The electromagnetic properties of superconductors

The London-Ginzburg-Landau concept of superconductivity as a macroscopic quantum state is reviewed. Experimental measurements are then discussed of resistance below $T_c$, and of enhanced diamagnetism above $T_c$, both caused by thermodynamic fluctuations away from the Ginzburg-Landau state of lowest free energy. Next the limitations on superconductivity at nonzero frequencies are reviewed: normal electron dissipation $\propto {\omega }^2$, and strong absorption above the energy gap frequency. Sum rule arguments relate the superfluid response at low frequencies to the gap; effects of strong electron-phonon coupling are also found. Finally, results of recent work on the resistive state of superconducting filaments above the critical current are summarized.