Electronic compressibility, the second derivative of ground state energy with respect to total electron number, is a measurable quantity that reveals the interaction strength of a system and can be used to characterize the orderly crystalline lattice of electrons known as the Wigner crystal. Here, we measure the electronic compressibility of individual suspended ultraclean carbon nanotubes in the low-density Wigner crystal regime. Using low-temperature quantum transport measurements, we determine the compressibility as a function of carrier number in nanotubes with varying band gaps. We observe two qualitatively different trends in compressibility versus carrier number, both of which can be explained using a theoretical model of a Wigner crystal that accounts for both the band gap and the confining potential experienced by charge carriers. We extract the interaction strength as a function of carrier number for individual nanotubes and show that the compressibility can be used to distinguish between strongly and weakly interacting regimes.
Spin and Valley dependent analysis of the two-dimensional low-density electron system in Si-MOSFETS
硅金属氧化物场效应晶体管（MOSFET）中的二维电子系统（2DES）由两种不同的电子流体相互作用组成。我们计算的总能量作为密度的函数$n$，和自旋极化$ζ$在强相关的低密度制度，使用一个经典的映射到一个超网链（CHNC）方程包括桥项。在这里，十个分布函数，所产生的自旋和谷指数，自洽计算，以获得总自由能，化学势，压缩性和自旋磁化率。将T=0的结果与Conti等人的2谷量子蒙特卡罗（QMC）数据（T=0时，$ζ=0$）进行了比较，发现两者非常吻合。然而，与单谷2DES不同，它表明{ \it非偏振相总是2谷系统中的稳定相}，直到在$r_s=42$处的维格纳结晶。这导致$g^*$对自旋极化和密度不敏感。从自由能计算的压缩性和自旋磁化率增强证实了一个简单的方法的有效性的耦合模式形成的基础上的两个谷响应。这三种方法，QMC，CHNC和耦合模理论是一致的。我们的结果不包含{ \it ad hoc}拟合参数。他们同意实验，并没有援引杂质效应或金属-绝缘体过渡现象。
