Josephson Junction: 18 flashcards

A Josephson junction is a device consisting of two superconductors separated by a thin insulating barrier (typically a few nanometers thick) through which Cooper pairs can tunnel quantum mechanically.

Cooper pairs are pairs of electrons bound together at low temperatures by an attractive interaction mediated by lattice vibrations (phonons), forming the charge carriers in a superconductor.

The DC Josephson effect is the phenomenon where a supercurrent flows across a Josephson junction with zero voltage across it, up to a critical current $I_c$.

The AC Josephson effect occurs when a constant DC voltage $V$ is applied across a Josephson junction, causing an alternating supercurrent with frequency $f = \frac{2eV}{h}$, where $e$ is the electron charge and $h$ is Planck's constant.

The critical current $I_c$ is the maximum supercurrent that can flow across a Josephson junction without a voltage appearing across it.

The Josephson penetration depth $\lambda_J$ is the characteristic length over which an external magnetic field penetrates a Josephson junction, given by $\lambda_J = \sqrt{\frac{\Phi_0}{2\pi \mu_0 j_c d}}$, where $\Phi_0$ is the flux quantum, $j_c$ is the critical current density, and $d$ is the junction thickness.

The flux quantum is $\Phi_0 = \frac{h}{2e} \approx 2.07 \times 10^{-15}$ Wb, representing the smallest unit of magnetic flux that can be quantized in a superconductor.

The gauge-invariant phase difference $\phi$ is the difference in the phase of the superconducting order parameter across the junction, adjusted for the vector potential, and it determines the supercurrent via $I = I_c \sin\phi$.

The DC Josephson relation is $I = I_c \sin\phi$, where $I$ is the supercurrent, $I_c$ is the critical current, and $\phi$ is the gauge-invariant phase difference.

The AC Josephson relation is $\frac{d\phi}{dt} = \frac{2eV}{\hbar}$, where $\phi$ is the phase difference, $V$ is the voltage across the junction, $e$ is the electron charge, and $\hbar$ is the reduced Planck constant.

A SQUID (Superconducting Quantum Interference Device) is a highly sensitive magnetometer that uses one or two Josephson junctions in a superconducting loop to measure extremely small magnetic fields via quantum interference.

The Josephson inductance is $L_J = \frac{\Phi_0}{2\pi I_c \cos\phi}$, representing the effective inductance of a Josephson junction due to the phase-dependent supercurrent.

The Resistively and Capacitively Shunted Junction (RCSJ) model describes a Josephson junction as an ideal Josephson element in parallel with a resistor $R$ and a capacitor $C$, used to analyze junction dynamics.

The plasma frequency is $\omega_p = \sqrt{\frac{2e I_c}{\hbar C}}$, representing the natural oscillation frequency of the phase difference in the RCSJ model.

The McCumber parameter is $\beta_c = \frac{2e I_c R^2 C}{\hbar}$, which characterizes the damping of a Josephson junction; $\beta_c \gg 1$ indicates underdamped behavior, $\beta_c \ll 1$ indicates overdamped.

The critical current $I_c$ depends on temperature as $I_c(T) \propto \Delta(T) \tanh\left(\frac{\Delta(T)}{2k_B T}\right)$ near $T_c$, where $\Delta(T)$ is the superconducting energy gap.

A Josephson vortex is a localized 2π phase twist in the phase difference across a long Josephson junction, carrying a single flux quantum $\Phi_0$, and can move under the influence of a bias current.

A magnetic field modulates the critical current of a Josephson junction, producing a diffraction-like pattern $I_c(B) = I_c(0) \left| \frac{\sin(\pi \Phi/\Phi_0)}{\pi \Phi/\Phi_0} \right|$, where $\Phi$ is the magnetic flux through the junction.