Motivated by recent developments on the fabrication and control of semiconductor-based quantum dots, we theoretically study a finite system of tunnel-coupled quantum dots with the electrons interacting through the long-range Coulomb interaction. When the interelectron separation is large and the quantum dot confinement potential is weak, the system behaves as an effective Wigner crystal with a period determined by the electron average density with considerable electron hopping throughout the system. For stronger periodic confinement potentials, however, the system makes a crossover to a Mott-type ground state where the electrons are completely localized at the individual dots with little interdot tunneling. In between these two phases, the system is essentially a strongly correlated electron liquid with intersite electron hopping constrained by strong Coulomb interaction. We characterize this Wigner-Mott-liquid quantum crossover with detailed numerical finite-size diagonalization calculations of the coupled interacting quantum dot system, showing that these phases can be smoothly connected by tuning the system parameters. Experimental feasibility of observing such a hopping-tuned Wigner-Mott-liquid crossover in currently available semiconductor quantum dots is discussed. In particular, we connect our theoretical results to recent quantum-dot-based quantum emulation experiments where a collective Coulomb blockade was demonstrated. We discuss realistic disorder effects on our theoretical findings. One conclusion of our work is that experiments must explore lower density quantum dot arrays in order to clearly observe the Wigner phase although the Mott-liquid crossover phenomenon should already manifest itself in the currently available quantum dot arrays. We also suggest a direct experimental electron density probe, such as atomic force microscopy or scanning tunneling microscopy, for a clear observation of the effective Wigner crystal phase.

}, doi = {10.1103/PhysRevResearch.2.023060}, author = {Vu, DinhDuy and Das Sarma, Sankar} }