Three-dimensional topological insulators (TIs) are characterized by their nontrivial surface states, in which electrons have their spin locked at a right angle to their momentum under the protection of time-reversal symmetry. The topologically ordered phase in TIs does not break any symmetry. The interplay between topological order and symmetry breaking, such as that observed in superconductivity, can lead to new quantum phenomena and devices. We fabricated a superconducting TI/superconductor heterostructure by growing dibismuth triselenide (Bi(2)Se(3)) thin films on superconductor niobium diselenide substrate. Using scanning tunneling microscopy and angle-resolved photoemission spectroscopy, we observed the superconducting gap at the Bi(2)Se(3) surface in the regime of Bi(2)Se(3) film thickness where topological surface states form. This observation lays the groundwork for experimentally realizing Majorana fermions in condensed matter physics.

Recent studies show that two low-energy van Hove singularities (VHSs) seen as two pronounced peaks in the density of states could be induced in a twisted graphene bilayer. Here, we report angle-dependent VHSs of a slightly twisted graphene bilayer studied by scanning tunneling microscopy and spectroscopy. We show that energy difference of the two VHSs follows ΔE(vhs)∼ℏν(F)ΔK between 1.0° and 3.0° [here ν(F)∼1.1 × 10(6) m/s is the Fermi velocity of monolayer graphene, and ΔK = 2Ksin(θ/2) is the shift between the corresponding Dirac points of the twisted graphene bilayer]. This result indicates that the rotation angle between graphene sheets does not result in a significant reduction of the Fermi velocity, which quite differs from that predicted by band structure calculations. However, around a twisted angle θ∼1.3°, the observed ΔE(vhs)∼0.11 eV is much smaller than the expected value ℏν(F)ΔK∼0.28 eV at 1.3°. The origin of the reduction of ΔE(vhs) at 1.3° is discussed.

By combining scanning tunneling microscopy and spectroscopy, angle-resolved photoemission spectroscopy, and density functional theory band calculations, we directly observe and resolve the one-dimensional edge states of single bilayer (BL) Bi(111) islands on clean Bi(2)Te(3) and Bi(111)-covered Bi(2)Te(3) substrates. The edge states are localized in the vicinity of step edges having an ∼2  nm wide spatial distribution in real space and reside in the energy gap of the Bi(111) BL. Our results demonstrate the existence of nontrivial topological edge states of single Bi(111) bilayer as a two-dimensional topological insulator.

This review paper focuses on interdigital electrodes-a geo