Two simple tight-binding estimates

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure · Free electrons, energy bands and electronic structure

Solid State Physics, Ch Tight binding and the band structures of real materials

Problem

Two simple tight-binding estimates, one for a narrow d band and one for graphene's Fermi velocity, can be tested against real spectroscopic data. ((a)) Photoemission on palladium metal finds that its 4d band spans a width of

2.6\,\mathrm{eV}

. Using the same rectangular density-of-states estimate used for nickel's d band (ten states per atom, spread evenly across the band, both spin states counted), estimate palladium's electronic heat capacity coefficient

\gamma

. The measured value is

\gamma_{\rm Pd}=9.42\,\mathrm{mJ\,mol^{-1}\,K^{-2}}

(tabulated, low-temperature specific heat). Compare your estimate with this value. ((b)) Angle-resolved photoemission on a single layer of graphene grown epitaxially on silicon carbide, held at room temperature, shows the

\pi

band near the

K

point rising linearly, with an energy change of

\Delta E=0.66\,\mathrm{eV}

over a wavevector interval of

\Delta k=0.10\,\mathrm{\AA^{-1}}

measured along the

\Gamma K

direction. Find the Fermi velocity

v_F

implied by this slope. Then compute the tight-binding prediction

v_F=3ta_{cc}/2\hbar

using

t=2.8\,\mathrm{eV}

and

a_{cc}=1.42\,\mathrm{\AA}

, and state the percentage difference between the two.

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