Question

Consider a metal-superconductor junction connected to a dc voltage \(V\). At \(T < T_c\), where \(T_c\) is the superconductor's transition temperature, the current \(I\) versus \(V\) behavior of this junction is shown schematically in the figure below.

If the superconducting energy gap is \(D\) meV, the value of \(D\) (rounded off to one decimal place) is

Hint:

Hint:
Read the threshold voltage \(V_{Th}\) where the current starts flowing on the graph, set \(eV_{Th} = \Delta\), then the full gap is \(D = 2\Delta\).

Answer 1

Correct Answer: 2

Step 1: Understanding the Concept:
In a superconductor the electrons pair up into Cooper pairs, and this pairing opens a gap in the single particle (quasiparticle) energy spectrum. No quasiparticle state exists within an energy \(\Delta\) of the Fermi level, so states are empty for energies less than \(\Delta\) above \(E_F\) and filled for energies less than \(\Delta\) below \(E_F\).

Step 2: Key Formula or Approach:
When this superconductor sits in a junction with a normal metal and a bias voltage \(V\) is applied, electrons from the metal at the Fermi level can only tunnel into the superconductor once they get enough extra energy to reach an allowed quasiparticle state. This condition is \(eV_{Th} = \Delta\), where \(V_{Th}\) is the threshold voltage at which the current first turns on.
The forbidden window in the quasiparticle spectrum runs from \(-\Delta\) to \(+\Delta\) around \(E_F\), so its full width, which is what the question means by the superconducting energy gap \(D\), is \(D = 2\Delta\).

Step 3: Detailed Explanation:
The graph shows the current staying at zero until \(V_{Th} = 1.0\) mV, after which it rises in a straight line. This flat region is exactly the signature of the gap in the density of states, so the threshold read off the graph gives \(\Delta\) directly:
\[ \Delta = eV_{Th} = 1.0 \text{ meV} \]
Using \(D = 2\Delta\):
\[ D = 2 \times 1.0 = 2.0 \text{ meV} \]

Final Answer:
The superconducting energy gap read from the junction's I-V curve works out to 2.0 meV. \[ \boxed{D = 2.0 \text{ meV}} \]