Excitonic Josephson effect in double-layer graphene junctions

Abstract

We show that double-layer graphene (DLG), where an external potential induces a charge imbalance between n-and p-type layers, is a promising candidate to realize an exciton condensate in equilibrium. To prove this phenomenon experimentally, we suggest coupling two DLG systems, separated by a thin insulating barrier, and measuring the excitonic Josephson effect. For this purpose we calculate the ac and dc Josephson currents induced by tunneling excitons and show that the former only occurs when the gate potentials of the DLG systems differ, irrespective of the phase relationship of their excitonic order parameters. A dc Josephson current develops if a finite order-parameter phase difference exists between two coupled DLG systems with identical gate potentials. The search for the long ago predicted excitonic insulator (EI) state has recently stimulated a lot of experimental work, e.g., on pressure sensitive rare-earth chalgogenides, transitionmetal dichalcogenides, or tantalum chalcogenides [1][2][3][4][5]. Theoretically the excitonic instability is expected to happen, when semimetals with very small band overlap or semiconductors with very small band gap are cooled to very low temperatures [6,7]. To date there exists no free of doubt realization of the EI, however, and even the applicability of the original EI scenario to the above material classes is a controversial issue [5,[8][9][10]. There are serious arguments why the EI in these bulk materials, if present at all, resembles rather a charge-density-wave state than a "true" superfluid exciton condensate exhibiting off-diagonal long-range order [11,12].On these grounds a nonambiguous experimental proof of a macroscopic phase coherent exciton condensate would be highly desirable. Spectroscopic analyses have not established an exciton condensate so far. The characteristics of junction devices, where at least in one component an EI is realized, may lead to valuable insights in this respect [13]. Due to the proximity effect a high resistance should appear across a semimetal-EI junction that distinctly differs from that of a semimetal-semiconductor device [14]. In coupled quantum wells, Josephson oscillations should accompany exciton condensation [15,16]. Here we will pursue a similar idea, namely, that a Josephson-type tunnel current might appear when two EI systems are coupled to each other by a thin insulating barrier such that coherence is established between the condensates. Two-layer systems of spatially separated electrons and holes that feature an attractive interlayer electron-hole coupling are particularly suitable for a Josephson-type tunnel experiment. In this case a condensate of excitons might occur when the tunneling between the layers is negligible, but the corresponding Coulomb interaction is not [17]. Double-layer systems thereby inhibit the obstacles coming from interband transitions or the coupling to phonons, which inevitably occur in bulk materials and prevent a possible exciton condensation by destroying the U (1) symmetry [12,18,19]. It is al...

Excitonic Tunneling in the AB-bilayer Graphene Josephson Junctions

“…This statement is also in agreement with the recent work in Ref. [66], where it has been shown that the excitonic Josephson current becomes extremely small before the EI state breaks down. A detailed analysis of the role of the CNP point W C = 1.48999γ 0 , for the case of interaction balanced BLGs, is given in Fig.…”

“…The excitonic Josephson tunneling effects and thermal transport properties in the electron-hole type double-layer graphene junctions, separated by a dielectric layer, have been recently considered in Refs. [66,67].…”

Role of the compensating current in the weak Josphson coupling regime: An extended study on excitonic Josephson junctions

“…Josephson effect is particularly attractive to condensed matter researchers because it serves as the striking manifestation of coherent condensation and the promising candidate for quantum technology. The unrelenting and strong attention has been recently received in opticallyexcited exciton or exciton-polariton cold gases [1][2][3][4][5][6][7] and graphene electron-hole bilayer exciton 8,9 . The quantum Hall bilayer, which is the most practicable one to achieve the exciton condensation , however, remains not studied extensively in the land of Josephson effect to date.…”

Josephson effect as signature of electron-hole superfluidity in bilayers of van der Waals heterostructures

“…Here we propose that the Josephson effect [10,11] can provide an unambiguous signal of the electron-hole superfluidity. In a Josephson junction, two superfluids are separated by a thin potential barrier, and a phase difference between the superfluids leads to a steady current flow.…”