By numerically solving the effective continuous model of a topological insulator with parameters corresponding to the band structure of the topological insulator Bi 2 Se 3 , we analyze possible appearance of one-dimensional states in various geometries. Massless Dirac fermions are found at the edges of thin ribbons with surface oriented not only along the van der Waals gap but also in the perpendicular direction. Thick rods and slabs with surface steps host massive modes localized on surface faces. We argue that the modes are massive and their origin is due to the difference in the Dirac point energy of adjacent faces. The absence of one-dimensional states near edges of a large rectangular rod and surface steps is demonstrated.

Electronic transport properties of the Si(111)-( √ 3 × √ 3)-Sn surface formed on low doped Si substrates are studied using two-probe conductivity measurements and tunnelling spectroscopy. We demonstrate that the ground state corresponds to Mott-Hubbard insulator with a band gap 2∆ = 70 meV, which vanishes quickly upon temperature increase. The temperature dependence of the surface conductivity above T > 50 K corresponds to the Efros-Shklovskii hopping conduction law. The energy gap at the Fermi level observed in tunnelling spectroscopy measurements at higher temperatures could be described in terms of dynamic Coulomb blockade approximation. The obtained localization length of electron is ξ = 7Å.

The results of ultra-high vacuum low-temperature scanning-tunneling microscopy (STM) and spectroscopy (STS) of atomically clean (111) surface of the topological insulator Bi2Se3 are presented. We observed several types of new subsurface defects whose location and charge correspond to p-type conduction of grown crystals. The sign of the thermoelectric effect also indicates p-type conduction. STM and STS measurements demonstrate that the chemical potential is always located inside the bulk band gap. We also observed changes in the local density of states in the vicinity of the quintuple layer steps at the studied surface. This changes correspond either to the shift of the Dirac cone position or to the shift of the chemical potential near the step edge.

The results of a detailed study of the topological insulator Bi2Se3 surface state energy structure in the vicinity of surface steps using scanning tunneling microscopy and spectroscopy methods are presented. An increase in the chemical potential level µ near the step edge is observed. The value of the increase δµ ∼ 0.1 eV is found to correlate with the step height. The effect is caused by redistribution of electron wave functions between the outer and inner edges of surface steps, as known for normal metals. The smaller value of the chemical potential shift and its larger characteristic length of ∼ 10 nm reflect specifics of the helical surface states. This increase is accompanied by enlargement of the normalized differential tunneling conductance in the helical surface states energy region and thereby produces the illusion of the appearance of edge states. We show that the enlargement is reproduced in the framework of the tunneling model taking into account the tunneling gap transparency change when the chemical potential moves away from the Dirac point. arXiv:1609.08911v5 [cond-mat.mtrl-sci]

Topologically protected surface states of three‐dimensional topological insulators provide a model framework for studying massless Dirac electrons in two dimensions. Usually a step on the surface of a topological insulator is treated as a scatterer for the Dirac electrons, and the study of its effect is focused on the interference of the incident and scattered electrons. Then a major role plays the warping of the Dirac cone far from the Dirac point. The existence of another significant effect near the Dirac point brought about by the presence of steps is experimentally demonstrated here. Namely the band bending in the vicinity of steps leads to formation of 1D bound states in the corresponding potential wells. The observation of bound states in such potential wells in our scanning tunneling microscopy and spectroscopy investigation of the surface of the topological insulator Bi2Se3 is reported. Numerical simulations support our conclusion and provide a recipe for the identification of such states.