We investigate the emergence of topological superconductivity and Majorana zero modes in the two-dimensional electron gas formed at the (001) ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface. Using a realistic multiband tight-binding model that incorporates the $t_{2g}$ orbital structure together with atomic and Rashba spin-orbit couplings, we determine the topological phase diagrams for both fully two-dimensional and quasi-one-dimensional geometries. In the two-dimensional limit, we show that a finite out-of-plane magnetic-field component is required to drive a topological phase transition. In this case, the critical field is strongly band dependent, and for higher-lying bands it is controlled by the interplay of spin and orbital Zeeman effects, as well as atomic spin-orbit coupling. Although a purely in-plane field is insufficient to induce the topological transition in a full 2D system, we demonstrate that a lateral confinement relaxes this constraint. In this case, the character of the edge modes depends sensitively on the field orientation, with out-of-plane fields producing conventional counterpropagating chiral modes and transverse in-plane fields giving rise to copropagating antichiral modes. Finally, Majorana zero modes in LAO/STO nanowires with varying widths are analyzed. We demonstrate that subbands predominantly composed of $d_{yz/xz}$ orbitals exhibit exceptionally long localization lengths, which may preclude the observation of Majorana bound states in nanowires of typical experimental dimensions.

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• Multiband superconductivity
• Superconductivity
• Topological superconductors
• Two-dimensional electron gas
• Two-dimensional electron system
• BCS theory
• Tight-binding model