What is the Fermi energy of (undoped) graphene?

  1. All of the sources I have found for this online have been wildly unclear. Many use the phrase "Fermi energy" to refer to the "Fermi level" (which is emphatically not what I'm looking for; I want the Fermi energy as defined in this Wikipedia article: http://en.wikipedia.org/wiki/Fermi_energy ). Fermi energy is always greater than zero.

    Has anyone ever measured the Fermi energy of graphene? Is there any way to calculate it from known quantities, such as the Fermi velocity, which is approx. [itex]10^6[/itex] m/s? i.e. is there a reason why the usual formula [itex]E_F = \tfrac{1}{2}m_e v_F^2[/itex] wouldn't work here? I read that the Fermi energy for undoped graphene is equal to the energy at the Dirac points, but I read elsewhere that that value is less than zero, which makes no sense because, again, Fermi energy is always greater than zero.
  2. jcsd
  3. UltrafastPED

    UltrafastPED 1,916
    Science Advisor
    Gold Member

  4. I think ,though many use the phrase "Fermi energy", they should know their "Fermi energy" just as the "Fermi level" in their mind. Even though wikipedia have already provided "a few key differences between the Fermi level and Fermi energy", we still need to consider them carefully for our specific system. Here,consider a simplest system (just,say,hydroden atom),we use a universal DFT tool (for example, Vasp.5.2)to examine the "Fermi level". The related energy results are as follows (which are extracted from OUTCAR):

    Free energy of the ion-electron system (eV)
    alpha Z PSCENC = 0.00238712
    Ewald energy TEWEN = -2.04282400
    -1/2 Hartree DENC = -5.62336435
    -exchange EXHF = 0.00000000
    -V(xc)+E(xc) XCENC = 1.90272023
    PAW double counting = 0.87256925 -0.87765194
    entropy T*S EENTRO = -0.02820948
    eigenvalues EBANDS = -6.30934890
    atomic energy EATOM = 12.07484263
    free energy TOTEN = -0.02887945 eV

    energy without entropy = -0.00066997 energy(sigma->0) = -0.01477471


    average (electrostatic) potential at core
    the test charge radii are 0.5201
    (the norm of the test charge is 1.0002)
    1 -41.6613

    E-fermi : -6.3093 XC(G=0): -0.4452 alpha+bet : -0.0289
    add alpha+bet to get absolut eigen values

    k-point 1 : 0.0000 0.0000 0.0000
    band No. band energies occupation
    1 -6.3093 1.00000
    2 -0.1793 0.00000
    3 0.8620 0.00000
    4 0.8620 0.00000
    5 0.8620 0.00000
    6 1.2780 0.00000

    Where,"E-fermi:-6.3093" is just the "Fermi level".Because here is only one electron in "Hydroden atom" system, the "Fermi level" is also equal to the "eigenvalues EBANDS",but,it is not equal to the total energy as wikipedia said.
    On the other hand, "Fermi energy" (not the real meaning of many people) can't be seen directly from the results above,because it is included in the total energy.
    From the view of classical theory,we may understand them easier. (see that:
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