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Under which conditions do the electrical transport properties of one-dimensional (1D) carbon nanotubes (CNTs) and 2D graphene become equivalent? We have performed atomistic calculations of the phonon-limited electrical mobility in graphene and in a wide range of CNTs of different types to address this issue. The theoretical study is based on a tight-binding method and a force-constant model from which all possible electron-phonon couplings are computed. The electrical resistivity of graphene is found in very good agreement with experiments performed at high carrier density. A common methodology is applied to study the transition from 1D to 2D by considering CNTs with diameter up to 16 nm. It is found that the mobility in CNTs of increasing diameter converges to the same value, the mobility in graphene. This convergence is much faster at high temperature and high carrier density. For small-diameter CNTs, the mobility strongly depends on chirality, diameter, and existence of a bandgap.
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We theoretically calculate the phonon scattering limited electron mobility in extrinsic (i.e. gated or doped with a tunable and finite carrier density) 2D graphene layers as a function of temperature $(T)$ and carrier density $(n)$. We find a temperature dependent phonon-limited resistivity $rho_{ph}(T)$ to be linear in temperature for $Tagt 50 K$ with the room temperature intrinsic mobility reaching values above $10^5$ cm$^2/Vs$. We comment on the low-temperature Bloch-Gr{u}neisen behavior where $rho_{ph}(T) sim T^4$ for unscreened electron-phonon coupling.
We calculate an electron-phonon scattering and intrinsic transport properties of black phosphorus monolayer using tight-binding and Boltzmann treatments as a function of temperature, carrier density, and electric field. The low-field mobility shows weak dependence on density and, at room temperature, falls in the range of 300 - 1000 cm^2/Vs in the armchair direction and 50 - 120 cm^2/Vs in the zig-zag direction with the anisotropy due to an effective mass difference. At high fields, drift velocity is linear with electric field up to 1 - 2 V/micron reaching values of 10^7 cm/s in the armchair direction, unless self-heating effects are included.
Smoothly varying lattice strain in graphene affects the Dirac carriers through a synthetic gauge field. When the lattice strain is time dependent, as in connection with phononic excitations, the gauge field becomes time dependent and the synthetic vector potential is also associated with an electric field. We show that this synthetic electric field has observable consequences. Joule heating associated with the currents driven by the synthetic electric field dominates the intrinsic damping, caused by the electron-phonon interaction, of many acoustic phonon modes of graphene and metallic carbon nanotubes when including the effects of disorder and Coulomb interactions. Several important consequences follow from the observation that by time-reversal symmetry, the synthetic electric field associated with the vector potential has opposite signs for the two valleys. First, this implies that the synthetic electric field drives charge-neutral valley currents and is therefore unaffected by screening. This frequently makes the effects of the synthetic vector potential more relevant than a competing effect of the scalar deformation potential which has a much larger bare coupling constant. Second, valley currents decay by electron-electron scattering (valley Coulomb drag) which causes interesting temperature dependence of the damping rates. While our theory pertains first and foremost to metallic systems such as doped graphene and metallic carbon nanotubes, the underlying mechanisms should also be relevant for semiconducting carbon nanotubes when they are doped.
Carbon nanotube field-effect transistors operate over a wide range of electron or hole density, controlled by the gate voltage. Here we calculate the mobility in semiconducting nanotubes as a function of carrier density and electric field, for different tube diameters and temperature. The low-field mobility is a non-monotonic function of carrier density, and varies by as much as a factor of 4 at room temperature. At low density, with increasing field the drift velocity reaches a maximum and then exhibits negative differential mobility, due to the non-parabolicity of the bandstructure. At a critical density $rho_csim$ 0.35-0.5 electrons/nm, the drift velocity saturates at around one third of the Fermi velocity. Above $rho_c$, the velocity increases with field strength with no apparent saturation.
We present transport measurements on high-mobility bilayer graphene fully encapsulated in hexagonal boron nitride. We show two terminal quantum Hall effect measurements which exhibit full symmetry broken Landau levels at low magnetic fields. From weak localization measurements, we extract gate-tunable phase coherence times $tau_{phi}$ as well as the inter- and intra-valley scattering times $tau_i$ and $tau_*$. While $tau_{phi}$ is in qualitative agreement with an electron-electron interaction mediated dephasing mechanism, electron spin-flip scattering processes are limiting $tau_{phi}$ at low temperatures. The analysis of $tau_i$ and $tau_*$ points to local strain fluctuation as the most probable mechanism for limiting the mobility in high-quality bilayer graphene.
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