Theoretical Nanophysics 9/2023

Take the simpler model of the Single Electron Box, i.e., without the tunneling-induced quantum corrections. Reducing the temperature by a factor of 2 ...

• does not change the capacitance peak height

• doubles the capacitance peak height

• halves the capacitance peak height

• exponentially suppresses the capacitance peak height

Take the simpler model of the Single Electron Box, i.e., without the tunneling-induced quantum corrections. Reducing the temperature by a factor of 2 ...

• does not change the capacitance peak width

• doubles the capacitance peak width

• halves the capacitance peak width

• exponentially suppresses the capacitance peak width

• 1/Joule

• 1/(Joule*meter³)

• meter³/Joule

• 1/Joule²

Consider 't', the tunneling energy parameter in the tunnel-junction Hamiltonian. How does it change, if we double the volumes of both leads?

• It does not change.

• It is reduced by a factor of 2.

• It is reduced by a factor of 4.

What is the first-order perturbed wave function of the state (1,0)^T, if t is the perturbation in the Hamiltonian?

What is the second-order energy correction of the state (1,0)^T, if t is the perturbation?

• -t

Take an SET in equilibrium (no bias voltage). Its `Coulomb staircase' is exhibited by which function?

• conductance G as function of gate voltage V_g

• capacitance C as function of gate voltage V_g

• charge N as function of gate voltage V_g

• charging energy E_c as function of gate voltage V_g

Take an SET. Its `Coulomb blockade diamonds' are features of which function?

• current as function of gate voltage

• current as function of bias voltage

• current as function of gate voltage and bias voltage

• bias voltage as function of gate voltage

Recall the perturbative calculation of the charge of a Single Electron Box that we performed up to leading order in the tunnel coupling `t'. For which gate voltage value does it break down?

• n_g = 0

• n_g = 1/4

• n_g = 1/2

• none

In the Single Electron Box at zero temperature, the Coulomb staircase develops ...

• if the conductance of the junction is much smaller than the conductance quantum

• if the conductance of the junction is much greater than the conductance quantum

• if the conductance of the junction equals the conductance quantum

• for any value of the conductance of the junction