Consequences of the Inherent Density Dependence in Dirac Materials

Dirac materials are systems in which the dispersion is linear in the vicinity of the Dirac points. As a consequence of this linear dispersion, these systems exhibit unusual behavior and possess unique physical properties that are of great interest. In this work we utilize the single walled carbon nanotube (SWNT) as a model Dirac material and examine the system within the framework of Tomanaga-Luttinger Liquid theory (TLL) revealing several unconventional properties unique to these systems. Specifically, the exponents of the Green's function are electron density independent leading to electron density independent thermodynamic quantities and speed of sound; both of which are vastly different from traditional TLL behavior. Additionally, we discuss the implications the Virial Theorem has for this system; in particular, the total average ground state energy is given by $E=\mathcal{B}/r_s$ where $\mathcal{B}$ is a constant independent of $r_s$. Finally, experimental techniques are discussed in which these predictions of density independent exponents and their behavior can be verified.