Current instability and diamagnetism in small-diameter carbon nanotubes

We investigate the electronic instabilities in carbon nanotubes of short radius, looking for the breakdown of the Luttinger liquid regime from the singular behavior of the charge stiffnesses at low energies. We show that such a breakdown is realized in the undoped (3,3) nanotubes through the onset of phase separation into regions with opposite electronic current. The phenomenology derived from this regime is consistent with the formation of a pseudogap in the single-particle spectrum as well as with a divergent diamagnetic susceptibility, as observed in the experiments carried out in carbon nanotubes of small diameter.Comment: 5 pages, submitted to PR

Magnetic and Kohn-Luttinger instabilities near a Van Hove singularity: monolayer versus twisted bilayer graphene

We investigate the many-body instabilities of electrons interacting near Van Hove singularities arising in monolayer and twisted bilayer graphene. We show that a pairing instability must be dominant over the tendency to magnetic order as the Fermi level is tuned to the Van Hove singularity in the conduction band of graphene. As a result of the extended character of the saddle points in the dispersion, we find that the pairing of the electrons takes place preferentially in a channel of f-wave symmetry, with an order parameter vanishing at the position of the saddle points along the Fermi line. In the case of the twisted bilayers, the dispersion has instead its symmetry reduced down to the C_{3v} group and, most importantly, it leads to susceptibilities that diverge at the saddle points but are integrable along the Fermi line. This implies that a ferromagnetic instability becomes dominant in the twisted graphene bilayers near the Van Hove singularity, with a strength which is amplified as the lowest subband of the electron system becomes flatter for decreasing twist angle.Comment: 16 pages, 10 figure

Phase diagram of the Quantum Electrodynamics of 2D and 3D Dirac semimetals

We study the Quantum Electrodynamics of 2D and 3D Dirac semimetals by means of a self-consistent resolution of the Schwinger-Dyson equations, aiming to obtain the respective phase diagrams in terms of the relative strength of the Coulomb interaction and the number N of Dirac fermions. In this framework, 2D Dirac semimetals have just a strong-coupling instability characterized by exciton condensation (and dynamical generation of mass) that we find at a critical coupling well above previous theoretical estimates, thus explaining the absence of that instability in free-standing graphene samples. On the other hand, we show that 3D Dirac semimetals have a richer phase diagram, with a strong-coupling instability leading to dynamical mass generation up to N = 4 and a line of critical points for larger values of N characterized by the vanishing of the electron quasiparticle weight in the low-energy limit. Such a critical behavior signals the transition to a strongly correlated liquid, characterized by noninteger scaling dimensions that imply the absence of a pole in the electron propagator and are the signature of non-Fermi liquid behavior with no stable electron quasiparticles.Comment: 11 pages, 11 figures, extended physical discussio

Rippling transition from electron-induced condensation of curvature field in graphene

A quantum field theory approach is applied to investigate the dynamics of flexural phonons in a metallic membrane like graphene, looking for the effects deriving from the strong interaction between the electronic excitations and elastic deformations. Relying on a self-consistent screening approximation to the phonon self-energy, we show that the theory has a critical point characterized by the vanishing of the effective bending rigidity of the membrane at low momentum. We also check that the instability in the sector of flexural phonons takes place without the development of an in-plane static distortion, which is avoided due to the significant reduction of the electron-phonon couplings for in-plane phonons at large momenta. Furthermore, we analyze the scaling properties of the many-body theory to identify the order parameter that opens up at the point of the transition. We find that the vanishing of the effective bending rigidity and the onset of a nonzero expectation value of the mean curvature are concurrent manifestations of the critical behavior. The results presented here imply that, even in the absence of tension, the theory has a critical point at which the flat geometry becomes an unstable configuration of the metallic membrane, with a condensation of the mean curvature field that may well reproduce the smooth distribution of ripples observed in free-standing graphene.Comment: 15 pages, 6 figure