Electronic Properties of Twisted Trilayer Graphene (1301.3052v1)

Abstract: We study the electronic properties of a twisted trilayer graphene, where two of the layers have Bernal stacking and the third one has a relative rotation with respect to the AB-stacked layers. Near the Dirac point, the AB-twisted trilayer graphene spectrum shows two parabolic Bernal-like bands and a twisted-like Dirac cone. For small twist angles, the parabolic bands present a gap that increases for decreasing rotation angle. There is also a shift in the twisted-like Dirac cone with a similar angle dependence. We correlate the gap in the trilayer with the shift of the Dirac cone in an isolated twisted bilayer, which is due to the loss of electron-hole symmetry caused by sublattice mixing in the rotated geometry. Using a tight-binding and a continuum model, we derive an effective Hamiltonian which accounts for the relevant low-energy properties of this system.

Overview of the Electronic Properties of Twisted Trilayer Graphene

The paper at hand explores the complex electronic properties associated with a twisted trilayer graphene, where two layers form a Bernal stacking with the third layer having a rotational angle relative to those layers. Employing both tight-binding and continuum models, the authors derive an effective Hamiltonian that captures the low-energy behaviors intrinsic to this graphene configuration.

Key Findings and Analytical Insights

The paper elucidates several core characteristics of twisted trilayer graphene:

1. Band Structure Composition:
   • The electron spectrum near the Dirac point comprises two parabolic Bernal-like bands and a twisted-like Dirac cone. For smaller twist angles, notable distinctions emerge: the parabolic bands display a gap that broadens as the rotation angle reduces, while the Dirac cone undergoes a shift with analogous angular dependence.
2. Loss of Electron-Hole Symmetry:
   • The gap in the trilayer is linked to the shift of the Dirac cone observed in isolated twisted bilayer graphene. This correlation is attributed to sublattice mixing in the rotated geometry, causing asymmetric electron-hole distributions.
3. Velocity Renormalization:
   • The velocity of carriers in twisted-like bands is significantly renormalized for small twist angles, decreasing towards zero as the angle approaches.
4. Effective Hamiltonian Development:
   • Combining tight-binding insights with continuum approximations, an effective Hamiltonian was formulated. This model provides a robust framework for understanding the low-energy physics of the system and accurately describes its dispersion relations.

Theoretical and Practical Implications

The findings from the paper of twisted trilayer graphene impart critical implications:

• Theoretical: The derived Hamiltonian and interpretation of band behaviors advance our understanding of layered graphene systems, especially in complex stacking scenarios. The insights into electron-hole symmetry and velocity dynamics offer valuable contributions to the theoretical modeling of graphene and may refine predictions in other multilayer structures.
• Practical: The electronic characteristics detailed in this paper are crucial for potential applications in graphene-based electronic devices. The ability to modulate band gaps and carrier velocities through precise control of layer orientations could facilitate the development of novel electronic components with tailored properties.

Future Research Directions

This work constitutes an analytical foundation for future investigations into rotated trilayer graphene and similar materials. Prospective studies could focus on:

• Examination of other stacking arrangements and their impact on electronic properties.
• Experimental validation of the theoretical predictions and effectiveness of the derived Hamiltonian.
• Exploration of the effects of external factors, such as electric fields, on electronic properties and incorporated device functionalities.

In sum, the paper successfully provides a comprehensive analysis of twisted trilayer graphene, blending theoretical insights with implications pertinent to future research in advanced graphene materials and their applications.