Effective Density of States for 2D Effective Mass Tensor, Dispersion relation in tight binding model with even indices only. https://doi.org/10.1016/j.physleta.2014.11.005. But how does one know that the Fermi velocity is given by $v_{\rm{F}} = \frac{3ta}{2}$? In "Star Trek" (2009), why does one of the Vulcan science ministers state that Spock's application to Starfleet was logical but "unnecessary"? In this case, $\frac{\partial\omega}{\partial k}=\frac 1 \hbar\frac{\partial E}{\partial k}$, which easily evaluates to $v_g=\frac{3ta}{2}=:v_f$ for $k=0$. The Dirac points are six locations in momentum space, on the edge of the Brillouin zone, divided into two non-equivalent sets of three points. Controlling the energy gap of graphene by Fermi velocity engineering. This expression arises from a tight-binding model, in fact $E =\frac{3\hbar ta}{2}|k|$ where $t$ is the nearest-neighbor hopping energy and $a$ the interatomic distance. The group velocity $v_g$ of a wave packet (that's the speed of the maximum of the wave packet) is given by $v_g=\frac{\partial\omega}{\partial k}$. In Monopoly, if your Community Chest card reads "Go back to ...." , do you move forward or backward? But in the absence of doping graphene has exactly one electron per \spin" per atom (2 per unit cell), so … Copyright © 2020 Elsevier B.V. or its licensors or contributors. Do other planets and moons share Earth’s mineral diversity? Limitations of Monte Carlo simulations in finance. Here vF ~ 106 m/s (.003 c) is the Fermi velocity in graphene, which replaces the velocity of light in the Dirac theory; σ →. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Are you sure that the definition of $v_{F}$ isn't the group velocity at $k=k_{F}$? Normally one would use $m_{\rm{eff}}^{-1} =\frac{1}{\hbar^{2}} \frac{\partial^{2}E}{\partial k^{2}}$ and $v_{\rm{F}} = \frac{\hbar k_{\rm{F}}}{m_{\rm{eff}}}$, but in this case $m_{\rm{eff}} = \infty$. The effective mass from solid state physics is indeed infinite. Why is the battery turned off for checking the voltage on the A320? How can you trust that there is no backdoor in your hardware? The electronic structure of a single-layer graphene with a periodic Fermi velocity modulation is investigated by using an effective Dirac-like Hamiltonian. It only takes a minute to sign up. Four electronic properties separate it from other condensed matter systems. Why does the concept of effective mass fail for linear dispersion relations? Was the theory of special relativity sparked by a dream about cows being electrocuted? Momentum space Hamiltonian of a disordered system of tight binding model, The 1-dimensional Kronig-Penney Model: Trying to understand the relation between hopping energy and effective mass. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. By continuing you agree to the use of cookies. Is there a name for applying estimation at a lower level of aggregation, and is it necessarily problematic? In a gapless graphene or in a graphene with a constant energy gap the modulation of the Fermi velocity, as expected, only changes the dispersion between energy and moment, turning the minibands narrower or less narrow than in the usual graphene depending on how the Fermi velocity is modulated and the energy gap remains the same. Why does Chrome need access to Bluetooth? The solid state physics effective mass doesn't work here, because the dispersion relation needs to be parabolic (not linear with a cusp), there are two papers about that on arXiv here and here. In graphene, we have (in the low energy limit) the linear energy-momentum dispersion relation: $E=\hbar v_{\rm{F}}|k|$. Why do electrons in graphene behave as Dirac fermions near the Dirac points? Is the word ноябрь or its forms ever abbreviated in Russian language? rev 2020.11.24.38066, The best answers are voted up and rise to the top, Physics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Should we leave technical astronomy questions to Astronomy SE? What if the P-Value is less than 0.05, but the test statistic is also less than the critical value? free electron gas). Asking for help, clarification, or responding to other answers. The sets give graphene a valley degeneracy of gv = 2. By contrast, for traditional semiconductors the primary point of interest is generally Γ, where momentum is zero.