Wednesday, December 25, 2019

quantum mechanics - Landau Levels and Magnetic length


I am looking into Landau Levels and keep coming across a magnetic length defined as follows for a 2D system:


$l_B=\sqrt{\frac{\hbar c}{e B}}$


I have seen numerous sources say this is:


$l_B\approx 26nm \sqrt{B[Tesla]} $


But by plugging those numbers in I don't see how this is the case - the units are just plain wrong. The thing is, I cannot for the life of me figure out what type of theorist units they used to 1) get this expression in the first place, and 2) calculate it for something realistic. The only hint I have is that it was done in the "Landau Gauge" - googling this yields nothing useful.



What units are being used, and how did they calculate this number?



Answer



In the first formula $l_B = \sqrt{\frac{ℏc}{eB}}$ , all constants are in CGS units and $B$ is in Tesla.


Constants in CGS-


$\hbar=1.05457266 *10^{-27}$ ergs s


$c=3*10^{10}$ cm/s


$e=4.8032068*10^{-10}$ esu


and


$1$ Tesla (SI)= $1*10^4$ G (CGS)


You will get the second formula.



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