Ever-present Majorana bound state in a generic one-dimensional superconductor with odd number of Fermi surfaces

Formalism of general continuum models with boundary conditions, propagation of bound states from nontrivial to trivial topological classes, and the general surface-state structure near one node of a Weyl semimetal

“…15 and for 1D C + charge-conjugation-symmetric superconductors with one Fermi surface in Ref. [19].) Such model has one rightand one left-moving mode and there is just one BC relation between them.…”

“…Together with the Hamiltonian of the most general form, these general BCs provide the continuum model of the most general form for a class-A system with a boundary. If present, symmetries can also be naturally incorporated [14,15,19] into the formalism of general BCs. Symmetries typically provide additional constraints, which lead to subfamilies of general BCs that satisfy these symmetries.…”

“…For continuum models, this description comes down to determining proper boundary conditions (BCs), formulated as linear homogeneous relations between the wave-function components and their derivatives at the boundary. It has been understood for quite some time [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] that BCs arise as the consequence of the fundamental principle of quantum mechanics: norm conservation of the wave function during the time evolution described by the Schrödinger equation, which leads to the hermiticity requirement for the Hamiltonian, which in turn leads to the conservation of the probability current at the boundary. This understanding naturally leads to the notion of general BCs, as a family of all possible BCs (for a given Hamiltonian) that satisfy the current-conservation principle.…”

“…Previously, general BCs have been derived from the current-conservation principle and used to study the bound-, edge-, or surface-state structures for specific continuum models: for the 1D quadratic-in-momentum one-component model [5] (a textbook nonrelativistic Schrödinger particle); for the 3D quadratic-in-momentum multi-component model [6], in the context of semiconductors; for the linear-in-momentum two-component model, in the context of 2D semimetals [3,14], 2D quantum anomalous Hall (QAH) systems [15], graphene [17], 1D insulators [13], and 3D Weyl semimetals [11,12]; for the linear-in-momentum four-component model of graphene [7][8][9][10] and 3D Dirac materials [18]; for the 3D quadratic-in-momentum two-component model of Weyl semimetals [16]; for the 1D linear-in-momentum four-component model of superconductors with one Fermi surface [19].…”

Intrinsic emergence of Majorana modes in Luttinger j=3/2 systems

“…It has been predicted that a semiconducting nanowire with s-wave proximitized SC and spin-orbit coupling (SOC) can host MBSs at its boundaries [4,[14][15][16][17][18]. These appear in a topological phase after a Zeeman field, perpendicular to the SOC field, inverts the SC gap.…”