We explore a combined effect of hexagonal warping and of finite effective mass on both the tunneling density of electronic states (TDOS) and structure of Landau levels (LLs) of 3D topological insulators. We find the increasing warping to transform th
e square-root van Hove singularity into a logarithmic one. For moderate warping an additional logarithmic singularity and a jump in the TDOS appear. This phenomenon is experimentally verified by direct measurements of the local TDOS in Bi$_2$Te$_3$. By combining the perturbation theory and the WKB approximation we calculate the LLs in the presence of hexagonal warping. We predict that due to the degeneracy removal the evolution of LLs in the magnetic field is drastically modified.
Using scanning tunneling spectroscopy (STS), we address the problem of the superconductor-insulator phase transition (SIT) in homogeneously disordered ultrathin (2-15 nm) films of NbN. Samples thicker than 8 nm, for which the Ioffe-Regel parameter $k
_F l geq 5.6$, manifest a conventional superconductivity : A spatially homogeneous BCS-like gap, vanishing at the critical temperature, and a vortex lattice in magnetic field. Upon thickness reduction, however, while $k_F l$ lowers, the STS revealed striking deviations from the BCS scenario, among which a progressive decrease of the coherence peak height and spatial inhomogeneities. The thinnest film (2.16 nm), while not being exactly at the SIT ($T_C approx 0.4 T_{C-bulk}$), showed astonishingly vanishing coherence peaks and the absence of vortices. In the quasi-2D limit, such clear signatures of the loss of long-range phase coherence strongly suggest that, at the SIT the superconductivity is destroyed by phase fluctuations.
We report the first experimental evidence for a strong electromechanical coupling in the Mott insulator GaTa4Se8 allowing a highly reproducible nano-writing with a Scanning Tunneling Microscope (STM). The local electric field across the STM junction
is observed to have a threshold value above which the clean (100) surface of GaTa4Se8 becomes mechanically instable: At voltage biases V > 1.1V the surface suddenly inflates and comes in contact with the STM tip, resulting in nanometer size craters. The formed pattern can be indestructibly read by STM at lower voltage bias, thus allowing a 5 Tdots/inch2 dense writing/reading at room temperature. The discovery of the electromechanical coupling in GaTa4Se8 might give new clues in the understanding of the Electric Pulse Induced Resistive Switching recently observed in this stoechiometric Mott insulator.
