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We calculate the phase diagram of a model for topological superconducting wires with local s-wave pairing, spin-orbit coupling $vec{lambda}$ and magnetic field $vec{B}$ with arbitrary orientations. This model is a generalized lattice version of the one proposed by Lutchyn $textit{et al.}$ [Phys. Rev. Lett. $textbf{105}$ 077001 (2010)] and Oreg $textit{et al.}$ [Phys. Rev. Lett. $textbf{105}$ 177002 (2010)], who considered $vec{lambda}$ perpendicular to $vec{B}$. The model has a topological gapped phase with Majorana zero modes localized at the ends of the wires. We determine analytically the boundary of this phase. When the directions of the spin-orbit coupling and magnetic field are not perpendicular, in addition to the topological phase and the gapped non topological phase, a gapless superconducting phase appears.
We characterize the Majorana zero modes in topological hybrid superconductor-semiconductor wires with spin-orbit coupling and magnetic field, in terms of generalized Bloch coordinates $varphi, theta, delta$, and analyze their transformation under SU(
For systems that can be modeled as a single-particle lattice extended along a privileged direction as, e.g., quantum wires, the so-called eigenvalue method provides full information about the propagating and evanescent modes as a function of energy.
The importance of models with an exact solution for the study of materials with non-trivial topological properties has been extensively demonstrated. Among these, the Kitaev model of a one-dimensional $p$-wave superconductor plays a guiding role in t
We study a one-dimensional topological superconductor, the Kitaev chain, under the influence of a non-Hermitian but $mathcal{PT}$-symmetric potential. This potential introduces gain and loss in the system in equal parts. We show that the stability of
We study a one-dimensional wire with strong Rashba and Dresselhaus spin-orbit coupling (SOC), which supports Majorana fermions when subject to a Zeeman magnetic field and in proximity of a superconductor. Using both analytical and numerical technique