Consider a onedimensional (1D) potential well turned into a closed loop by connecting the ends: the wave function of an electron that propagates along the loop without loss of phase coherence has to be continuous at the joined ends. Because of the ring topology and the resulting energy level structure, quantum rings offer the possibility to explore fundamental quantum phenomena like the AharonovBohm effect or persistent currents. They can also be employed for implementing logic gate function.
Quantum rings have been realized in semiconductor materials, for example, by growing quantum dots and transforming them to ringlike structures or by depleting a twodimensional electron gas using the electric field effect or local oxidation techniques. In our work, we use atom manipulation by cryogenic scanning tunneling microscopy (STM) to assemble individual atomic rings on a semiconductor surface. This approach is unique in the sense that it provides perfection in structure and the capability to modify it at the atomic level.
Our scanning tunneling spectroscopy data reveal the generic energy level structure of a quantum ring including its single ground state and doublydegenerate excited states. Owing to the symmetry of the supporting surface the rings are hexagonal in shape. This leads to a periodic potential modulation and thereby a perturbation of the level structure that can be understood in analogy to band gap formation in a 1D periodic potential. The modulation can be modified by further adding or removing single atoms with the STM tip. Our results demonstrate the possibility of designing electron dynamics in a tunable periodic potential, holding promise for the construction of “quantum materials” in terms of twodimensional artificial lattices with broadly variable and precisely controlled properties.
1  Author  V. D. Pham , K. Kanisawa , S. Fölsch 
Title 
Quantum rings engineered by atom manipulation 

Source  Phys. Rev. Lett. , 123 , 066801 ( 2019 )  
DOI : 10.1103/PhysRevLett.123.066801  Download: PDF  Cite : Bibtex RIS 