Pseudospin Soliton in the $ u=1$ Bilayer Quantum Hall State

We investigate a domain structure of pseudospins, a soliton lattice in the bilayer quantum Hall state at total Landau level filling factor $ u =1$, in a tilted magnetic field, where the pseudospin represents the layer degree of freedom. An anomalous peak in the magnetoresistance $R_{xx}$ appears at the transition point between the commensurate and incommensurate phases. The $R_{xx}$ at the peak is highly anisotropic for the angle between the in-plain magnetic field $B_parallel $ and the current, and indicates a formation of the soliton lattice aligned parallel to $B_parallel $. Temperature dependence of the $R_{xx}$ peak reveals that the dissipation is caused by thermal fluctuations of pseudospin solitons. We construct a phase diagram of the bilayer $ u =1$ system as a function of $B_parallel$ and the total electron density. We also study effects of density imbalance between the two layers.