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Topological superconductors supporting Majorana Fermions with non-abelianstatistics are presently a subject of intense theoretical and experimentaleffort. It has been proposed that the observation of a half-frequency or afractional Josephson effect is a more reliable test for topologicalsuperconductivity than the search for end zero modes. Low-energy end modes canoccur accidentally due to impurities. In fact, the fractional Josephson effecthas been observed for the semiconductor nanowire system. Here we consider theac Josephson effect in a conventional s-wave superconductor-normalmetal-superconductor junction at a finite voltage. Using a Floquet-Keldyshtreatment of the finite voltage junction, we show that the power dissipatedfrom the junction, which measures the ac Josephson effect, can show a peak athalf (or even incommensurate fractions) of the Josephson frequency. A similarconclusion is shown to hold for the Shapiro step measurement. The ac fractionalJosephson peak can also be understood simply in terms of Landau-Zener processesassociated with the Andreev bound state spectrum of the junction.

On the possibility of the fractional ac Josephson effect in non-topological conventional superconductor-normal-superconductor junctions