Colloidal nanocrystals underwent a tremendous development with full control over dimensions and surface chemistry, resulting in vast opto-electronic applications. Can they also form a platform for quantum materials, in which electronic coherence is key? We use colloidal, two-dimensional Bi₂Se₃ crystals, uniform in thickness and with limited lateral dimensions, as a model system to study the evolution of a three-dimensional topological insulator to the technologically important case of two-dimensions and limited crystal domains.

Individual Bi₂Se₃ platelets with diameter in the 100-200 nm range and well-defined thickness (1-6 quintuple layers) with cryogenic scanning tunneling microscopy and spectroscopy. For 4-6 Bi₂Se₃ quintuple layers, we observe an edge state, 8 nm wide, around the entire crystal. The edge state is faint or absent for thinner (1-2 QLs) Bi₂Se₃ platelets. The edge states are resilient under a perpendicular magnetic field. Ab-initio calculations confirm that crystals with 3 QLs or more have a non-trivial band structure with a one-dimensional quantum channel at the edge. The quantum channel consists of 2 counter propagating states with momentum-spin locking, key for non-dissipative information transfer and quantum computing.

We've performed optical spectroscopy in the high energy region (1-3 eV). We coud classify the optical transitions as (1) transitions due to the surface (outer QLs) or (2) due to the inner QLs. By comparison with GW simulations, we identified all transitions in a (energy, momentum in x, momentum in y) two-dimensional Brillouin zone frame. Some transitions show electron and hole cooling in which the carriers separate in momentum space.

Colloidal Bi2Se3 platelets are not only a model system for a two-dimensional toplogical insulator, but also a layer semi-metal with exotic optical transitions. The processability and dimensional control of topological insulator colloidal nanocrystals opens a unique window to devices with a large density of addressable quantum states. 

REFERENCES

J. Moes et al., manuscript in preparation

Swart, I., Liljeroth, P. & Vanmaekelbergh, D. Scanning probe microscopy and spectroscopy of colloidal semiconductor nanocrystals and assembled structures. Chem. Rev. 116, 11181-11219 (2016).

Kane, C. L. & Mele, E. J. Z(2) topological order and the quantum spin Hall effect. Physical Review Letters 95 (2005).

Zhang, H. J. et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nature Physics 5, 438-442 (2009).

Yazyev, O. V. et al.   Spin Polarization and Transport of Surface States in the Topological Insulators Bi2Se3 and Bi2Te3 from First Principles. Physical Review Letters 105 (2010).

Zhang, Y. et al. Crossover of the three-dimensional topological insulator Bi2Se3 to the two-dimensional limit.  Nature Physics 6, 584-588 (2010).

Liu, C. X. et al. Oscillatory crossover from two-dimensional to three-dimensional topological insulators. Physical Review B 81 (2010).

Neupane, M. et al. Observation of quantum-tunnelling-modulated spin texture in ultrathin topological insulator Bi2Se3 films. Nature Communications 5 (2014).

Chiatti, O. et al. 2D layered transport properties from topological insulator Bi2Se3 single crystals and micro flakes. Sci Rep 6 (2016).