Electron properties of carbon nanotubes in a periodic potential

Abstract

A periodic potential applied to a nanotube is shown to lock electrons into incompressible states that can form a devil's staircase. Electron interactions result in spectral gaps when the electron density (relative to a half-filled Carbon pi-band) is a rational number per potential period, in contrast to the single-particle case where only the integer-density gaps are allowed. When electrons are weakly bound to the potential, incompressible states arise due to Bragg diffraction in the Luttinger liquid. Charge gaps are enhanced due to quantum fluctuations, whereas neutral excitations are governed by an effective SU(4)~O(6) Gross-Neveu Lagrangian. In the opposite limit of the tightly bound electrons, effects of exchange are unimportant, and the system behaves as a single fermion mode that represents a Wigner crystal pinned by the external potential, with the gaps dominated by the Coulomb repulsion. The phase diagram is drawn using the effective spinless Dirac Hamiltonian derived in this limit. Incompressible states can be detected in the adiabatic transport setup realized by a slowly moving potential wave, with electron interactions providing the possibility of pumping of a fraction of an electron per cycle (equivalently, in pumping at a fraction of the base frequency).

arXiv comment21 pgs, 8 figs

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Cited by in corpus (15)

• New Generation of Massless Dirac Fermions in Graphene under External Periodic Potentials
• Emerging Zero Modes for Graphene in a Periodic Potential
• The spin-incoherent Luttinger liquid
• Coulomb drag between two spin incoherent Luttinger liquids
• Emerging Dirac and Majorana fermions for carbon nanotubes with proximity-induced pairing and spiral magnetic field
• Dirac-Kronig-Penney model for strain-engineered graphene
• Dirac Spectrum in Piecewise Constant One-Dimensional Potentials
• Theory of the electronic and transport properties of graphene under a periodic electric or magnetic field
• A primer on twistronics: A massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene
• Critical conductance of a one-dimensional doped Mott insulator
• Finite-gap twists of carbon nanotubes and an emergent hidden supersymmetry
• Quantum Pump for Fractional Charge
• Zigzag and armchair nanotubes in external fields
• Effect of periodic potential on exciton states in semiconductor carbon nanotubes
• Schrödinger operator on the zigzag half-nanotube in magnetic field