  We describe XNOR gate response in a mesoscopic ring threaded by a magnetic
flux $\phi$. The ring is attached symmetrically to two semi-infinite
one-dimensional metallic electrodes and two gate voltages, viz, $V_a$ and
$V_b$, are applied in one arm of the ring which are treated as the inputs of
the XNOR gate. The calculations are based on the tight-binding model and the
Green's function method, which numerically compute the conductance-energy and
current-voltage characteristics as functions of the ring-to-electrode coupling
strength, magnetic flux and gate voltages. Our theoretical study shows that,
for a particular value of $\phi$ ($=\phi_0/2$) ($\phi_0=ch/e$, the elementary
flux-quantum), a high output current (1) (in the logical sense) appears if both
the two inputs to the gate are the same, while if one but not both inputs are
high (1), a low output current (0) results. It clearly exhibits the XNOR gate
behavior and this aspect may be utilized in designing an electronic logic gate.

Mesoscale and Nanoscale Physics;Materials Science