Pseudogap phase and fractionalization: Predictions for Josephson junction setup

The pseudogap regime of the underdoped cuprates arguably remains one of the\nmost enigmatic phenomena of correlated quantum matter. Recent theoretical ideas\nsuggest that a pair density wave (PDW) or a "fractionalized PDW" could be a key\ningredient for the understanding of the pseudogap physics. These ideas are to\nbe contrasted to the scenario where charge density wave order and\nsuperconductivity coexist at low temperatures. In this paper, we present a few\ntests to compare the two scenarios in a Josephson junction setup. For a PDW\nscenario, we observe a beat-like structure of AC Josephson current. The\nadditional frequencies for the AC Josephson current appear at the half-odd\ninteger multiple of the standard Josephson frequency. We can extract the\nmodulation wavevector of the PDW state by studying the average Josephson\ncurrent. Furthermore, the usual sharp Shapiro steps break down. In contrast,\nthese signatures are absent for the simple coexistence of orders. Any detection\nof such signatures in a similar experimental setup will strongly support the\nPDW scenario for the pseudogap phase.\n