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Pr. 1.4a:

Pr. 1.4a:. This is a single electron transistor split gate with a parabolic confinement in y and of course quantum confinement in z with well separated energy level such that n z =1 is all you need consider. Add a uniform B-field in z. z. B-field. y. x.

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Pr. 1.4a:

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  1. Pr. 1.4a: This is a single electron transistor split gate with a parabolic confinement in y and of course quantum confinement in z with well separated energy level such that nz =1 is all you need consider. Add a uniform B-field in z z B-field y x

  2. 1-DEG (parabolic potential) + B energy eigenvalues: where and ES kx DE between each level: hbarwc0 Easiest to evaluate at kx = 0 ½ hbarwc0

  3. What to expect: B = 0: Ef fixed ES kx DE between each level: hbarwc0 = hbarw0 1/2 hbarw0 This case has the smallest spacing between levels and the smallest ‘extra’ needed to reach the bottom of the lowest conduction band. If Ef as shown, 4 levels are occupied.

  4. What to expect: B = moderately large: Ef fixed ES kx DE between each level: hbarwc0 is larger 1/2 hbarwc0 is larger With the B-field present, the spacing between the levels and the ‘extra’ are both larger. As shown, the bottom of the top level is now at an energy greater than the value of Ef . Therefore only 3 levels are occupied. And the sub-band curves are getting flatter.

  5. What to expect: B = large: Other two levels off the page DE between each level: hbarwc0 Ef 1/2 hbarwc0 fixed ES kx The B-field is so large that, as shown, the bottom of the bottom level is now at an energy greater than the value of Ef . No levels are occupied: magnetic switch is OFF. Magneto-electro sub-bands are really getting flat.

  6. How to count: Looking for how many DEs plus one extra ½ hbarwc0 fit in Ef – ES This is

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