I am trying to find the effective mass of the electron within the first Brillouin zone in a particular direction in a crystal where the energy of the electron varies with some wave vector ##E(k)=Ak^2+Bk^4##. But I need to express this as a fraction of the electron rest mass.(adsbygoogle = window.adsbygoogle || []).push({});

I know that the effective mass (from Newton's 2^{nd}law) is given by:

##m^* = \frac{\hbar^2}{d^2E/dk^2}##

At the first Brillouin zone boundary we have ##k =\pi / a##. Also the second derivative of the E(k) is ##\frac{d^2E}{dk^2}=2A+12Bk^2##.

Substituting these in I think the effective mass is:

##m^* = \frac{\hbar^2}{2A+12B (\frac{\pi}{a})^2}##

Now, how does one express this as a fraction of the electron rest mass m (511 KeV)?

Any suggestion or correction is appreciated.

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# Effective Electron Mass

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