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What is the Fermi energy of (undoped) graphene? 
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#1
May214, 06:17 PM

P: 117

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
May314, 02:50 AM

Sci Advisor
Thanks
PF Gold
P: 1,908

See http://journals.aps.org/prl/abstract...ett.108.116404
"Direct Measurement of the Fermi Energy in Graphene Using a DoubleLayer Heterostructure" 


#3
May814, 03:55 AM

P: 33

Free energy of the ionelectron 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 Efermi : 6.3093 XC(G=0): 0.4452 alpha+bet : 0.0289 add alpha+bet to get absolut eigen values kpoint 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,"Efermi: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: http://guide.ceit.metu.edu.tr/thinkquest/apndx3.htm) 


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