Confining electrons to an atomic-scale roundabout

Periodic boundary conditions represent a standard mathematical tool in condensed matter physics to calculate the properties of crystalline solids. But they are also a defining aspect of real objects in the quantum world, so-called quantum rings.

(a) STM topography image of a hexagonal ring structure consisting of 36 indium adatoms on an InAs(111)A surface; 6 auxiliary adatoms were added to the corners to enhance the electron confinement in those locations. (b) Spatial conductance maps revealing the probability density of two confined states below the Fermi level of the sample. The state at lower energy (left) is centered at the corners (artificial atoms) and has nodes in between (fully antibonding s orbital character, σS*) while the state at higher energy (right) has nodes at the corners and lobes in between (fully bonding p orbital character, σp), equivalent to the wave function symmetry of the band-edge states associated with the energy band gap emerging for electrons in a 1D periodic potential.

Consider a one-dimensional (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 Aharonov-Bohm 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 ring-like structures or by depleting a two-dimensional 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 doubly-degenerate 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 two-dimensional artificial lattices with broadly variable and precisely controlled properties.

1 Author V. D. Pham , K. Kanisawa , S. Fölsch

Quantum rings engineered by atom manipulation

Source Phys. Rev. Lett. , 123 , 066801 ( 2019 )
DOI : 10.1103/PhysRevLett.123.066801 | Download: PDF | 3103 Cite : Bibtex RIS
V. D. Pham, K. Kanisawa, and S. Fölsch