# 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 ${\displaystyle G=2e^{2}/h}$. The current in a wire is the velocity of the electrons multiplied by the charge and number per unit length, ${\displaystyle I=veN/L}$ or ${\displaystyle G=veN/LV}$. This gives a conductance of ${\displaystyle G=ve^{2}N/LE}$. In nano scale bridges the conductance falls in discrete steps of multiples of the quantum conductance ${\displaystyle G=2e^{2}/h}$.