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The incommensurate 30$^{circ}$ twisted bilayer graphene possesses both relativistic Dirac fermions and quasiperiodicity with 12-fold rotational symmetry arising from the interlayer interaction [Ahn et al., Science textbf{361}, 782 (2018) and Yao et al., Proc. Natl. Acad. Sci. textbf{115}, 6928 (2018)]. Understanding how the interlayer states interact with each other is of vital importance for identifying and subsequently engineering the quasicrystalline order for the applications in future electronics and optoelectronics. Herein, via symmetry and group representation theory we unravel an interlayer hybridization selection rule for $D_{6d}$ bilayer consisting of two $C_{6v}$ monolayers no matter the system size, i.e., only the states from two $C_{6v}$ subsystems with the same irreducible representations are allowed to be hybridized with each other. The hybridization shows two categories including the equivalent and non-equivalent hybridizations with corresponding 12-fold symmetrical and 6-fold symmetrical antibonding (bonding) states, which are respectively generated from $A_1+A_1$, $A_2+A_2$, $E_1+E_1$, and $E_2+E_2$ four paring states and $B_1+B_1$ and $B_2+B_2$ two paring states. With the help of $C_6$ and $sigma_x$ symmetry operators, calculations on the hybridization matrix elements verify the characteristic of the zero non-diagonal and nonzero diagonal patterns required by the hybridization selection rule. In reciprocal space, a vertical electric field breaks the 12-fold symmetry of originally resonant quasicrystalline states and acts as a polarizer allowing the hybridizations from two $E_1$, $E_2$ and $B_2$ paring states but blocking others. Our theoretical framework also paves a way for revealing the interlayer hybridization for bilayer system coupled by the van der Waals interaction.
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Dodecagonal bilayer graphene quasicrystal has 12-fold rotational order but lacks translational symmetry which prevents the application of band theory. In this paper, we study the electronic and optical properties of graphene quasicrystal with large-scale tight-binding calculations involving more than ten million atoms. We propose a series of periodic approximants which reproduce accurately the properties of quasicrystal within a finite unit cell. By utilizing the band-unfolding method on the smallest approximant with only 2702 atoms, the effective band structure of graphene quasicrystal is derived. Novel features, such as the emergence of new Dirac points (especially the mirrored ones), the band gap at M point and the Fermi velocity are all in agreement with recent experiments. The properties of quasicrystal states are identified in the Landau level spectrum and optical excitations. Importantly, our results show that the lattice mismatch is the dominant factor determining the accuracy of layered approximants. The proposed approximants can be used directly for other layered materials in honeycomb lattice, and the design principles can be applied for any quasi-periodic incommensurate structures.
With the motivation of improving the performance and reliability of aggressively scaled nano-patterned graphene field-effect transistors, we present the first systematic experimental study on charge and current distribution in multilayer graphene field-effect transistors. We find a very particular thickness dependence for Ion, Ioff, and the Ion/Ioff ratio, and propose a resistor network model including screening and interlayer coupling to explain the experimental findings. In particular, our model does not invoke modification of the linear energy-band structure of graphene for the multilayer case. Noise reduction in nano-scale few-layer graphene transistors is experimentally demonstrated and can be understood within this model as well.
In van der Waals bonded or rotationally disordered multilayer stacks of two-dimensional (2D) materials, the electronic states remain tightly confined within individual 2D layers. As a result, electron-phonon interactions occur primarily within layers and interlayer electrical conductivities are low. In addition, strong covalent in-plane intralayer bonding combined with weak van der Waals interlayer bonding results in weak phonon-mediated thermal coupling between the layers. We demonstrate here, however, that Coulomb interactions between electrons in different layers of multilayer epitaxial graphene provide an important mechanism for interlayer thermal transport even though all electronic states are strongly confined within individual 2D layers. This effect is manifested in the relaxation dynamics of hot carriers in ultrafast time-resolved terahertz spectroscopy. We develop a theory of interlayer Coulomb coupling containing no free parameters that accounts for the experimentally observed trends in hot-carrier dynamics as temperature and the number of layers is varied.
As a critical way to modulate thermal transport in nanostructures, phonon resonance hybridization has become an issue of great concern in the field of phonon engineering. In this work, we optimized phonon transport across graphene nanoribbon and obtained minimized thermal conductance by means of designing pillared nanostructures based on resonance hybridization. Specifically, the optimization of thermal conductance was performed by the combination of atomic Green` s function and Bayesian optimization. Interestingly, it is found that thermal conductance decreases non-monotonically with the increasing of number for pillared structure, which is severed as resonator and blocks phonon transport. Further mode-analysis and atomic Green` s function calculations revealed that the anomalous tendency originates from decreased phonon transmission in a wide frequency range. Additionally, nonequilibrium molecular dynamics simulations are performed to verify the results with the consideration of high-order phonon scattering. This finding provides novel insights into the control of phonon transport in nanostructures.
We discuss the conditions under which the predicted (but not yet observed) zero-field interlayer excitonic condensation in double layer graphene has a critical temperature high enough to allow detection. Crucially, disorder arising from charged impurities and corrugation in the lattice structure --- invariably present in all real samples --- affects the formation of the condensate via the induced charge inhomogeneity. In the former case, we use a numerical Thomas-Fermi-Dirac theory to describe the local fluctuations in the electronic density in double layer graphene devices and estimate the effect these realistic fluctuations have on the formation of the condensate. To make this estimate, we calculate the critical temperature for the interlayer excitonic superfluid transition within the mean-field BCS theory for both optimistic (unscreened) and conservative (statically screened) approximations for the screening of the interlayer Coulomb interaction. We also estimate the effect of allowing dynamic contributions to the interlayer screening. We then conduct similar calculations for double quadratic bilayer graphene, showing that the quadratic nature of the low-energy bands produces pairing with critical temperature of the same order of magnitude as the linear bands of double monolayer graphene.
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