Single-electron superconducting tunneling

Single-electron superconducting tunneling transfers individual Electrons across a barrier into or out of quasiparticle states of a material with superconductivity. In a normal-metal–insulator–superconductor junction, abbreviated NIS, only one electrode has superconductivity. Such a junction can reveal a superconducting energy gap without supporting a DC Josephson effect between two superconducting reservoirs.

For an elementary interpretation, assume an opaque barrier, approximately constant normal-electrode density of states, and an energy-independent tunneling matrix element over the range probed. Write the superconducting density of states divided by its normal-state value as $n_s(E)$, with $E$ measured from its chemical potential. A signed voltage convention chosen for positive normal-electrode injection giveswhere $f$ is the Fermi-Dirac distribution at a common temperature and $R_N$ is the normal-state junction electrical resistance. This current convention is local to the NIS measurement. The expression counts occupied initial and empty final states; it is a quasiparticle transport model, not a current-phase relation of a superconducting weak link.

An original analytic illustration uses the ideal fully gapped BCS theory spectrum at zero temperature, with positive gap edge $\Delta$:For positive $V$, the occupation difference restricts the integral to $0<E<eV$. Since $d\sqrt{E^2-{\Delta }^2}/dE=E/\sqrt{E^2-{\Delta }^2}$, integration and odd extension giveThe threshold is $\Delta /e$ for this NIS model. In the corresponding zero-temperature single-electron process between two fully gapped superconductors, creating excitations on both sides instead requires $|eV|\ge {\Delta }_1+{\Delta }_2$. That quasiparticle threshold does not forbid coherent pair electric current below it. At finite temperature, thermally populated quasiparticles soften the simple threshold argument.

At zero temperature in the NIS approximation, $R_{N}d{I}_{\mathrm{qp}}/dV=n_s(eV)$ away from the singular gap edge. Thus a voltage sweep probes the excitation density of states. The ideal divergence is rounded in real measurements, and at nonzero temperature the derivative samples a thermally broadened range of energies. For $|eV|>\Delta$, the model has $V{I}_{\mathrm{qp}}>0$: electrical work creates excitations and is dissipated on relaxation. This distinguishes its steady transport from the conservative Josephson coupling energy.

Ivar Giaever's gap experiment used a metal–insulator–metal sandwich. His lecture describes evaporating aluminium onto glass, briefly exposing it to air to form an oxide barrier, then evaporating lead cross-strips. Cooling in liquid helium made the lead superconducting while the aluminium stayed normal in the measurements compared. A voltmeter and ammeter supplied the junction electric potential difference and electric current readouts. Thick oxides initially gave unmeasurably small electric currents; the thinner barrier made the measurement practical. Temperature comparisons and a subsequent controlled magnetic field test changed the current-voltage characteristic with the superconducting state. ^[ref]

The 1960 letter compares measurements at $4.2$ and $1.6\mathrm{K}$. An applied parallel magnetic field of $2.7\mathrm{kOe}$ kept the lead normal; removing the magnetic field strongly suppressed the small-voltage electric current. Figure 2 divides the superconducting $dI/dV$ by the normal-state slope. The letter calls its gap estimates preliminary and notes a temperature-dependent broadened peak. It also flags a limitation of interpreting tunneling directly through the density of states; the ideal NIS calculation above states additional assumptions explicitly. ^[ref]

The central inference is that the barrier lets electric current interrogate available quasiparticle states. Suppression at small electric potential difference and the rise near the gap edge support a gapped spectrum; tracking the superconducting state helps distinguish that feature from an arbitrary nonlinear barrier. A leakage path through a metallic short, imperfect barrier, or an energy-dependent tunneling matrix element limits a literal density of states interpretation. The preparation and state controls therefore matter as much as seeing a nonlinear current-voltage characteristic.