论文标题
在分析可解决的两波段模型中调整$ p $ - 波的超导性的拓扑
Tuning the topology of $p$-wave superconductivity in an analytically solvable two-band model
论文作者
论文摘要
我们在方格上介绍并解决了两种无旋转费米的模型，并用$ p_x $ - 波配对。该模型将每个plaquette的半流量量化和弱耦合的基塔夫链减少到众所周知的扩展Harper-Hofstadter模型。我们表明，其相图包含拓扑非平凡的弱配对阶段以及一个微不足道的强配对阶段，因为配对振幅和跳跃的比率被调整了。将定期驾驶引入模型，我们观察到一系列具有良好定义的准式差距的cascade阶段，并在零或$π$ -GAP或两者兼有手性Majoragan Edge模式。获得了动力拓扑不变的，以表征每个阶段，并解释在异常阶段中的边缘模式的出现，在此阶段中，所有的否定段带的Chern数为零。分析解决方案是通过利用模型的广义镜子对称性来实现的，从而使有效的哈密顿量分解为磁场中的旋转$ 1/2 $的对称性，并且环路单位算子成为自旋旋转。我们进一步将动态不变性显示为HOPF链接数字。
We introduce and solve a two-band model of spinless fermions with $p_x$-wave pairing on a square lattice. The model reduces to the well-known extended Harper-Hofstadter model with half-flux quanta per plaquette and weakly coupled Kitaev chains in two respective limits. We show that its phase diagram contains a topologically nontrivial weak pairing phase as well as a trivial strong pairing phase as the ratio of the pairing amplitude and hopping is tuned. Introducing periodic driving to the model, we observe a cascade of Floquet phases with well defined quasienergy gaps and featuring chiral Majorana edge modes at the zero- or $π$-gap, or both. Dynamical topological invariants are obtained to characterize each phase and to explain the emergence of edge modes in the anomalous phase where all the quasienergy bands have zero Chern number. Analytical solution is achieved by exploiting a generalized mirror symmetry of the model, so that the effective Hamiltonian is decomposed into that of spin-$1/2$ in magnetic field, and the loop unitary operator becomes spin rotations. We further show the dynamical invariants manifest as the Hopf linking numbers.
