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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.
Electron-electron interactions strongly affect the behavior of low-dimensional systems. In one dimension (1D), arbitrarily weak interactions qualitatively alter the ground state producing a Luttinger liquid (LL) which has now been observed in a numbe
Recent NMR experiments by Singer et al. [Singer et al. Phys. Rev. Lett. 95, 236403 (2005).] showed a deviation from Fermi-liquid behavior in carbon nanotubes with an energy gap evident at low temperatures. Here, a comprehensive theory for the magneti
We present a detailed theoretical analysis of the Wigner crystal states in confined semiconducting carbon nanotubes. We show by robust scaling arguments as well as by detailed semi-microscopic calculations that the effective exchange interaction has
Conventional wisdom had long held that a composite particle behaves just like an ordinary Newtonian particle. In this paper, we derive the effective dynamics of a type-I Wigner crystal of composite particles directly from its microscopic wave functio
Carbon nanotubes (CNTs) are a promising material for high-performance electronics beyond silicon. But unlike silicon, the nature of the transport band gap in CNTs is not fully understood. The transport gap in CNTs is predicted to be strongly driven b