Platforms for creating Majorana quasiparticles rely on superconductivity and breaking of time-reversal symmetry. By studying continuous deformations to known trivial states, we find that the relationship between superconducting pairing and time reversal breaking imposes rigorous bounds on the topology of the system. Applying these bounds to $s$-wave systems with a Zeeman field, we conclude that a topological phase transition requires that the Zeeman energy at least locally exceed the superconducting pairing by the energy gap of the full Hamiltonian. Our results are independent of the geometry and dimensionality of the system.

中文翻译：

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超导体拓扑转换的最小塞曼场要求

创建Majorana准粒子的平台依赖于超导性和打破时间反转对称性。通过研究连续变形到已知的琐碎状态，我们发现超导配对和时间反转中断之间的关系对系统的拓扑结构施加了严格的界限。将这些边界应用于具有塞曼场的波系统，我们得出的结论是，拓扑相变要求塞曼能量至少局部超过超导对，并超过整个哈密顿量的能隙。我们的结果与系统的几何形状和尺寸无关。