Why counterflow dissipation stays finite in quantum Hall exciton condensates
In plain words
Two closely spaced electron layers in a strong magnetic field, each half filled, form an exciton condensate in which electrons of one layer bind to empty states (holes) of the other. Opposite currents in the two layers should then flow without resistance, yet a residual resistance persists at the lowest temperatures.
Precise statement
In GaAs double quantum wells and graphene double layers at total filling $\nu_{T} = 1$ with layer separation $d/l_{B}$ below the critical value (about 1.8 to 2 in GaAs; $l_{B}$ is the magnetic length), the counterflow longitudinal resistance stays finite and activated or saturating as $T \to 0$, and interlayer tunneling has a finite critical current. Identify the dissipation mechanism (thermally activated or disorder-pinned meron-antimeron vortices, charged-quasiparticle leakage, puddles from density inhomogeneity) and predict the counterflow resistance versus $T$ and $d/l_{B}$. An answer is a model fitting $R_{CF}(T, d/l_{B})$ in both GaAs and graphene devices.
What would settle it
Counterflow resistance measured versus temperature, disorder and $d/\ell_{B}$ in devices of controlled disorder, matched by a vortex or quasiparticle transport calculation.
Status in the literature
Graphene double-layer experiments since 2017 show the same finite counterflow dissipation at higher temperatures than GaAs, without a settled mechanism.