Magnetic breakdown and Landau-level spectra of a tunable double-quantum-well Fermi surface

By measuring longitudinal resistance, we map the Landau-level spectra of double quantum wells as a function of both parallel (${\mathrm{B}}_{\mathrm{\parallel }}$) and perpendicular (${\mathrm{B}}_{\mathrm{\perp }}$) magnetic fields. In this continuously tunable highly nonparabolic system, both the cyclotron mass and Fermi energy of the two Fermi surface orbits change in opposite directions with ${\mathrm{B}}_{\mathrm{\parallel }}$. The two corresponding ladders of Landau levels formed at finite ${\mathrm{B}}_{\mathrm{\perp }}$ thus exhibit multiple crossings. A third set of Landau levels, independent of ${\mathrm{B}}_{\mathrm{\parallel }}$, arises from magnetic breakdown of the Fermi surface. Semiclassical calculations show good agreement with the data.