# Electromigrated nanogaps

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A nanosized contact formed by electromigration acts like a waveguide for electrons. The nanocontact essentially acts like a one-dimensional wire with a conductance of $G =2e^2/h$. The current in a wire is the velocity of the electrons multiplied by th charge and number per unit length, $I = veN/L$ or $G=veN/LV$. This gives a conductance of $G=ve^2N/LE$. In nano scale bridges the conductance falls discrete steps of multiples of the quantum conductance $G =2e^2/h$.