A phenomenology condition other than zero resistance and a possible pairing mechanism of holes-electrons for superconductivity

The underlying mechanism of unconventional high-temperature superconductivity is a great challenge to condensed matter physics. However, zero dissipation of electric current is the commonness of superconductors whether they are conventional or unconventional ones. In this presentation, the Ohm law in a nonmagnetic conductor is derived from a set of modified electromagnetic equations that involve Maxwell ones. It is found that, the steady current dissipation in a conductor can be expressed as ${J} \cdot {E} = {c^2}\rho /(u{\epsilon _r}{\mu _r})$,whereJ,E,$\rho$,c,u,${\epsilon_r}$and${\mu_r}$ are the electric current density, electric field strength, free electric charge density, light speed in vacuum, effective mobility of carriers, relative dielectric constant and permeability, respectively. This relation indicates that, in a steady state of $J\mathrm{\ne }0$, if $\rho =0$, then $J\cdot E=0$ and the conductor comes into a superconducting state. It is also found that the condition $\rho =0$ is valid for superconductivity of magnetic materials and is a sufficient than necessary one. When $\rho =0$ the (involving the Hall electric field strength) becomes zero, which solves the pending problem why vanishing of Hall-effect in some superconducting states, besides, suggests a superconductive pairing mechanism of holes and electrons. Two examples of superconducting state under the condition $\rho =0$ are discussed.