True large-separation coherence scale of the quantum Hall bilayer

Determine the exact large-$d/\ell$ dependence of the interlayer-coherence scale in the $\nu_T=1$ quantum Hall bilayer beyond uniform lowest-Landau-level Hartree–Fock theory, including the effects of intralayer composite-fermion correlations and gauge fluctuations.

Background

Uniform lowest-Landau-level Hartree–Fock theory predicts a coherent state at every finite separation and a coherence scale with a $1/d$ tail. The paper emphasizes that this tail omits the correlations present in the separately formed composite-fermion liquids at large separation.

The authors expect the true scale to be much smaller than the Hartree–Fock result, but they note that competing theories predict different asymptotic behavior, including exponential and algebraic laws. No controlled calculation selects among these possibilities.

References

The large-$d$ law is not settled: gauge-fluctuation treatments give an algebraic gap, $\Delta\propto1/d2$ up to logarithms, strongly reduced by pair breaking .

— Exciton superfluidity in two-dimensional bilayers at zero and high magnetic fields  (2610.22037 - Sarma et al., 15 Oct 2026) in Section 10.5, “Beyond Hartree-Fock at $\nu_T=1$: expectations”; Section 10.6, “What the zero-field results imply for $\nu_T=1$, and what they do not”

It is a conjecture, not a result of this paper. We expect HF to be qualitatively right in its main conclusion: there is no zero-temperature transition at a finite $d/\ell$ at which interlayer coherence is lost.

— Exciton superfluidity in two-dimensional bilayers at zero and high magnetic fields  (2610.22037 - Sarma et al., 15 Oct 2026) in Section 10.5, “Beyond Hartree-Fock at $\nu_T=1$: expectations”; Table 3, “Status of the results”