标题： 最低朗道能级中的威格纳晶体化对于$ν\ge 1/5$ 显示英文标题

标题： Wigner Crystalization in the Lowest Landau Level for $ν\ge 1/5$

摘要： 通过精确对角化，我们研究了在圆柱形外部势场中被限制的七电子的低能态，该势场模拟宏观系统的其余部分，从而控制填充因子$\nu $。 发现当电子通过裸 Coulomb 势相互作用时，在填充因子$ \nu = 1/3$和$ \nu = 1/5$之间，Wigner 晶体是基态。 即使在$\nu =1/5$时，固态的能量也低于 Laughlin 态，尽管两者能量非常接近。 我们还讨论了最低 Landau 能级中伪势参数的作用，并证明当相互作用的短程部分被抑制时出现的早期报道的无间隙态与纯 Coulomb 情况下的 Wigner 晶体化毫无共同之处。 显示英文摘要

摘要： By means of exact diagonalization we study the low-energy states of seven electrons in the lowest Landau level which are confined by a cylindric external potential modelling the rest of a macroscopic system and thus controlling the filling factor $\nu $. Wigner crystal is found to be the ground state for filling factors between $ \nu = 1/3$ and $ \nu = 1/5$ provided electrons interact via the bare Coulomb potential. Even at $\nu =1/5$ the solid state has lower energy than the Laughlin's one, although the two energies are rather close. We also discuss the role of pseudopotential parameters in the lowest Landau level and demonstrate that the earlier reported gapless state, appearing when the short-range part of the interaction is suppressed, has nothing in common with the Wigner crystalization in pure Coulomb case.