arXiv:1408.1831v1 [cond-mat.mes-hall] 8 Aug 2014 Crossing of spin energy sublevels in InSb-based stepped quantum wells under in-plane magetic field: Intersubband optical absorption. A.Hern´andez-Cabrera ∗ and P. Aceituno † Dpto. F´ ısica B´asica, Universidad de La Laguna, La Laguna, 38206-Tenerife, Spain, and Instituto Universitario de Estudios Avanzados (IUdEA) en F´ ısica At´ omica, Molecular y Fot´ onica, Universidad de La Laguna, La Laguna, 38206 Tenerife, Spain (Dated: August 11, 2014) We study the energy dispersion relations for InSb- based stepped quantum wells when Zeeman splitting is present. Spin level crossing can be achieved by applying certain pairs of transverse electric and in-plane magnetic field values. We use an im- proved 4 × 4 version of the Transfer Matrix Approach which, together with first order boundary conditions, leads to a momentum dependent pseudo Wronskyan matrix. Roots of this matrix give the dispersion relations showing spin level crossings and anticrossings. In order to analyze the effects of spin crossing we calculate linear and non-linear absorption coefficients for transitions between the four deepest sublevels after Zeeman splitting. We also consider depolarization shift caused by different charge concentrations. Results show a noticeable difference on the structure of the intersubband absorption spectrum when spin sublevel crossing is present. PACS numbers: 72.25.-b; 73.21.-b * Electronic address: ajhernan@ull.edu.es † Electronic address: paceitun@ull.edu.es