Magneto-quantum-resistance oscillations in tunnel-coupled double quantum wells in tilted magnetic fields: Variable Landau biladders

We present a linear-response theory of magneto-quantum-resistance oscillations of the in-plane resistances $R_{\mathrm{xx}}$ and $R_{\mathrm{yy}}$ in two coupled quasi-two-dimensional electron layers in tilted magnetic fields $\mathbf{B}{=(B}_{\parallel }{,B}_{\perp }),$ and explain recent data from ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ double quantum wells. In this system, the electrons are in the two tunnel-split ground sublevels. The cyclotron masses of the two orbits on the Fermi surface have opposite dependences on the in-plane field $B_{\parallel }:$ one increases monotonically, while the other decreases as a function of $B_{\parallel }$ in the regime of interest. As a result, the rungs of one Landau ladder sweep up through the Fermi level, while those of the other Landau ladder sweep down when $B_{\parallel }$ is increased at a fixed perpendicular field $B_{\perp }.$ Ridges are obtained in the three-dimensional plots of both $R_{\mathrm{xx}}$ and $R_{\mathrm{yy}}$ and the density of states versus ${(B}_{\parallel }{,B}_{\perp })$ due to Fermi-level crossing by the rungs of the Landau ladders. Giant peaks are obtained when two ridges intersect each other. The ${(B}_{\parallel }{,B}_{\perp })$ dependence of $R_{\mathrm{xx}}$ as well as theoretical evidence of magnetic breakdown yields good agreement with recent data from ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ double quantum wells.