Scanning tunneling microscopy and spectroscopy have been used to investigate the femtosecond dynamics of Dirac fermions in the topological insulator Bi$_2$Se$_3$ ultrathin films. At two-dimensional limit, bulk electrons becomes quantized and the quantization can be controlled by film thickness at single quintuple layer level. By studying the spatial decay of standing waves (quasiparticle interference patterns) off steps, we measure directly the energy and film thickness dependence of phase relaxation length $l_{phi}$ and inelastic scattering lifetime $tau$ of topological surface-state electrons. We find that $tau$ exhibits a remarkable $(E-E_F)^{-2}$ energy dependence and increases with film thickness. We show that the features revealed are typical for electron-electron scattering between surface and bulk states.
Topological insulators represent a paradigm shift in surface physics. The most extensively studied Bi$_2$Se$_3$-type topological insulators exhibit layered structures, wherein neighboring layers are weakly bonded by van der Waals interactions. Using first principles density-functional theory calculations, we investigate the impact of the stacking sequence on the energetics and band structure properties of three polymorphs of Bi$_2$Se$_3$, Bi$_2$Te$_3$, and Sb$_2$Te$_3$. Considering their ultrathin films up to 6 nm as a function of its layer thickness, the overall dispersion of the band structure is found to be insensitive to the stacking sequence, while the band gap is highly sensitive, which may also affect the critical thickness for the onset of the topologically nontrivial phase. Our calculations are consistent with both experimental and theoretical results, where available. We further investigate tribological layer slippage, where we find a relatively low energy barrier between two of the considered structures. Both the stacking-dependent band gap and low slippage energy barriers, suggest that polymorphic stacking modification may offer an alternative route for controlling the properties of this new state of matter.
We use scanning tunneling microscopy to map the surface structure, nanoscale electronic inhomogeneity, and vitreous vortex phase in the hole-doped superconductor Sr$_{0.75}$K$_{0.25}$Fe$_2$As$_2$ with $T_c$=32 K. We find the low-$T$ cleaved surface is dominated by a half-Sr/K termination with $1times 2$ ordering and ubiquitous superconducting gap, while patches of gapless, unreconstructed As termination appear rarely. The superconducting gap varies by $sigma/bar{Delta}$=16% on a $sim$3 nm length scale, with average $2bar{Delta}/k_B T_c=3.6$ in the weak coupling limit. The vortex core size provides a measure of the superconducting coherence length $xi$=2.3 nm. We quantify the vortex lattice correlation length at 9 T in comparison to several iron-based superconductors. The comparison leads us to suggest the importance of dopant size mismatch as a cause of dopant clustering, electronic inhomogeneity, and strong vortex pinning.
