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The interface effects of quark matter play important roles in the propertiesof compact stars and small nuggets such as strangelets and $ud$QM nuggets. Byintroducing a density derivative term to the Lagrangian density and adoptingThomas-Fermi approximation, we find it is possible to reproduce the resultsobtained by solving Dirac equations. Adopting certain parameter sets, theenergy per baryon of $ud$QM nuggets decreases with baryon number $A$ and becomemore stable than nuclei at $A\gtrsim 300$. The effects of quark matter symmetryenergy are examined, where $ud$QM nuggets at $A\approx 1000$ can be more stablethan others if large symmetry energy is adopted. In such cases, larger $ud$QMnuggets will decay via fission and the surface of an $ud$QM star will fragmentinto a crust made of $ud$QM nuggets and electrons, which resembles the cases ofa strange star's crust. The corresponding microscopic structures are theninvestigated adopting spherical and cylindrical approximations for theWigner-Seitz cells, where the droplet phase is found to be the most stableconfiguration with $ud$QM stars' crusts and $ud$QM dwarfs made of $ud$QMnuggets ($A\approx 1000$) and electrons. For the cases considered here, thecrust thickness of $ud$QM stars is typically $\sim$200 m, which reaches a fewkilometers if we neglect the interface effects and adopt Gibbs construction.The masses and radii of $ud$QM dwarfs are smaller than typical white dwarfs,which would increase if the interface effects are neglected.

Interface effects of quark matter: Light-quark nuggets and compact stars