[Paper Review] Electron properties of Carbon nanotubes in the field effect regime

Dmitry S. Novikov, Leonid Levitov|arXiv (Cornell University)|Apr 23, 2002

Carbon Nanotubes in Composites6 citations

TL;DR

This paper proposes that strong transverse electric fields can dramatically alter electron properties in carbon nanotubes by reversing Fermi velocity in metallic tubes and flipping effective mass sign in semiconducting tubes, leading to Fermi surface breakup and gap suppression. Using a chiral anomaly-based screening model, it shows the required fields are experimentally feasible due to a universal, radius-independent screening factor of ~5, enabling access to novel quantum states like excitonic pairing.

ABSTRACT

Electron properties of Carbon nanotubes can change qualitatively in a transverse electric field. In metallic tubes the sign of Fermi velocity can be reversed in a sufficiently strong field, while in semiconducting tubes the effective mass can change sign. These changes in the spectrum manifest themselves in a breakup of the Fermi surface and in the energy gap suppression, respectively. The effect is controlled by the field inside the tube which is screened due to the polarization induced on the tube. The theory of screening links it with the chiral anomaly for 1D fermions and obtains a universal screening function determined solely by the Carbon pi electron band.

Motivation & Objective

• To investigate how strong transverse electric fields modify electron band structure in carbon nanotubes, particularly in the field effect regime.
• To understand the role of electron screening in determining the effective field inside nanotubes under external transverse fields.
• To establish the connection between field screening and the chiral anomaly in one-dimensional Dirac fermions.
• To determine whether experimentally achievable fields can induce topological and many-body effects such as Fermi velocity reversal and effective mass sign change.
• To assess the feasibility of observing novel quantum phenomena like excitonic pairing in nanotubes under strong transverse fields.

Proposed method

• Models the electron system in carbon nanotubes using a massless Dirac Hamiltonian near the K and K' points, incorporating transverse electric fields via a gauge transformation.
• Applies degenerate perturbation theory to derive the energy spectrum, showing Fermi velocity reversal at roots of the Bessel function J₀(2u).
• Uses bosonization and regularization techniques to derive the chiral anomaly contribution to the ground state energy, linking it to field screening.
• Evaluates the screening function via a sum over matrix elements and level shifts, showing a universal, R-independent screening factor.
• Combines perturbative and non-perturbative approaches (including bosonization at k=0) to validate the screening result across field strengths.
• Derives the effective external field required, accounting for screening, and confirms feasibility using realistic parameters (e.g., e²/ħv = 2.7).

Experimental results

Research questions

• RQ1 Can a transverse electric field induce a sign reversal of the Fermi velocity in metallic carbon nanotubes, leading to Fermi surface breakup?
• RQ2 Does a strong transverse field cause the effective mass in semiconducting nanotubes to change sign, resulting in suppression of the band gap?
• RQ3 How is the internal electric field in a nanotube screened under strong external fields, and what determines the screening factor?
• RQ4 What is the connection between the screening of transverse fields and the chiral anomaly in one-dimensional Dirac fermions?
• RQ5 Are the required electric fields for observing these effects experimentally feasible, given realistic screening and material parameters?

Key findings

• Fermi velocity reversal in metallic nanotubes occurs at transverse fields u ≈ μ₁/2 ≈ 0.61, where μ₁ is the first root of J₀(2u), leading to a breakup of the Fermi surface.
• In semiconducting nanotubes, the effective mass sign flips at u ≈ 1.4, causing strong suppression of the band gap, as shown in Fig. 1.
• The screening factor for the internal field is universal and R-independent, yielding a ratio of external to internal field of approximately 5.24 (δ=1/3) or 4.87 (δ=0).
• The screening mechanism is linked to the chiral anomaly, with the anomaly energy contribution derived from regularization and confirmed via bosonization.
• The required external field for these effects is feasible: E ≈ 5.26 / R² MV/cm, achievable with modern 2D gated structures (up to 50 MV/cm).
• The system supports a novel metallic state with intertwined electron and hole Fermi surfaces, potentially unstable to excitonic pairing, with a gapless Goldstone mode due to chiral gauge symmetry.