We model theoretically a two-dimensional electron gas (2DEG) covered by a superconductor and demonstrate that topological superconducting channels are formed when stripes of the superconducting layer are removed. As a consequence, Majorana bound states (MBS) are created at the ends of the stripes. We calculate the topological invariant and energy gap of a single stripe, using realistic values for an InAs 2DEG proximitized by an epitaxial Al layer. We show that the topological gap is enhanced when the structure is made asymmetric. This can be achieved by either imposing a phase difference (by driving a supercurrent or using a magnetic-flux loop) over the strip or by replacing one superconductor by a metallic gate. Both strategies also enable control over the MBS splitting, thereby facilitating braiding and readout schemes based on controlled fusion of MBS. Finally, we outline how a network of Majorana stripes can be designed.PACS numbers: 71.10. Pm, 74.50.+r, Majorana bound states (MBS) are states localized at the edges of topological superconductors [1][2][3][4]. They have nonlocal properties that may be utilized for storage and manipulation of quantum information in a topologically protected way [5][6][7]. However, the realization of MBS requires superconducting p-wave pairing, which appears only in exotic materials. Therefore, there is currently a search for ways to engineer p-wave pairing by combining s-wave superconductors with strong spinorbit materials. Recent experiments looked for evidence of MBS in, for example, semiconducting nanowires [8][9][10][11][12][13][14], topological insulators [15], and magnetic atom chains [16, 17]. These systems may also allow demonstration experiments of the nonlocal properties of MBS, for example using recent suggestions for controlling MBS in prototypical architectures [18][19][20][21][22][23]. However, to go beyond basic demonstration experiments a scalable and flexible platform for large-scale MBS networks is needed.Here, we suggest one such flexible platform based on a two-dimensional electrons gas (2DEG) with strong spinorbit coupling in proximity to a superconductor [24]. Such structures, reviewed in Ref. [25], have been realized by contacting InAs surface inversion layers [26,27] We show how to design and control MBS in a pS system with a stripe of the superconducting layer removed to form an effective one-dimensional topological supercon- ductor. This forms a pS-N-pS junction as sketched in Fig. 1(a), which can be fabricated by standard lithographic techniques. We show, similar to other semiconductorbased setups [34][35][36][37][38], that this system undergoes several topological phase transitions when increasing a magnetic field parallel to the stripe for parameters readily available in the lab. We base our findings on a numerical tightbinding calculation of the energy spectrum, the topological invariant, as well as transport calculations [33]. We discuss how the topological energy gap depends on various parameters, which is vital for the topological protection ...