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Numerical investigation of the structure factors of the Read-Rezayi series 对雷德-雷扎伊数列结构因子的数值研究
IF 3.7 2区 物理与天体物理 Q1 Physics and Astronomy Pub Date : 2024-07-23 DOI: 10.1103/physrevb.110.045143
Loïc Herviou, Frédéric Mila
We numerically investigate the guiding center structure factors of several states in the Read-Rezayi family. Using exact diagonalizations on the torus and density matrix renormalization group on an infinite cylinder, we test a conjecture proposed in Can et al. [Phys. Rev. Lett. 113, 046803 (2014)] for the ν=35 and ν=46 Read-Rezayi states. Furthermore, we discuss the strong finite-size effects present in numerically accessible wavefunctions, and provide a simple recipe to minimize them on manifolds where non-Abelian theories have topological degeneracies.
我们用数值方法研究了Read-Rezayi家族中几个状态的指导中心结构因子。利用环上的精确对角化和无限圆柱体上的密度矩阵重正化群,我们检验了 Can 等人[Phys. Rev. Lett. 113, 046803 (2014)]针对 ν=35 和 ν=46 Read-Rezayi 状态提出的猜想。此外,我们还讨论了数值波函数中存在的强烈的有限大小效应,并提供了一个简单的方法,在非阿贝尔理论具有拓扑退行性的流形上最小化这些效应。
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引用次数: 0
Thermoelectric transport and current noise through a multilevel Anderson impurity: Three-body Fermi liquid corrections in quantum dots and magnetic alloys 通过多级安德森杂质的热电传输和电流噪声:量子点和磁性合金中的三体费米液体校正
IF 3.7 2区 物理与天体物理 Q1 Physics and Astronomy Pub Date : 2024-07-23 DOI: 10.1103/physrevb.110.035308
Yoshimichi Teratani, Kazuhiko Tsutsumi, Kaiji Motoyama, Rui Sakano, Akira Oguri
We present a comprehensive Fermi liquid description for thermoelectric transport and current noise, applicable to multilevel quantum dots (QD) and magnetic alloys (MA) without electron-hole or time-reversal symmetry. Our formulation for the low-energy transport is based on an Anderson model with N discrete impurity levels, and is asymptotically exact at low energies, up to the next-leading order terms in power expansions with respect to temperature T and bias voltage eV. The expansion coefficients can be expressed in terms of the Fermi liquid parameters, which include the three-body correlation functions defined with respect to the equilibrium ground state in addition to the linear susceptibilities and the occupation number Nd of impurity electrons. We apply this formulation to the SU(N) symmetric QD and MA, and calculate the correlation functions for N=4 and 6, using numerical renormalization group approach. The three-body correlations are shown to be determined by a single parameter over a wide range of electron fillings 1NdN1 for strong Coulomb interactions U, and they also exhibit the plateau structures due to the SU(N) Kondo effects at integer values of Nd. We find that the Lorenz number L=κ/(Tσ) for QD and MA, defined as the ratio of the thermal conductivity κ to the electrical conductivity σ, deviates from the universal Wiedemann-Franz value π2/(3e2) as the temperature increases from T=0, showing the
我们提出了热电输运和电流噪声的费米液体综合描述,适用于无电子-空穴或时间反转对称性的多级量子点(QD)和磁性合金(MA)。我们的低能输运公式基于具有 N 个离散杂质级的安德森模型,在低能时近似精确,直到与温度 T 和偏置电压 eV 有关的幂级数展开的下一阶项。膨胀系数可以用费米液体参数来表示,其中除了线性感性和杂质电子的占据数 Nd 外,还包括针对平衡基态定义的三体相关函数。我们将这一公式应用于苏(N)对称 QD 和 MA,并利用数值重正化群方法计算了 N=4 和 6 的相关函数。结果表明,在强库仑相互作用 U 下,三体相关函数在电子填充 1≲Nd≲N-1 的宽范围内由单一参数决定,而且在 Nd 的整数值时,它们还表现出 SU(N) Kondo 效应导致的高原结构。我们发现,QD 和 MA 的洛伦兹数 L=κ/(Tσ) 定义为热导率 κ 与电导率 σ 之比,随着温度从 T=0 升高,洛伦兹数偏离了通用的维德曼-弗朗茨值 π2/(3e2),显示出与 T2 有关,其系数取决于远离半填充的三体相关性。此外,我们发现 SU(4) 量子点的电流噪声和 SU(6) 量子点的电流噪声在四分之一 Nd/N=1/4 和 3/4 填充时有明显差异。特别是,N=4 的线性噪声表现出一个平坦的峰值,而 N=6 的峰值则表现出一个圆形,这反映出在这些填充点,SU(N) Kondo 效应发生在 N≡0 (mod 4),而中间价波动发生在 N≡2 (mod 4)。我们还证明了三体关联对非线性电流噪声和其他输运系数的作用。
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引用次数: 0
Controllable trions in buckled two-dimensional materials 屈曲二维材料中的可控三离子
IF 3.7 2区 物理与天体物理 Q1 Physics and Astronomy Pub Date : 2024-07-23 DOI: 10.1103/physrevb.110.035425
Roman Ya. Kezerashvili, Shalva M. Tsiklauri, Anastasia Spiridonova
We predict the formation of intravalley and intervalley controllable trions in buckled two-dimensional (2D) materials such as silicene, germanene, and stanene monolayers in an external electric field. A study is performed within the framework of a nonrelativistic potential model using the method of hyperspherical harmonics (HH). We solve the three-body Schrödinger equation with the Rytova-Keldysh potential by expanding the wave functions of a trion in terms of the HH. A resultant system of coupled differential equations is solved numerically. Controllable ground-state energies of intravalley and intervalley trions by the external electric field are presented. The dependencies of the binding energy (BE) of trions in silicene, germanene, and stanene as a function of the electric field are qualitatively similar. BEs of trions formed by A and B excitons have a non-negligible difference that increases slightly as the electric field increases. It is demonstrated that trion BEs can be controlled by the external electric field, and the dielectric environment has a significant effect on the trion BE. The capability to control the BE and compactness of trions in buckled 2D materials by an external electric field suggests a possible trions crystallization in Xenes.
我们预测了硅烯、锗烯和链烷烯单层等降压二维(2D)材料在外加电场中形成的谷内和谷间可控三离子。研究在非相对论势模型的框架内使用超球谐波(HH)方法进行。我们利用 Rytova-Keldysh 势,通过以 HH 展开三元体的波函数来求解三体薛定谔方程。我们对由此产生的耦合微分方程系统进行了数值求解。提出了通过外部电场控制谷内和谷间三离子的基态能量。硅烯、锗烯和链烷烯中三离子的结合能(BE)与电场的函数关系在本质上是相似的。由 A 和 B 激子形成的三离子结合能具有不可忽略的差异,并随着电场的增加而略有增加。实验证明,三离子的 BE 可由外部电场控制,而电介质环境对三离子的 BE 有显著影响。通过外电场控制屈曲二维材料中三元子的BE和致密性的能力表明,三元子可能在氙中结晶。
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引用次数: 0
Unconventional spin-orbit torques from sputtered MoTe2 films 来自溅射 MoTe2 薄膜的非常规自旋轨道力矩
IF 3.7 2区 物理与天体物理 Q1 Physics and Astronomy Pub Date : 2024-07-23 DOI: 10.1103/physrevb.110.024426
Shuchen Li, Jonathan Gibbons, Stasiu Chyczewski, Zetai Liu, Hsu-Chih Ni, Jiangchao Qian, Jian-Min Zuo, Jun-Fei Zheng, Wenjuan Zhu, Axel Hoffmann
Materials with strong spin-orbit coupling and low crystalline symmetry are promising for generating large unconventional spin-orbit torques (SOTs), such as in-plane fieldlike (FL) torques and out-of-plane dampinglike (DL) torques, which can effectively manipulate and deterministically switch an out-of-plane magnetization without the need for additional external in-plane magnetic fields. Here, we report SOTs generated by magnetron-sputtered 1TMoTe2/Permalloy (Py; Ni80Fe20)/MgO heterostructures using both spin-torque ferromagnetic resonance (ST-FMR) and second harmonic Hall measurements. We observed unconventional FL and DL torques in our samples due to spins polarized normal to the interface of MoTe2 and Py layers, and studied the influence of crystallographic order and MoTe2 layer thickness on the SOTs. By comparing the Raman spectra of 1TMoTe2 samples prepared in different ways, we found a tensile strain in sputtered MoTe2 films, which might further enhance the generation of unconventional torques by reducing the symmetry of 1TMoTe2.
具有强自旋轨道耦合和低晶体对称性的材料有望产生巨大的非常规自旋轨道力矩(SOT),例如面内类磁场力矩(FL)和面外类阻尼力矩(DL),它们可以有效地操纵和确定性地切换面外磁化,而无需额外的面内磁场。在这里,我们利用自旋力矩铁磁共振(ST-FMR)和二次谐波霍尔测量方法,报告了磁控溅射 1T′MoTe2/Permalloy (Py; Ni80Fe20)/MgO 异质结构产生的 SOT。我们观察到样品中由于自旋极化到 MoTe2 和 Py 层界面的法线而产生的非常规 FL 和 DL 扭矩,并研究了晶体学顺序和 MoTe2 层厚度对 SOT 的影响。通过比较以不同方法制备的 1T′MoTe2 样品的拉曼光谱,我们发现在溅射 MoTe2 薄膜中存在拉伸应变,这可能会通过降低 1T′MoTe2 的对称性而进一步增强非常规扭矩的产生。
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引用次数: 0
Hierarchy of exchange-correlation functionals in computing lattice thermal conductivities of rocksalt and zinc-blende semiconductors 计算岩盐和蓝晶锌半导体晶格热导率时交换相关函数的层次结构
IF 3.7 2区 物理与天体物理 Q1 Physics and Astronomy Pub Date : 2024-07-23 DOI: 10.1103/physrevb.110.035205
Jiacheng Wei, Zhonghao Xia, Yi Xia, Jiangang He
Lattice thermal conductivity (κL) is a crucial characteristic of crystalline solids with significant implications for thermal management, energy conversion, and thermal barrier coating. The advancement of computational tools based on density functional theory (DFT) has enabled the effective utilization of phonon quasiparticle-based approaches to unravel the underlying physics of various crystalline systems. While the higher order of anharmonicity is commonly used for explaining extraordinary heat transfer behaviors in crystals, the impact of exchange-correlation (XC) functionals in DFT on describing anharmonicity has been largely overlooked. The XC functional is essential for determining the accuracy of DFT in describing interactions among electrons/ions in solids and molecules. However, most XC functionals in solid-state physics are primarily focused on computing the properties that only require small atomic displacements from the equilibrium (within the harmonic approximation), such as harmonic phonons and elastic constants, while anharmonicity involves larger atomic displacements. Therefore, it is more challenging for XC functionals to accurately describe atomic interactions at the anharmonicity level. In this study, we systematically investigate the room-temperature κL of 16 binary compounds with rocksalt and zinc-blende structures using various XC functionals such as local density approximation (LDA), Perdew-Burke-Ernzerhof (PBE), revised PBE for solid and surface (PBEsol), optimized B86b functional (optB86b), revised Tao-Perdew-Staroverov-Scuseria (revTPSS), strongly constrained and appropriately normed functional (SCAN), regularized SCAN (rSCAN), and regularized-restored SCAN (r2SCAN) in combination with different perturbation orders, including phonon within harmonic approximation (HA) plus three-phonon scattering (HA+3ph), phonon calculated using self-consistent phonon theory (SCPH) plus three-phonon scattering (SCPH + 3ph), and SCPH phonon plus three- and four-phonon scattering (SCPH + 3,4ph). Our results show that the XC functional exhibits strong entanglement with perturbation order and the mean relative absolute error (MRAE) of the computed κL is strongly influenced by both the XC functional and perturbation order, leading to error c
晶格热导率(κL)是晶体固体的一个重要特性,对热管理、能量转换和热障涂层具有重要影响。基于密度泛函理论(DFT)的计算工具的发展,使得基于声子准粒子的方法得以有效利用,从而揭示了各种晶体系统的基本物理原理。虽然高阶非谐波性通常用于解释晶体中的非凡传热行为,但 DFT 中的交换相关(XC)函数对描述非谐波性的影响却在很大程度上被忽视了。XC 函数对于确定 DFT 描述固体和分子中电子/离子间相互作用的准确性至关重要。然而,固体物理中的大多数 XC 函数主要侧重于计算只需要从平衡状态(在谐波近似范围内)发生较小原子位移的性质,如谐波声子和弹性常数,而非谐波性则涉及较大的原子位移。因此,XC 函数在非谐波水平上准确描述原子相互作用更具挑战性。在本研究中,我们使用各种 XC 函数,如局部密度近似(LDA)、Perdew-Burke-Ernzerhof(PBE)、针对固体和表面的修正 PBE(PBEsol)、优化 B86b 函数(optB86b)、修正陶-Perdew-Staroverov-Scuseria(revTPSS)、强约束和适当规范化函数(SCAN),系统地研究了 16 种具有岩盐和蓝晶锌结构的二元化合物的室温κL、我们将强约束和适当规范函数(SCAN)、正则化 SCAN(rSCAN)和正则化-恢复 SCAN(r2SCAN)与不同的扰动阶数相结合,包括谐波近似(HA)内声子加上三声子散射(HA+3ph)、使用自洽声子理论(SCPH)计算的声子加上三声子散射(SCPH + 3ph)以及 SCPH 声子加上三和四声子散射(SCPH + 3,4ph)。我们的研究结果表明,XC 函数与扰动阶数表现出很强的纠缠性,计算出的κL 的平均相对绝对误差(MRAE)受 XC 函数和扰动阶数的影响很大,从而导致误差抵消或放大。在 HA + 3ph 级使用 revTPSS (rSCAN)、在 SCPH + 3ph 级使用 SCAN (r2SCAN)、在 SCPH + 3,4ph 级使用 PBEsol (rSCAN) 时,MRAE 最小(最大)。在这些函数中,PBEsol 在最高扰动阶时的精度最高。与 SCAN 相关的函数表现出中等精度,但存在数值不稳定和计算成本高等问题。此外,所有 XC 函数都能识别出岩石和锌蓝晶结构中的四次非谐波对κL 的不同影响,这归因于这两种结构中不同的晶格非谐波。这些发现为选择描述非谐波声子的适当函数提供了宝贵的参考,并为高阶力常数计算提供了启示,有助于为固体材料开发更精确的 XC 函数。
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引用次数: 0
Prediction of ambient superconductivity in ternary thorium-silicon superhydrides with a breathing kagome lattice 三元钍硅超氢中的环境超导性预测与呼吸卡戈米晶格
IF 3.7 2区 物理与天体物理 Q1 Physics and Astronomy Pub Date : 2024-07-23 DOI: 10.1103/physrevb.110.024513
Xiaomeng Wang, Chi Ding, Qing Lu, Tianheng Huang, Yuhang Li, Junjie Wang, Yu Han, Dingyu Xing, Jian Sun
A major focus of current research on superconducting superhydrides is to achieve superconductivity at lower pressures, especially ambient pressure. Here we present the prediction of a class of high-temperature ternary hydrogen-rich superconductors, which are metastable at mild pressure and dynamically stable at ambient pressure using crystal structure searching. Our findings reveal the existence of a hexagonal ThSiH7 compound with a superconducting Tc of 61.5 K at ambient pressure, as estimated by electron-phonon coupling calculations. Interestingly, the H sites in ThSiH7 materialize a breathing kagome network, equivalent to a triangular lattice of trimer plaquettes, which is entirely different from previously known hydrogen clathrate structures. By substituting Th with lanthanide elements, we discovered that LaSiH7 and CeSiH7 are also dynamically stable at 0 GPa, while PrSiH7 and NdSiH7 are dynamically stable at 10 and 15 GPa with high Tc values of 63.9 and 65.9 K, respectively. Our results provide a system for superconducting hydrides and open a promising avenue for studying ambient pressure high-temperature superconductors.
目前超导超氢化物研究的一个重点是在较低压力,尤其是环境压力下实现超导。在这里,我们利用晶体结构搜索技术预测了一类高温三元富氢超导体,它们在温和压力下是瞬变的,而在环境压力下则是动态稳定的。我们的发现揭示了一种六方 ThSiH7 化合物的存在,根据电子-声子耦合计算的估计,它在常压下的超导 Tc 为 61.5 K。有趣的是,ThSiH7 中的氢位点形成了一个会呼吸的卡戈米网络,相当于三聚方格的三角形晶格,这与之前已知的氢凝胶结构完全不同。通过用镧系元素替代钍,我们发现 LaSiH7 和 CeSiH7 在 0 GPa 下也是动态稳定的,而 PrSiH7 和 NdSiH7 则在 10 和 15 GPa 下动态稳定,Tc 值分别高达 63.9 和 65.9 K。我们的研究结果提供了一个超导氢化物体系,为研究常压高温超导体开辟了一条前景广阔的途径。
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引用次数: 0
Electric field gradients at the nuclei from all-electron four-component relativistic density functional theory using Gaussian-type orbitals 利用高斯型轨道的全电子四分量相对论密度泛函理论得出的原子核处的电场梯度
IF 3.7 2区 物理与天体物理 Q1 Physics and Astronomy Pub Date : 2024-07-23 DOI: 10.1103/physrevb.110.045141
Marc Joosten, Michal Repisky, Marius Kadek, Pekka Pyykkö, Kenneth Ruud
We present an all-electron, four-component relativistic implementation of electric field gradients (EFGs) at the nuclei using Gaussian-type orbitals and periodic boundary conditions. This allows us to include relativistic effects variationally, which is important for compounds containing heavy elements and for a property dependent on the electronic structure close to the nuclei. The all-electron approach ensures an accurate treatment of both core and valence orbitals, as both are important in the evaluation of EFGs. Computational efficiency is achieved through the use of a recent implementation of density fitting in combination with quaternion algebra and restricted kinetic balance. We use the relativistic approach to calculate the EFGs in different arsenic, antimony, and bismuth halides and oxyhalides, and explore the importance of relativistic effects on EFGs in solids and compare these with results obtained for molecular species. Our calculations contribute to establishing a reliable estimate for the nuclear quadrupole moment of Bi209, for which our best estimate is 428(17) mb, in excellent agreement both with molecular data and a recent reevaluation of the nuclear quadrupole moment obtained from atomic data and ab initio calculations. Our results suggest that there is a need to revisit the experimental data for the EFGs of several bismuth oxyhalides.
我们利用高斯型轨道和周期性边界条件,提出了原子核处电场梯度(EFGs)的全电子四分量相对论实现方法。这使我们能够将相对论效应变化纳入其中,这对于含有重元素的化合物和依赖于靠近原子核的电子结构的性质非常重要。全电子方法确保了对核轨道和价轨道的精确处理,因为这两种轨道在 EFG 评估中都很重要。通过使用最新实现的密度拟合,结合四元数代数和受限动力学平衡,实现了计算效率。我们使用相对论方法计算了不同砷、锑和铋卤化物和氧卤化物中的 EFGs,探讨了相对论效应对固体中 EFGs 的重要性,并将其与分子物种的计算结果进行了比较。我们的计算有助于为 Bi209 的核四极矩建立一个可靠的估计值,我们的最佳估计值为-428(17) mb,这与分子数据以及最近从原子数据和 ab initio 计算中获得的核四极矩的重新评估结果非常一致。我们的结果表明,有必要重新审视几种氧卤化铋的 EFG 的实验数据。
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引用次数: 0
Exact surface energy of the Hubbard model with nonparallel boundary magnetic fields 具有非平行边界磁场的哈伯德模型的精确表面能
IF 3.7 2区 物理与天体物理 Q1 Physics and Astronomy Pub Date : 2024-07-23 DOI: 10.1103/physrevb.110.035153
Pei Sun, Yi Qiao, Tao Yang, Junpeng Cao, Wen-Li Yang
In this study, we explore the precise physical quantities in the thermodynamic limit of the one-dimensional Hubbard model with nonparallel boundary magnetic fields based on the off-diagonal Bethe ansatz solution. A particular emphasis is placed on the half-filling condition to investigate the distinct patterns of Bethe roots in the reduced Bethe ansatz equations for different boundary parameters. The ground state of the system can be divided into five regions according to the distribution of Bethe roots. By analyzing these patterns, we calculate the densities of states, ground-state energy density, and surface energy. The results reveal the existence of stable-boundary bound states, which are dependent on specific constraints regarding the boundary magnetic fields.
在本研究中,我们基于非对角贝采解析解,探索了具有非平行边界磁场的一维哈伯德模型热力学极限中的精确物理量。本文特别强调了半填充条件,以研究不同边界参数下还原贝特方差方程中贝特根的不同模式。根据贝特根的分布,系统的基态可分为五个区域。通过分析这些模式,我们计算了状态密度、基态能量密度和表面能。结果揭示了稳定边界束缚态的存在,这些束缚态取决于边界磁场的特定约束条件。
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引用次数: 0
Atomic-level precision creation and manipulation of interfacial Se chemisorbates in graphene/WSe2 heterostructures 在石墨烯/WSe2 异质结构中原子级精确创建和操纵界面硒化学吸附剂
IF 3.7 2区 物理与天体物理 Q1 Physics and Astronomy Pub Date : 2024-07-23 DOI: 10.1103/physrevb.110.l041405
Mo-Han Zhang, Fei Gao, Aleksander Bach Lorentzen, Ya-Ning Ren, Ruo-Han Zhang, Xiao-Feng Zhou, Rui Dong, Shi-Wu Gao, Mads Brandbyge, Lin He
It has long been an ultimate goal to introduce chemical doping at the atomic level to precisely tune properties of materials. Two-dimensional materials have a natural advantage due to their high surface to volume ratio, but achieving this goal experimentally remains a huge challenge. Here, we demonstrate the ability to introduce chemical doping in graphene with atomic-level precision by controlling chemical adsorption of individual Se atoms, which are extracted from the WSe2 that is underneath, at the interface of the graphene/WSe2 heterostructures. Our scanning tunneling microscopy (STM) measurements, combined with first-principles calculations, reveal that individual Se atoms can chemisorb on three possible positions in graphene, which generate distinct pseudospin-mediated atomic-scale vortices in graphene. Furthermore, the chemisorbed positions of individual Se atoms can be manipulated by the STM tip, which enables us to achieve atomic-scale control of quantum interference of the pseudospin-mediated vortices in graphene. This result offers the promise of controlling properties of materials with atomic-level precision through chemical doping.
长期以来,在原子层面引入化学掺杂以精确调节材料特性一直是我们的终极目标。二维材料具有高表面体积比的天然优势,但要在实验中实现这一目标仍是一个巨大的挑战。在这里,我们展示了通过控制石墨烯/WSe2 异质结构界面上单个 Se 原子的化学吸附,在石墨烯中引入原子级精度的化学掺杂的能力。我们的扫描隧道显微镜(STM)测量结果与第一原理计算相结合,揭示了单个硒原子可以在石墨烯的三个可能位置上发生化学吸附,从而在石墨烯中产生不同的伪ospin 介导的原子尺度漩涡。此外,单个硒原子的化学吸附位置可以通过 STM 针尖进行操纵,这使我们能够实现对石墨烯中伪斯宾介导的漩涡的原子尺度量子干涉控制。这一结果为通过化学掺杂以原子级精度控制材料特性带来了希望。
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引用次数: 0
Non-Bloch band theory of subsymmetry-protected topological phases 次对称保护拓扑相的非布洛克带理论
IF 3.7 2区 物理与天体物理 Q1 Physics and Astronomy Pub Date : 2024-07-23 DOI: 10.1103/physrevb.110.035424
Sonu Verma, Moon Jip Park
Bulk-boundary correspondence (BBC) of symmetry-protected topological (SPT) phases relates the nontrivial topological invariant of the bulk to the number of topologically protected boundary states. Recently, a finer classification of SPT phases in Hermitian systems has been discovered, known as subsymmetry-protected topological (sub-SPT) phases [Wang et al., Nat. Phys. 19, 992 (2023)]. In sub-SPT phases, a fraction of the boundary states is protected by the subsymmetry of the system, even when the full symmetry is broken. While the conventional topological invariant derived from the Bloch band is not applicable to describe the BBC in these systems, we propose to use the non-Bloch topological band theory to describe the BBC of sub-SPT phases. Using the concept of the generalized Brillouin zone (GBZ), where Bloch momenta are generalized to take complex values, we show that the non-Bloch band theory naturally gives rise to a non-Bloch topological invariant, establishing the BBC in both SPT and sub-SPT phases. In a one-dimensional system, we define the winding number, whose physical meaning corresponds to the reflection amplitude in the scattering matrix. Furthermore, the non-Bloch topological invariant characterizes the hidden intrinsic topology of the GBZ under translation symmetry-breaking boundary conditions. The topological phase transitions are characterized by the generalized momenta touching the GBZ, which accompanies the emergence of diabolic or band-touching points. Additionally, we discuss the BBCs in the presence of local or global full-symmetry or subsymmetry-breaking deformations.
对称保护拓扑(SPT)相的体-界对应(BBC)关系到体的非难拓扑不变性和拓扑保护边界态的数量。最近,人们发现了赫米特系统中一种更精细的 SPT 相分类,即亚对称保护拓扑(sub-SPT)相 [Wang 等,Nat. Phys. 19, 992 (2023)]。在亚 SPT 相中,即使系统的完全对称性被打破,也会有一部分边界态受到系统的亚对称性保护。虽然从布洛赫带推导出的传统拓扑不变量不适用于描述这些系统中的 BBC,但我们建议使用非布洛赫拓扑带理论来描述亚 SPT 相的 BBC。利用广义布里渊区(GBZ)的概念(其中布洛赫矩被广义化为复值),我们证明了非布洛赫带理论自然产生了非布洛赫拓扑不变量,从而建立了 SPT 和 sub-SPT 相的 BBC。在一维系统中,我们定义了绕组数,其物理意义相当于散射矩阵中的反射振幅。此外,非布洛赫拓扑不变量表征了 GBZ 在平移对称破界条件下的隐藏内在拓扑。拓扑相变的特征是广义矩触及 GBZ,并伴随着双曲点或带触点的出现。此外,我们还讨论了存在局部或全局全对称或次对称破缺变形的 BBCs。
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引用次数: 0
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Physical Review B
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