Molecule-type phases and Hund's rule in vertically coupled quantum dots

Relativistic artificial molecule of two coupled graphene quantum dots at tunable distances

In a molecule formed by two atoms, energy difference between bonding and antibonding orbitals depends on distance between the two atoms. However, exploring molecular orbitals of two natural atoms with tunable distance has remained an outstanding experimental challenge. Graphene quantum dots can be viewed as relativistic artificial atoms, thus offering a unique platform to study molecular physics. Here, through scanning tunneling microscope, we create and directly visualize the formation process of relativistic artificial molecules based on two coupled graphene quantum dots with tunable distance. Our study indicates that energy difference between the bonding and antibonding orbitals of the lowest quasibound state increases linearly with inverse distance between the two graphene quantum dots due to the relativistic nature of the artificial molecule. For quasibound states with higher orbital momenta, the coupling between these states leads to half-energy spacing of the confined states because the length of the molecular-like orbit is approximately twice that of the atomic-like orbit. Evolution from ring-like whispering-gallery modes in the artificial atoms to figure-eight orbitals in the artificial molecules is directly imaged. The ability to resolve the coupling and orbitals of the relativistic artificial molecule at the nanoscale level yields insights into the behavior of quantum-relativistic matter.

Relativistic Artificial Molecules Realized by Two Coupled Graphene Quantum Dots

Coupled quantum dots (QDs), usually referred to as artificial molecules, are important not only in exploring fundamental physics of coupled quantum objects but also in realizing advanced QD devices. However, previous studies have been limited to artificial molecules with nonrelativistic Fermions. Here, we show that relativistic artificial molecules can be realized when two circular graphene QDs are coupled to each other. Using scanning tunneling microscopy (STM) and spectroscopy (STS), we observe the formation of bonding and antibonding states of the relativistic artificial molecule and directly visualize these states of the two coupled graphene QDs. The formation of the relativistic molecular states strongly alters distributions of massless Dirac Fermions confined in the graphene QDs. Moreover, our experiment demonstrates that the degeneracy of different angular-momentum states in the relativistic artificial molecule can be further lifted by external magnetic fields. Then, both the bonding and antibonding states are split into two peaks.

Magnetically tunable Kondo-Aharonov-Bohm effect in a triangular quantum dot

The role of discrete orbital symmetry in mesoscopic physics is manifested in a system consisting of three identical quantum dots forming an equilateral triangle. Under a perpendicular magnetic field, this system demonstrates a unique combination of Kondo and Aharonov-Bohm features due to an interplay between continuous [spin-rotation SU(2)] and discrete (permutation C3v) symmetries, as well as U(1) gauge invariance. The conductance as a function of magnetic flux displays sharp enhancement or complete suppression depending on contact setups.

Correlation energy and spin polarization in the 2D electron gas

The ground-state energy of the two-dimensional uniform electron gas has been calculated with a fixed-node diffusion Monte Carlo method, including backflow correlations, for a wide range of electron densities as a function of spin polarization. We give a simple analytic representation of the correlation energy which fits our simulation data and includes several known high- and low-density limits. This parametrization provides a reliable local spin density energy functional for two-dimensional systems and an estimate for the spin susceptibility. Within the proposed model for the correlation energy, a weakly first-order polarization transition occurs shortly before Wigner crystallization as the density is lowered.

Dissociation of vertical semiconductor diatomic artificial molecules

We investigate the dissociation of few-electron circular vertical semiconductor double quantum dot artificial molecules at 0 T as a function of interdot distance. A slight mismatch introduced in the fabrication of the artificial molecules from nominally identical constituent quantum wells induces localization by offsetting the energy levels in the quantum dots by up to 2 meV, and this plays a crucial role in the appearance of the addition energy spectra as a function of coupling strength particularly in the weak coupling limit.