Depinning, melting, and sliding of generalized Wigner crystals in Moiré systems

We numerically examine the depinning, sliding, and melting of commensurate and incommensurate Wigner crystals on two-dimensional hexagonal periodic substrates near fillings of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mn>1</a:mn><a:mo>/</a:mo><a:mn>3</a:mn><a:mo>,</a:mo><a:mn>1</a:mn><a:mo>/</a:mo><a:mn>2</a:mn></a:mrow></a:math>, and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mn>2</b:mn><b:mo>/</b:mo><b:mn>3</b:mn></b:mrow></b:math> to model the dynamics of generalized Wigner crystals in moiré heterostructures. At low temperatures where thermal fluctuations are irrelevant, for commensurate fillings we find a strongly pinned state that depins into a sliding crystal, while at incommensurate fillings the depinning threshold is strongly reduced. For fillings below <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mn>1</c:mn><c:mo>/</c:mo><c:mn>2</c:mn></c:mrow></c:math>, the depinning occurs in a two-step process. Above the first depinning threshold, there is an extended range of drives where the conduction occurs via the sliding of antikinks along the charge stripes, followed by a second threshold where all the charges begin to slide. At finite temperatures, the external driving reduces the effective melting temperature at commensurate fillings and enhances creep at incommensurate fillings. We show that depinning into different sliding states, such as moving fluids or moving crystals, produces nonlinear features in the transport curves. We also show that transport is asymmetric on either side of a commensurate filling due to the different dynamics for interstitials versus holes in the commensurate structure. A variety of sliding states should be accessible for generalized Wigner crystals at finite temperatures even for low drives. If experiments can realize sliding dynamics in moiré systems, it would open another class of commensurate and incommensurate phases for study. Additionally, the sliding dynamics and antikink flow could provide unique functionalities for charge transport in moiré heterostructures.