  Mean-field theory predicts that bilayer quantum Hall systems at odd integer
total filling factors can have stripe ground states in which the top Landau
level is occupied alternately by electrons in one of the two layers. We report
on an analysis of the properties of these states based on a coupled Luttinger
liquid description that is able to account for quantum fluctuations of
charge-density and position along each stripe edge. The soft modes associated
with the broken symmetries of the stripe state lead to an unusual coupled
Luttinger liquid system with strongly enhanced low-temperature heat capacity
and strongly suppressed low-energy tunneling density of states. We assess the
importance of the intralayer and interlayer back-scattering terms in the
microscopic Hamiltonian, which are absent in the Luttinger liquid description,
by employing a perturbative renormalization group approach which re-scales time
and length along but not transverse to the stripes. With interlayer
back-scattering interactions present the Luttinger liquid states are unstable
either to an incompressible striped state that has spontaneous interlayer phase
coherence and a sizable charge gap even at relatively large layer separations,
or to Wigner crystal states. Our quantitative estimates of the gaps produced by
back-scattering interactions are summarized in Fig. [phase_diagram] by a
schematic phase diagram intended to represent predicted experimental findings
in very high mobility bilayer systems at dilution refrigerator temperatures as
a function of layer separation and bilayer density balance.
