ZrBr单层掺杂诱导的自旋/反常霍尔响应切换的重点在于把前置条件、操作顺序和容易误判的地方分清楚。

{"type":"doc","content":[{"type":"heading","attrs":{"id":"c3750cce-2f20-4560-961f-a5199cf4bfbd","textAlign":"inherit","indent":0,"level":1,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"ZrBr单层掺杂诱导的自旋/反常霍尔响应切换"}]},{"type":"paragraph","attrs":{"id":"dfe49baf-778c-4632-a5da-df82fc3da0c4","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"ADVANCED QUANTUM TECHNOLOGIES 2026"}]},{"type":"paragraph","attrs":{"id":"b3761726-179a-427d-bd0e-1367aa59f885","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"ZrBr单层掺杂诱导的自旋/反常霍尔响应切换"}]},{"type":"paragraph","attrs":{"id":"8741d16f-f41d-4159-98ef-7321f05abc28","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"Doping-Induced Switching Between Spin and Anomalous Hall Responses in ZrBr Monolayers"}]},{"type":"paragraph","attrs":{"id":"5921fc01-2858-444f-9445-bb534f61d437","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"导读 导读：通过第一性原理DFT与Wannier插值，系统研究了Ti、Ni、Nb掺杂对六方ZrBr单层电子结构、Berry曲率和霍尔输运的调控。原始ZrBr展示高SHC（91.23 ℏ/e·S/cm），Ti掺杂完全淬灭SHC，Ni掺杂诱导SHC→AHC反转（AHCz=−116.68 S/cm），Nb掺杂保留拓扑特征。该工作确立了掺杂ZrBr作为Berry曲率工程和可编程自旋电子学的多功能平台。"}]},{"type":"image","attrs":{"id":"8e259c14-af30-4366-9904-be2a6360d2c1","src":"https://developer.qcloudimg.com/http-save/audit-12559234/e69a512476f18a10e2efc38cb95f393b.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"bc458e6c-dbdf-4617-a877-7d2df3407aed","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"一、前言背景"}]},{"type":"paragraph","attrs":{"id":"ec7e3b65-3348-48f3-8b29-144b63317607","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"二维拓扑绝缘体与自旋霍尔效应"}]},{"type":"paragraph","attrs":{"id":"b8601c83-f470-4dd9-b3ad-be8fdd3a9447","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 量子自旋霍尔绝缘体（QSHI）：体态绝缘，边缘存在受时间反演对称性保护的无耗散自旋极化导电通道"}]},{"type":"paragraph","attrs":{"id":"1ed8db1f-63a1-4c18-b6d1-37e604662250","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 自旋霍尔效应（SHE）：通过自旋-轨道耦合将电荷流转换为横向纯自旋流——无需外磁场"}]},{"type":"paragraph","attrs":{"id":"1ede8e16-bf56-476f-abf1-2aa339116f11","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• SHC效率由Berry曲率决定：在Dirac点和能带反交叉附近达到峰值"}]},{"type":"paragraph","attrs":{"id":"6d9e768a-061d-49ed-9e20-0d14b4e80fe9","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 高通量计算已筛选出数千种候选SHC材料，但许多2D拓扑绝缘体面临窄带隙、低迁移率等实际挑战"}]},{"type":"paragraph","attrs":{"id":"4245db4f-3ee6-4146-8521-2cc566b2f96f","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 金属体系：更高电导率和更强自旋输运响应，但缺乏拓扑保护"}]},{"type":"paragraph","attrs":{"id":"438ac81b-16e6-4afb-8246-cea19d38030e","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"ZrBr单层：非Dirac拓扑特征的六方层状材料"}]},{"type":"paragraph","attrs":{"id":"6df4343e-37de-4a96-a62c-0b0444bba97b","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• ZrBr结晶为六方层状结构，a=3.53 Å，c=28.86 Å，Zr-Br层间距1.93 Å"}]},{"type":"paragraph","attrs":{"id":"0a9abaae-892a-4b5d-a12e-32f360cd5158","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 原始ZrBr：Z₂=1确认非平庸拓扑相，但Dirac锥略微抛物线化（非理想线性）"}]},{"type":"paragraph","attrs":{"id":"582d4739-fbaf-4f6b-8358-4f9756121fc7","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 高Fermi速度（8610 m/s）和显著SHC（~120 ℏ/e·S/cm @ 7 eV）"}]},{"type":"paragraph","attrs":{"id":"313592f9-6667-4fd4-aea6-747012029b3e","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 边缘态：Chern绝缘相，C=1，全局带隙内存在单一拓扑保护边缘模式"}]},{"type":"paragraph","attrs":{"id":"851dd37f-5595-4fff-a53b-69c52953bae6","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 核心问题：掺杂能否调控Berry曲率分布，实现SHC和AHC之间的可控切换？"}]},{"type":"paragraph","attrs":{"id":"242d9f3c-9b15-465b-8076-98a5780016ba","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"掺杂策略：Ti、Ni、Nb的电子结构效应"}]},{"type":"paragraph","attrs":{"id":"5d75b856-6806-43fa-8380-2236bc831389","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Ti（IV族，与Zr同族）：等电子掺杂，低原子质量 → 不同轨道能量 → 微妙电子重构"}]},{"type":"paragraph","attrs":{"id":"f1d2efb8-c9ad-43e8-aeed-a93a86205394","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Ni（X族）：大量额外d电子 → 重电子掺杂 磁性引入"}]},{"type":"paragraph","attrs":{"id":"839a5ea4-b88e-4d5b-a83c-1da73b516f73","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Nb（V族）：多一个价电子 → n型掺杂，Fermi面上移"}]},{"type":"paragraph","attrs":{"id":"f8393c7f-7b2b-418b-bd88-d8b26872d6d7","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 目标：系统揭示掺杂如何调制电子结构、重塑Berry曲率、诱导SHC/AHC之间的转变"}]},{"type":"paragraph","attrs":{"id":"ff64b4b6-d254-4956-8046-b15028c05baf","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"二、计算方法"}]},{"type":"paragraph","attrs":{"id":"70ae3d6e-82be-4cc0-89fb-7607daea045f","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"DFT与Wannier插值框架"}]},{"type":"paragraph","attrs":{"id":"aa2b26c5-9439-43b9-b550-1ac2d3f93ae7","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• DFT计算：Quantum ESPRESSO，模守恒赝势，GGA-PBE泛函，动能截断100 Ry"}]},{"type":"paragraph","attrs":{"id":"a6418497-0b31-497d-a1e7-45546b47daf7","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 弹性常数：Thermopw包计算，Born稳定性判据验证力学稳定性"}]},{"type":"paragraph","attrs":{"id":"7e92e5de-a96d-4c00-89df-e107fd598b20","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 声子谱：PHONOPY包，1×1×1超胞，评估动力学稳定性"}]},{"type":"paragraph","attrs":{"id":"290f50fe-3c75-478c-8871-e5623aed4b33","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 形成能：E_f判定热力学稳定性——Nb和Ti掺杂E_f为负 → 稳定；Ni掺杂E_f为正 → 不稳定"}]},{"type":"paragraph","attrs":{"id":"e0842f64-9c0a-43e6-95fe-dd3731366657","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Wannier90：最大局域化Wannier函数投影，50×50×50密集k点网格插值"}]},{"type":"paragraph","attrs":{"id":"54da8088-6fe9-44d2-8dd8-505b6a054f6e","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"SHC与AHC的Kubo公式"}]},{"type":"paragraph","attrs":{"id":"02e89098-f4c3-4985-987a-66667abb7eb3","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• SHC：自旋流算符 Ĵ_i^k = {v̂_i, σ̂_k}/2 的Berry曲率在Brillouin区的积分"}]},{"type":"paragraph","attrs":{"id":"8e9ffcb8-e8bd-4de3-91ea-9d8fcaad4c8a","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• AHC：速度算符v̂_α的Berry曲率积分——铁磁系统中破缺时间反演对称性"}]},{"type":"paragraph","attrs":{"id":"cca3e073-9ca2-4aa6-a461-413c0a8b9deb","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 自旋流算符中的Pauli矩阵σ̂_k对应自旋分量k（x, y, z）"}]},{"type":"paragraph","attrs":{"id":"fa10e434-dace-46df-9553-ac2c2c5772ab","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 零温近似：费米-狄拉克分布函数f_n(k)取阶跃函数"}]},{"type":"image","attrs":{"id":"69fb55c0-22fc-4557-9e2d-f4f865efbc57","src":"https://developer.qcloudimg.com/http-save/audit-12559234/572c30605da708f1ff1ee9c62fbbba0f.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"b7355340-6c3a-4e15-994c-37313198e1de","textAlign":"center","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"掺杂形成能——热力学稳定性判据"}]},{"type":"image","attrs":{"id":"424a82aa-447c-4318-b4ef-1ac443adacd1","src":"https://developer.qcloudimg.com/http-save/audit-12559234/bf52b747ef36b84b061dcea5deb7c06f.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"3ce1e13f-e257-49ad-ba6b-6c88ab536dc0","textAlign":"center","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"自旋霍尔电导率的Kubo公式——Berry曲率Ω^k_ij(k)在Brillouin区的积分"}]},{"type":"image","attrs":{"id":"e9ab0d01-b203-4da0-a3b9-92e32bd7ca74","src":"https://developer.qcloudimg.com/http-save/audit-12559234/829c1cdf55b645b78d0a6942986d87a3.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"766ab6cd-5bdb-4902-8bd9-0d2c2752b957","textAlign":"center","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"自旋流Berry曲率的定义——涉及自旋流算符和速度算符的矩阵元"}]},{"type":"image","attrs":{"id":"5139cce7-adde-4d64-8f32-3e9ce0a7e4fd","src":"https://developer.qcloudimg.com/http-save/audit-12559234/ed013fe280433df49944071a8f21e1c6.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"f0f2510a-d537-46f2-b50a-084f1269f792","textAlign":"center","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"反常霍尔电导率——破缺时间反演对称性下的Berry曲率积分"}]},{"type":"paragraph","attrs":{"id":"5067874a-99cc-400f-a97c-c9be0bcaac3b","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"三、掺杂稳定性与电子结构"}]},{"type":"image","attrs":{"id":"b9048f6f-3663-4664-b559-38572168da8b","src":"https://developer.qcloudimg.com/http-save/audit-12559234/cdf60d864dc337d4f9223899022a898e.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"44f710b2-a710-4b4f-b2de-8ae781f06366","textAlign":"center","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"图1 | ZrBr单层的原子结构与声子谱。(a)侧视图、(b)俯视图——Zr（绿）、Br（蓝）、掺杂元素（红）。(c-e) Ti、Ni、Nb掺杂ZrBr的声子色散。无显著虚频确认动力学稳定性。"}]},{"type":"paragraph","attrs":{"id":"529db9bb-46d5-4753-bce9-38eee6eac8f4","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"稳定性分析"}]},{"type":"paragraph","attrs":{"id":"c7520774-122a-4a05-b6e4-5beb79460bce","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Nb和Ti掺杂：形成能E_f为负 → 热力学稳定；Ni掺杂E_f为正 → 不稳定"}]},{"type":"paragraph","attrs":{"id":"01ab3683-f78b-4d78-ab4b-0efa7ec83c64","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 弹性常数：Nb和Ti掺杂满足Born判据 → 力学稳健；Ni掺杂不满足C₆₆>0和全局稳定性条件"}]},{"type":"paragraph","attrs":{"id":"8273f4b0-3422-4e18-93b1-f86ecb3912cd","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 声子谱：所有掺杂体系无显著虚频 → 动力学稳定（低频微小负值为伪影）"}]},{"type":"paragraph","attrs":{"id":"3f62bd29-9d6b-4606-8c6b-d0583ddcce37","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 结论：Nb和Ti掺杂同时满足热力学、力学和动力学稳定性；Ni掺杂仅供理论分析"}]},{"type":"image","attrs":{"id":"f73dafa1-eecd-4468-81c1-79cb14914087","src":"https://developer.qcloudimg.com/http-save/audit-12559234/f90380940d4a0ea2d7aaeed9c5d730cf.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"f3f1b1a8-168c-4bf5-b3da-392c2621f229","textAlign":"center","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"图2 | 原始ZrBr的投影能带结构(a)和半无限系统边缘态(b)。Γ点附近非Dirac交叉，Chern数C=1，单一拓扑边缘态穿越带隙。"}]},{"type":"paragraph","attrs":{"id":"0bbd6ee9-94d5-42af-9e0b-d181fa9e474c","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"掺杂对电子结构的差异化影响"}]},{"type":"paragraph","attrs":{"id":"a8b56214-e577-4601-87bf-b023e1af6d09","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Ti掺杂：Ti-d与Zr-d轨道杂化 → 带隙打开~80 meV，能带显著扁平化，Fermi速度骤降至3.6×10² m/s"}]},{"type":"paragraph","attrs":{"id":"92a04d2f-ad41-4ea8-84d2-818b12a4e9a7","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Nb掺杂：Dirac锥下移至Fermi面以下，但整体色散特征保留 → n型掺杂特征"}]},{"type":"paragraph","attrs":{"id":"9f959181-6351-4827-9e10-fab6f1b49eef","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Ni掺杂：Ni-d态高度局域化在Fermi面以下，带隙~89 meV，Fermi速度降至9.1×10³ m/s"}]},{"type":"paragraph","attrs":{"id":"f94c8e69-23f7-4f25-86f4-c1fe8114dc72","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 磁性：Ti掺杂引入1.78 μ_B磁矩 → 破缺时间反演对称性；Ni掺杂0.28 μ_B；Nb掺杂几乎无磁性"}]},{"type":"image","attrs":{"id":"6dacafa3-1c9b-4402-8968-d90cf8294b33","src":"https://developer.qcloudimg.com/http-save/audit-12559234/46021520947390f01a88917917f845c2.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"2bc24823-3a3d-4bfc-be75-a7adb561ed1c","textAlign":"center","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"图3 | 掺杂ZrBr的投影能带结构及Fermi面附近放大。(a,b) Ti掺杂、(c,d) Nb掺杂、(e,f) Ni掺杂。Ti和Ni掺杂打开带隙，Nb保留Dirac特征。"}]},{"type":"paragraph","attrs":{"id":"5893c4ca-9dda-47ea-a83c-15763e010134","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"四、自旋霍尔电导率（SHC）"}]},{"type":"image","attrs":{"id":"8700bc0d-6f2d-4a48-8f0c-3dc7ae3db700","src":"https://developer.qcloudimg.com/http-save/audit-12559234/993103baf97fe1013f5df280e7551523.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"bf96ccd9-39af-4de1-af52-26fcab9e01c1","textAlign":"center","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"图4 | (a) 原始和掺杂ZrBr的SHC随能量变化。(b) Nb掺杂ZrBr的GGA SOC投影能带与SHC。(c) Ti掺杂ZrBr的GGA SOC投影能带与SHC。"}]},{"type":"paragraph","attrs":{"id":"ce54646e-290f-49e3-9440-a4c9f05d85aa","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"SHC的掺杂调控"}]},{"type":"paragraph","attrs":{"id":"2676a937-d645-46a9-a3e4-85db81dc8f9e","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 原始ZrBr：Fermi速度8610 m/s，SHC峰值超120 ℏ/e·S/cm @ 7 eV，显著符号翻转"}]},{"type":"paragraph","attrs":{"id":"31b05154-6093-4a4a-90f4-dd66cf0d6caa","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Ti掺杂：SHC几乎完全淬灭——最大值~0.006 ℏ/e·S/cm → 能带扁平化破坏自旋输运"}]},{"type":"paragraph","attrs":{"id":"024bd1e6-86c6-43d1-b132-37c80d510923","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Nb掺杂：SHC显著降低至0.2−0.4 ℏ/e·S/cm，Nb-d态更色散但与Zr-d杂化缺乏强反交叉"}]},{"type":"paragraph","attrs":{"id":"dad19c7d-7012-4a32-a7c6-8da2bd050d4d","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Ni掺杂：SHC在−20到 10 ℏ/e·S/cm间波动，强负值和剧烈振荡 → 磁性杂质态引入复杂自旋输运"}]},{"type":"paragraph","attrs":{"id":"5758e035-f454-4145-9dc5-275fdfe71978","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Fermi面SHC：原始ZrBr 91.23，Ti掺杂−0.0017，Ni掺杂−1.23，Nb掺杂0.022 ℏ/e·S/cm"}]},{"type":"paragraph","attrs":{"id":"c4f8ea88-ce6a-4cdc-a799-aa121b3c590d","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"SHC变化的物理机制"}]},{"type":"paragraph","attrs":{"id":"cd0f6699-b0ad-4e24-80f1-5d9c0e62865b","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 对称性破缺：掺杂打破反演对称性 → 简并解除，SOC驱动能带劈裂"}]},{"type":"paragraph","attrs":{"id":"4d454899-70aa-4c23-b8ee-8e55adc1976a","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Ti掺杂：Ti-d态局域化 → 能带扁平化 → 载流子有效质量增大 → Berry曲率减小"}]},{"type":"paragraph","attrs":{"id":"424f2279-a1fd-4ad9-ab4e-02e52c90e7f9","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Nb掺杂：保留Dirac特征但Fermi面与更平坦能带相交 → Fermi速度降低"}]},{"type":"paragraph","attrs":{"id":"c1c50bb2-0339-498c-aeab-fcb9cb01035d","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Ni掺杂：重电子掺杂 部分填充Ni-d局域态 → 破坏拓扑保护 → 复杂SHC行为"}]},{"type":"paragraph","attrs":{"id":"3feb734c-101e-4462-b8a1-10577622c2c5","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• SHC符号翻转：所有掺杂体系均出现 → 反映自旋流主导方向随能量的变化"}]},{"type":"paragraph","attrs":{"id":"ffca1d65-7d94-4dfc-945d-babc39b13e65","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"五、反常霍尔电导率与Berry曲率"}]},{"type":"image","attrs":{"id":"a54161d0-5afa-4498-b380-75eaa2df4725","src":"https://developer.qcloudimg.com/http-save/audit-12559234/5fd5d49aed2d3798774ab1199c52f875.webp","extension":"","align":"center","alt":"","showAlt":false,"href":"","boxShadow":"","width":"","aspectRatio":0,"status":"success","showText":true,"isPercentage":false,"percentage":0,"isHoverDragHandle":false}},{"type":"paragraph","attrs":{"id":"f6a3b1f9-3846-4ed0-853f-a3783b5cdcfc","textAlign":"center","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"图5 | 原始和掺杂ZrBr的动量分辨Berry曲率 sgn(Ω_y)log(|Ω_z|)。红框标注与能带交叉/反交叉相关的Berry曲率热点，主导霍尔输运。"}]},{"type":"paragraph","attrs":{"id":"434a48d2-a709-4e96-9b8f-aa72a18b5c0f","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"Berry曲率分布与AHC"}]},{"type":"paragraph","attrs":{"id":"5833d9c3-429c-449c-a3fe-f3acb70def10","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 原始ZrBr：Γ-K和H-A区域出现Berry曲率热点 → 能带反转特征 → 非平庸拓扑"}]},{"type":"paragraph","attrs":{"id":"b849a899-3011-4b36-80cf-46575a4b72c4","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Nb掺杂：Berry曲率轮廓与原始ZrBr相似，Γ-K热点保留 → 拓扑特征维持但强度略微降低"}]},{"type":"paragraph","attrs":{"id":"b9c498a6-346f-40c6-a6d6-07fbfcf0775c","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Ti掺杂：Berry曲率剧烈重构——额外热点沿Γ-K和L-M出现 → 不规则分布但抑制相干自旋输运"}]},{"type":"paragraph","attrs":{"id":"a57d7b1d-3c93-4bdb-9e0f-1b0d65fc9293","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Ni掺杂：引入磁性 → 多个强Berry曲率峰（Γ-K和H-A） → SHC/AHC竞争"}]},{"type":"paragraph","attrs":{"id":"3c561475-a649-4c23-a9c1-3e10e6425e8c","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• AHC值：原始ZrBr AHCz=−0.0063 S/cm；Ti掺杂全部归零；Ni掺杂AHCz=−116.68 S/cm；Nb掺杂AHCz=0.054 S/cm"}]},{"type":"paragraph","attrs":{"id":"e2046827-cba4-41fe-9209-a142e401b1a6","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"掺杂驱动的SHC↔AHC转变"}]},{"type":"paragraph","attrs":{"id":"e45a1036-2f15-4dc2-8aee-b35b816cfe8c","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 原始ZrBr：高SHC/低AHC → 自旋霍尔主导"}]},{"type":"paragraph","attrs":{"id":"3b0bbf92-c5f5-4bad-bc5b-cb21e8b7111a","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Ti掺杂：SHC和AHC均被抑制 → 平庸态"}]},{"type":"paragraph","attrs":{"id":"f7916371-8886-4697-ab8d-537216ba615a","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Ni掺杂：SHC→AHC反转 → 从自旋霍尔主导转变为反常霍尔主导"}]},{"type":"paragraph","attrs":{"id":"907f7d90-74bd-42af-ae0a-01bed84f9c0c","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• Nb掺杂：保留拓扑特征，SHC和AHC均减弱 → 拓扑金属"}]},{"type":"paragraph","attrs":{"id":"adb967e8-2e0b-436b-9882-7e00779440f4","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"• 核心结论：靶向掺杂可在ZrBr单层中实现量子输运态之间的可控转变"}]},{"type":"paragraph","attrs":{"id":"accb3e86-91be-43de-b5d2-bfeac3349a60","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"六、总结"}]},{"type":"paragraph","attrs":{"id":"8287d6df-e260-4fce-812b-281b4c5e4785","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"核心发现"}]},{"type":"paragraph","attrs":{"id":"f78bfb57-fd01-48bb-a224-32d3a8abcfc2","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"(1) 原始ZrBr单层：稳定六方晶格，Dirac-like色散，高Fermi速度，显著内禀SHC（91.23 ℏ/e·S/cm）"}]},{"type":"paragraph","attrs":{"id":"f8cf609e-5fef-476d-966f-9e1488513599","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"(2) Ti掺杂：等电子但能带扁平化 → SHC淬灭至~0.0017 ℏ/e·S/cm，不适合自旋电子学应用"}]},{"type":"paragraph","attrs":{"id":"0f832b19-a398-4afc-a274-7efe723802af","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"(3) Ni掺杂：引入局域d态和磁性 → 破坏反演对称性 → SHC/AHC反转（AHCz=−116.68 S/cm）"}]},{"type":"paragraph","attrs":{"id":"1e4182dc-7fc2-4bfc-948c-15b798851549","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"(4) Nb掺杂：保留能带特征但Fermi面上移 → 拓扑特征维持但SHC降低"}]},{"type":"paragraph","attrs":{"id":"283c74fe-8196-4202-bae6-39c2f6f135f5","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"(5) 掺杂工程在ZrBr单层中实现了从自旋霍尔导体到反常霍尔系统的可控量子态转变"}]},{"type":"paragraph","attrs":{"id":"e4d325bd-3d9a-4a44-bcc2-7177cd7cfef6","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"(6) 该可调性使掺杂ZrBr成为设计可编程2D自旋电子学和拓扑量子器件的理想平台"}]},{"type":"paragraph","attrs":{"id":"18c37812-1c94-468b-84a1-74fb14a4e63d","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"参考文献"}]},{"type":"paragraph","attrs":{"id":"e8224bdc-c065-449d-a8c3-938cc2e63cb3","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"[1] Zergou I, Zaari H, Bouhani H, et al. Adv. Quantum Technol. 9, e00552 (2026) — 本工作"}]},{"type":"paragraph","attrs":{"id":"f45f2cd5-ee50-4816-ad8c-bb6846ea9711","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"[2] Zergou I, et al. Comput. Mater. Sci. 246, 113498 (2025) — ZrBr拓扑特征"}]},{"type":"paragraph","attrs":{"id":"bd68e1fc-16f6-44f6-9b09-0e6066effcd9","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"[3] Sinova J, et al. Rev. Mod. Phys. 87, 1213 (2015) — 自旋霍尔效应综述"}]},{"type":"paragraph","attrs":{"id":"aac53354-4dfd-40e9-9929-16996ac4f254","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"[4] Zhang Y, et al. npj Comput. Mater. 7, 1 (2021) — 高通量SHC筛选"}]},{"type":"paragraph","attrs":{"id":"2bc19233-215b-44d8-aeb4-e3c935ba2781","textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"[5] Pizzi G, et al. J. Phys.: Condens. Matter 32, 165902 (2020) — Wannier90"}]},{"type":"paragraph","attrs":{"id":"d4b2a3ac-5ca1-44cc-a2a3-74266f4fe2da","textAlign":"center","indent":0,"color":null,"background":null,"isHoverDragHandle":false},"content":[{"type":"text","marks":[{"type":"textStyle","attrs":{"color":"","background":""}}],"text":"I. Zergou, H. Zaari, H. Bouhani, et al. | Adv. Quantum Technol. 9, e00552 (2026) | 2D拓扑材料 · 自旋霍尔效应 · Berry曲率 · 掺杂工程"}]},{"type":"paragraph","attrs":{"id":null,"textAlign":"inherit","indent":0,"color":null,"background":null,"isHoverDragHandle":false}}]}","createTime":1785938493,"ext":{"closeTextLink":0,"comment_ban":0,"description":"","focusRead":0},"favNum":0,"html":"","isOriginal":0,"likeNum":0,