Dirac cone appears at the projection of the Γ point of the two-dimensional Brillouin zone, in the SnSe (111)oriented layers three Dirac cones at M points projections are predicted.

Exciton condensation, a Bose-Einstein-like condensation of excitons, was recently reported in an electronic double layer (EDL) of graphene. We show that a universal quantum signature for exciton condensation can be used to both identity and quantify exciton condensation in molecular systems from direct calculations of the two-electron reduced density matrix. Computed large eigenvalues in the particle-hole reduced density matrices of pentacene and hexacene EDLs reveal the beginnings of condensation, suggesting the potential for exciton condensation in smaller scale molecular EDLs.