Coulomb staircase and Wigner crystalline states in single-electron tunneling through one-dimensional arrays

We show that steps in the I-V characteristic for tunneling transport through one-dimensional arrays of small quantum dots correspond to alternation of the charge density between distinct Wigner crystalline phases. We show that these phases, at fixed voltage, are given approximately by a minimum force principle for each total soliton number NT. We develop a continuum transmission line model and an order parameter to characterize the stability of the various crystal phases as the current increases.