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: Picture the density of states.
Draw the superconductor's quasiparticle density of states against energy. It is zero in a band centered on the Fermi energy $E_F$ and rises sharply just outside that band. Call the half width of this empty band $\Delta$, so the band runs from $E_F - \Delta$ to $E_F + \Delta$.

Step 2: Connect the empty band to the I-V graph.
Tunneling current can only flow once electrons from the metal are pushed, by the bias $eV$, past this empty band into the first available quasiparticle states. The graph shows exactly that: current stays pinned at zero up to $V_{Th}$ and only grows once $V$ passes it. So the energy $eV_{Th}$ measures how far the electron had to be pushed to clear the empty band starting from $E_F$, which means $eV_{Th} = \Delta$.

Step 3: Read the number and get the full gap.
From the plot, $V_{Th} = 1.0$ mV, so $\Delta = 1.0$ meV. The full empty band, running from $E_F - \Delta$ to $E_F + \Delta$, has width $2\Delta$, and this total width is what the question calls the superconducting energy gap $D$:
\[ D = 2\Delta = 2(1.0) = 2.0 \text{ meV} \]

Final Answer:
Reading the empty band's width symmetric about the Fermi level gives the same result as the threshold-voltage route. \[ \boxed{D = 2.0 \text{ meV}} \]