p_x+ip_y超导体中涡旋芯马约拉纳与手性边缘的耦合：非单调谱重组与相干费米子宇称动力学
Vortex-core Majorana coupling to a chiral edge in a $p_x+ip_y$ superconductor: Nonmonotonic spectral reorganization and coherent fermion-parity dynamics
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中文总结 AI 辅助
该研究分析p_x+ip_y超导体中涡旋-边缘耦合的非单调谱重组，发现保留范数大不代表谱集中或持久宇称记忆，为马约拉纳量子操作提供依据。
中文摘要 AI 辅助
我们研究有限二维p_x+ip_y超导盘中，涡旋-边缘耦合如何随涡旋-边界间距d重组其低能部分，并探究这种重组对给定涡旋芯马约拉纳波包相关宇称记忆的意义，该波包是基于马约拉纳的量子操作的资源。Bogoliubov-de Gennes计算显示，最低正能有限圆盘本征态的芯-边缘重组呈非单调特性，在d≈7ξ处（ξ为相干长度）变化尤为迅速。为将该本征态重组与给定态的谱表示区分，我们将中心涡旋芯参考波包刚性平移至每个固定涡旋位置，限制其在目标圆盘内，且不经中间归一化地投影到粒子-空穴完备的低能子空间。对于Δ₀/E_F=0.36、圆盘半径R=30ξ的情况，在4.25≤d/ξ≤8.25的6个采样间距下，所得保留范数均超过0.98；而根据d的不同，谱权重可集中于零能、分散在多个低能级，或由有限能权重主导。相应地，带符号宇称关联函数呈现缓慢时间变化、快速相干退相，或符号变化振荡，后期可能出现有限尺寸重现。因此，大的保留范数本身并不意味着谱集中或持久的宇称记忆。
英文摘要
We study how vortex--edge coupling reorganizes the low-energy sector of a finite two-dimensional \(p_x+ip_y\) superconducting disk as a function of the vortex--boundary separation \(d\) and examine what this reorganization implies for the parity memory associated with a prescribed vortex-core Majorana wave packet, a resource relevant to Majorana-based quantum operations. Bogoliubov--de Gennes calculations reveal nonmonotonic core--edge reorganization of the lowest positive-energy finite-disk eigenstate, with particularly rapid variation near \(d\simeq7ξ\), where \(ξ\) is the coherence length. To separate this eigenstate reorganization from the spectral representation of a prescribed state, we rigidly translate a centered-vortex core-reference packet to each fixed vortex position, restrict it to the target disk, and project it, without intermediate normalization, onto the particle-hole-complete low-energy subspace. For \(Δ_0/E_F=0.36\) and disk radius \(R=30ξ\), the resulting retained norm exceeds \(0.98\) at all six sampled separations, \(4.25\leq d/ξ\leq8.25\), while, depending on \(d\), the spectral measure is concentrated near zero energy, fragmented over several low-energy levels, or dominated by finite-energy weight. Correspondingly, the signed parity correlator displays slow temporal variation, rapid coherent dephasing, or sign-changing oscillations, with possible finite-size recurrences at later times. Thus a large retained norm does not by itself imply spectral concentration or persistent parity memory.
发表机构
- Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）
- School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
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