Realizing of the relativistic artificial molecule with tunable coupling and orbitals by two coupled graphene quantum dots

Graphene quantum dots have electronic structures resembling these of atoms. Our recent paper uses two coupled graphene quantum dots to construct artificial molecules and study their electronic properties at tunable distances.
Published in Physics
Realizing of the relativistic artificial molecule with tunable coupling and orbitals by two coupled graphene quantum dots
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  In the nature, two real atoms typically present two scenarios: either the two atoms remain isolated when they are far apart, or they rapidly couple and form a molecule when they are close enough. This has made it an outstanding challenge to conduct in-depth investigations of evolution from two isolated atoms to a molecule. However, in early studies on traditional semiconductor quantum dots (QDs), researchers discovered that QDs can confine electrons in discrete energy levels, similar to atomic nuclei to confine electrons. As a result, QDs are often referred to artificial atoms. In the same way, when two QDs are brought close to each other, their respective energy levels can linearly combine, forming bonding and antibonding states similar to those in molecules. Therefore, two coupled QDs are also commonly referred to an artificial molecule. These results offer a unique platform to study molecular physics.

  In recent years, researchers have developed numerous methods to fabricate traditional semiconductor QDs to study the confinement of the non-relativistic fermions. And they have preliminarily achieved the change from artificial atoms to artificial molecules. But in fact, the systematic study of this process and the evolution of the relativistic fermions are still lacking. In our paper, we use graphene quantum dots (GQDs) as a platform and achieve continuous nanoscale tuning of the distance between two GQDs through STM tip manipulation. This allows us to investigate the coupling process from two relativistic artificial atoms to relativistic artificial molecules.

Fig. 1 | a, STM images of two coupled GQDs with 12 nm apart. b, The -d3I/dV3 STS maps versus the spatial position along the red arrow in panel a. c, The energy-fixed dI/dV mappings at the N1+ and N1- marked in panel b. d, The energy spacing ΔE of N1+ and N1- as a function of 1/d between the two GQDs obtained in experiment and in theory. e, Zoom-in -d3I/dV3 STS map of the black dashed rectangle in panel b. f,g, The energy-fixed dI/dV maps at N2+ and N2- marked in panel e.

  First, when the distance between the two GQDs is relatively large, the characteristics of the quasibound states in each GQD are essentially the same as those observed in an isolated GQD. It indicates that the coupling between the two GQDs is very weak at this distance. Thus, they can still be regarded as two artificial atoms.

  Then, as reducing the distance between the two GQDs until their boundaries come into full contact as shown in Fig. 1a, we observed gradual evolution in the distribution of the quasibound states. The lowest quasibound state begins to split, forming bonding and antibonding states as shown in Fig. 1b. The splitting becomes more pronounced as the distance decreases. And the bonding and antibonding states are attractive and repulsive respectively as shown in Fig. 1c. These features indicate that the molecular states are formed. And the coupling strength increases with the distance decreasing. Eventually, the characteristics of the quasibound states transition from two circular GQDs to a single elliptical GQD, indicating the complete transformation from artificial atoms to artificial molecules.

  Furthermore, we quantitatively studied the relation between the splitting of the lowest quasibound state and the inverse distance between the two GQDs. Surprisingly, it reveals an approximately linear relationship as shown in Fig. 1d, which contrasts with the exponential or logarithmic dependence observed in conventional semiconductor QDs. This distinct behavior highlights the uniqueness of relativistic artificial molecules compared to traditional molecules formed by natural atoms or semiconductor QDs.

  Finally, besides the studying of the lowest quasibound states, the quasibound states with higher angular momenta are also coupled with the distance decreasing as shown in Fig. 1e. However, there is a lack of real-space imaging of this effect. Our work fills this gap. As shown in Figs. 1f and 1g, the bonding and antibonding states at higher angular momenta display an attractive figure-eight distribution and a repulsive distribution, respectively.

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Nanophysics
Physical Sciences > Physics and Astronomy > Condensed Matter Physics > Nanophysics

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