**Abstract**

Exciton condensate states can be realized in systems consisting of two closely spaced layers, where one of the layers has excess electrons and the other equal number of excess holes. A particularly well-studied system for this purpose is the double-layer quantum Hall state occurring when the Landau level filling is fractional in each separate layer but the total filling is an integer [1]. This state is theoretically expected to realize a Bose-Einstein condensate of excitons, which is characterized by remarkable electronic properties such as counterflow superconductivity and a tunneling supercurrent similar to the Josephson current between two superconductors. Experimentally, a spectacular enhancement of the tunneling conductance at small interlayer bias voltage and almost dissipationless counterflow currents have been observed. In this talk, I will review the experimental observations in quantum Hall exciton condensates and I will show that they can be well-described using a theory which takes into account disorder-induced fractionally charged topological defects (merons) [2]. I will also discuss the analogies and differences between the Josephson effects in superconductors and double-layer exciton condensates.

Finally, I will talk about some interesting recent predictions and observations related to transport phenomena in double-layer exciton condensates. In particular, I will discuss our theoretical prediction of a confinement-deconfinement transition in helical quantum Hall exciton condensates [3] and the experimental observation of Josephson-like tunneling in double bilayer graphene in the absence of magnetic field [4].

[1] J. P. Eisenstein and A. H. MacDonald, “Bose–Einstein Condensation of Excitons in Bilayer Electron Systems,” Nature 432, 691 (2004).

[2] T. Hyart and B. Rosenow, “Quantitative Description of Josephson-Like Tunneling in 𝜈T=1 Quantum Hall Bilayers,” Phys. Rev. B 83, 155315 (2011).

[3] D. I. Pikulin, P. G. Silvestrov, and T. Hyart, “Confinement-Deconfinement Transition Due to Spontaneous Symmetry Breaking in Quantum Hall Bilayers,” Nat. Commun. 7, 10462 (2016).

[4] G. W. Burg, N. Prasad, K. Kim, T. Taniguchi, K. Watanabe, A. H. MacDonald, L. F. Register, and E. Tutuc, “Strongly Enhanced Tunneling at Total Charge Neutrality in Double-Bilayer Graphene-WSe2 Heterostructures,” Phys. Rev. Lett. 120, 177702 (2018).