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Three-dimensional bonding anisotropy of bulk hexagonal metal titanium demonstrated by high harmonic generation 用高谐波产生法证明了体体六方金属钛的三维键合各向异性
IF 5.4 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-12-18 DOI: 10.1038/s42005-024-01906-0
Ikufumi Katayama, Kento Uchida, Kimika Takashina, Akari Kishioka, Misa Kaiho, Satoshi Kusaba, Ryo Tamaki, Ken-ichi Shudo, Masahiro Kitajima, Thien Duc Ngo, Tadaaki Nagao, Jun Takeda, Koichiro Tanaka, Tetsuya Matsunaga
High harmonic generation (HHG) in solid-state materials is an emerging field of photonics research that can unveil the detailed electronic structure of materials, bond strengths and scattering processes of electrons. Although HHG in semiconducting and insulating materials has been intensively investigated both experimentally and theoretically, metals have rarely been explored because the strong screening effect of high-density free electrons is considered to significantly weaken the HHG signal. Here, we investigated HHG upon infrared excitation in bulk hexagonal metal titanium (Ti), a typical building block for practical lightweight structural materials. By analyzing the polarization dependence, the approach revealed the three-dimensional (3D) anisotropy in the electronic states. The results demonstrated the potential of HHG spectroscopy for characterizing 3D bonding anisotropy in metallic systems that are of fundamental importance for designing lightweight and strong structural materials. High harmonics generation (HHG) is a promising way of investigating electronic structures and anisotropy in materials. The authors demonstrate the observation of HHG in simple structural material, hexagonal metal titanium, and experimentally clarified the anisotropy in the electronic states from the polarization dependence.
固体材料中的高谐波产生(HHG)是光子学研究的一个新兴领域,它可以揭示材料的详细电子结构、键强度和电子散射过程。虽然半导体和绝缘材料中的HHG已经在实验和理论上得到了深入的研究,但金属很少被探索,因为高密度自由电子的强屏蔽效应被认为会显着削弱HHG信号。在这里,我们研究了红外激发下块状六方金属钛(Ti)的HHG,这是一种典型的实用轻量化结构材料。通过分析偏振依赖性,该方法揭示了电子态的三维各向异性。结果证明了HHG光谱在表征金属体系中三维键合各向异性方面的潜力,这对设计轻质强结构材料具有重要意义。高谐波产生(HHG)是研究材料电子结构和各向异性的一种很有前途的方法。作者在简单结构材料六方金属钛中进行了HHG的观测,并从极化依赖的角度阐明了电子态的各向异性。
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引用次数: 0
A topological route to engineering robust and bright supersymmetric laser arrays 设计坚固明亮的超对称激光阵列的拓扑途径
IF 5.4 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-12-18 DOI: 10.1038/s42005-024-01905-1
Soujanya Datta, Mohammadmahdi Alizadeh, Ramy El-Ganainy, Krishanu Roychowdhury
In recent years, several proposals that leverage principles from condensed matter and high-energy physics for engineering laser arrays have been put forward. The most important among these concepts are topology, which enables the construction of robust zero-mode laser devices, and supersymmetry (SUSY), which holds the potential for achieving phase locking in laser arrays. In this work, we show that the relation between supersymmetric coupled bosonic and fermionic oscillators on one side, and bipartite networks (and hence chiral symmetry) on another side can be exploited together with non-Hermitian engineering for building one- and two-dimensional laser arrays with in-phase synchronization. To demonstrate our strategy, we present a concrete design starting from the celebrated Su-Schrieffer-Heeger (SSH) model to arrive at a SUSY laser structure that enjoys two key advantages over those reported in previous works. Firstly, the design presented here features a near-uniform geometry for both the laser array and supersymmetric reservoir (i.e., the widths and distances between the cavity arrays are almost the same). Secondly, the uniform field distribution in the presented structure leads to a far-field intensity that scales as N2 where N is the number of lasing elements. Taken together, these two features can enable the implementation of higher-power laser arrays that are easy to fabricate, and hence provide a roadmap for pushing the frontier of SUSY laser arrays beyond the proof-of-concept phase. In-phase synchronization of laser arrays remains one of the most important open problems in laser science. This work utilizes the relationship between chiral symmetric tight-binding models and supersymmetry to engineer a near-uniform laser array with a superior far-field intensity scaling, extending the frontiers of laser technology.
近年来,人们提出了几个利用凝聚态和高能物理原理的工程激光阵列的建议。在这些概念中,最重要的是拓扑,它能够构建稳健的零模激光器件,以及超对称(SUSY),它具有在激光阵列中实现锁相的潜力。在这项工作中,我们证明了超对称耦合玻色子和费米子振荡子与另一侧的二部网络(因此手性对称)之间的关系可以与非厄米工程一起利用,用于构建具有同相同步的一维和二维激光阵列。为了展示我们的策略,我们提出了一个具体的设计,从著名的Su-Schrieffer-Heeger (SSH)模型开始,到达一个SUSY激光结构,与以前的作品相比,它具有两个关键优势。首先,本文提出的设计具有激光阵列和超对称储层接近均匀的几何形状(即,腔阵列之间的宽度和距离几乎相同)。其次,所述结构中的均匀场分布导致远场强度缩放为N2,其中N为激光元素的数量。综上所述,这两个特性可以实现易于制造的高功率激光阵列,从而为推动SUSY激光阵列超越概念验证阶段提供了路线图。激光阵列的同相同步仍然是激光科学中最重要的开放性问题之一。这项工作利用手性对称紧密结合模型和超对称之间的关系来设计具有优越远场强度缩放的近均匀激光阵列,扩展了激光技术的前沿。
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引用次数: 0
Machine-learning-enhanced automatic spectral characterization of x-ray pulses from a free-electron laser 机器学习增强的自由电子激光器x射线脉冲的自动光谱表征
IF 5.4 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-12-18 DOI: 10.1038/s42005-024-01900-6
Danilo Enoque Ferreira de Lima, Arman Davtyan, Joakim Laksman, Natalia Gerasimova, Theophilos Maltezopoulos, Jia Liu, Philipp Schmidt, Thomas Michelat, Tommaso Mazza, Michael Meyer, Jan Grünert, Luca Gelisio
A reliable characterization of x-ray pulses is critical to optimally exploit advanced photon sources, such as free-electron lasers. In this paper, we present a method based on machine learning, the virtual spectrometer, that improves the resolution of non-invasive spectral diagnostics at the European XFEL by up to 40%, and significantly increases its signal-to-noise ratio. This improves the reliability of quasi-real-time monitoring, which is critical to steer the experiment, as well as the interpretation of experimental outcomes. Furthermore, the virtual spectrometer streamlines and automates the calibration of the spectral diagnostic device, which is otherwise a complex and time-consuming task, by virtue of its underlying detection principles. Additionally, the provision of robust quality metrics and uncertainties enable a transparent and reliable validation of the tool during its operation. A complete characterization of the virtual spectrometer under a diverse set of experimental and simulated conditions is provided in the manuscript, detailing advantages and limits, as well as its robustness with respect to the different test cases. A reliable characterization of x-ray pulses is critical to optimally exploit advanced photon sources, such as free-electron lasers. The authors present a method based on machine learning which improves the resolution and signal-to-noise ratio of the non-invasive spectral diagnostics available at European XFEL, and streamlines its operation.
可靠的x射线脉冲表征对于优化利用先进的光子源(如自由电子激光器)至关重要。在本文中,我们提出了一种基于机器学习的方法,即虚拟光谱仪,该方法将欧洲XFEL的非侵入性光谱诊断分辨率提高了40%,并显着提高了信噪比。这提高了准实时监测的可靠性,这对于指导实验以及解释实验结果至关重要。此外,由于其潜在的检测原理,虚拟光谱仪简化和自动化了光谱诊断设备的校准,否则这是一项复杂而耗时的任务。此外,提供可靠的质量度量和不确定性,可以在工具运行期间对工具进行透明和可靠的验证。在手稿中提供了虚拟光谱仪在各种实验和模拟条件下的完整表征,详细说明了优点和局限性,以及它在不同测试用例中的鲁棒性。可靠的x射线脉冲表征对于优化利用先进的光子源(如自由电子激光器)至关重要。作者提出了一种基于机器学习的方法,提高了欧洲XFEL非侵入性光谱诊断的分辨率和信噪比,并简化了其操作。
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引用次数: 0
Online calibration of deep learning sub-models for hybrid numerical modeling systems 混合数值模拟系统中深度学习子模型的在线标定
IF 5.4 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-12-18 DOI: 10.1038/s42005-024-01880-7
Said Ouala, Bertrand Chapron, Fabrice Collard, Lucile Gaultier, Ronan Fablet
Defining end-to-end (or online) training schemes for the calibration of neural sub-models in hybrid systems requires working with an optimization problem that involves the solver of the physical equations. Online learning methodologies thus require the numerical model to be differentiable, which is not the case for most modeling systems. To overcome this, we present an efficient and practical online learning approach for hybrid systems. The method, called EGA for Euler Gradient Approximation, assumes an additive neural correction to the physical model, and an explicit Euler approximation of the gradients. We demonstrate that the EGA converges to the exact gradients in the limit of infinitely small time steps. Numerical experiments show significant improvements over offline learning, highlighting the potential of end-to-end learning for hybrid modeling. End-to-end learning in hybrid numerical models involves solving an optimization problem that integrates the model’s solver. In many fields, these solvers are written in low-abstraction programming languages that lack automatic differentiation. This work presents a practical approach to solving the optimization problem by efficiently approximating the gradient of the end-to-end objective function.
为混合系统中神经子模型的校准定义端到端(或在线)训练方案需要处理一个涉及物理方程求解器的优化问题。因此,在线学习方法要求数值模型是可微的,这对于大多数建模系统来说并非如此。为了克服这个问题,我们提出了一种高效实用的混合系统在线学习方法。该方法被称为欧拉梯度近似的EGA,它假设对物理模型进行加性神经校正,并对梯度进行显式欧拉近似。我们证明了EGA在无限小的时间步长极限下收敛于精确梯度。数值实验显示了离线学习的显著改进,突出了端到端混合建模学习的潜力。混合数值模型的端到端学习涉及求解一个集成模型求解器的优化问题。在许多领域,这些解算器是用缺乏自动区分的低抽象编程语言编写的。本文提出了一种实用的方法,通过有效地逼近端到端目标函数的梯度来解决优化问题。
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引用次数: 0
Cosmic entanglement sudden birth: expansion-induced entanglement in hydrogen atoms 宇宙纠缠突然诞生:氢原子中的膨胀诱导纠缠
IF 5.4 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-12-18 DOI: 10.1038/s42005-024-01907-z
Yusef Maleki, Alireza Maleki, M. Suhail Zubairy
Hydrogen is the most dominant atom in the universe and is considered the main component of baryonic matter. Thus far, the quantum features of the unbounded hydrogen atoms in the background of the universe and the possibility of emerging unique quantum effects, such as entanglement on the cosmological scale, have not been considered. In this work, we demonstrate that the dynamical expansion of the universe leads to the emergence of natural entanglement in the hyperfine structure of atomic hydrogen. Our findings reveal that there exists a critical age for the universe where hydrogen atoms naturally build up entanglement, resulting from the expansion of the universe. More precisely, when the universe reaches the age of about 2.5 × 1018 seconds (about 80 billion years old), the hyperfine structure entanglement in hydrogen atoms naturally takes off, demonstrating a peculiar quantum phenomenon known as entanglement sudden birth. This expansion-induced entanglement becomes maximum at about 3.6 × 1018 seconds (about 115 billion years), after the Big Bang. By analyzing the fate of seed atoms formed in the early universe, this study underscores the significance of unique quantum mechanical features, such as entanglement, on cosmological scales. The authors investigate quantum entanglement in the hyperfine structure of the neutral hydrogen atom in thermal equilibrium with the cosmological microwave background radiation. They demonstrate that when the universe is around 80 billion years old, neutral hydrogen atoms begin to form entangled states, displaying a phenomenon known as entanglement sudden birth.
氢是宇宙中最主要的原子,被认为是重子物质的主要成分。到目前为止,还没有考虑到宇宙背景中无界氢原子的量子特征以及出现独特量子效应的可能性,例如宇宙尺度上的纠缠。在这项工作中,我们证明了宇宙的动态膨胀导致原子氢的超精细结构中出现自然纠缠。我们的研究结果表明,宇宙中存在一个关键的年龄,在这个年龄,氢原子会自然地形成纠缠,这是宇宙膨胀的结果。更准确地说,当宇宙达到大约2.5 ;× ;1018秒(大约800亿年)的年龄时,氢原子中的超精细结构纠缠自然起飞,展示了一种被称为纠缠突然诞生的奇特量子现象。这种由膨胀引起的纠缠在大爆炸后约36  ;× ;1018秒(约1150亿年)达到最大值。通过分析早期宇宙中形成的种子原子的命运,这项研究强调了独特的量子力学特征的重要性,比如在宇宙尺度上的纠缠。利用宇宙微波背景辐射研究了中性氢原子热平衡超精细结构中的量子纠缠。他们证明,当宇宙大约有800亿年的历史时,中性氢原子开始形成纠缠态,表现出一种被称为纠缠突然诞生的现象。
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引用次数: 0
Hour-glass spectra due to oxygen doping in cobaltates 钴酸盐中的氧掺杂导致的小时玻璃光谱
IF 5.4 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-12-16 DOI: 10.1038/s42005-024-01898-x
W. Peng, H. Guo, W. Schmidt, A. Piovano, H. Luetkens, C.-T. Chen, Z. Hu, A. C. Komarek
The magnetic excitation spectrum of most high-temperature superconducting (HTSC) cuprates is hour-glass shaped. The observation of hour-glass spectra in the isostructural Sr-doped cobaltates La2−xSrxCoO4 gives rise to a deeper understanding of these spectra. So far, hour-glass spectra have been only observed in those systems that evolve from incommensurate magnetic peaks. Here, we report on the appearance of hour-glass spectra in oxygen-doped cobaltates La2CoO4+δ. The high-energy part of the hour-glass spectrum of oxygen doped cobaltates is extremely anisotropic with a very prominent stripe-like appearance not seen that clearly in purely Sr-doped compounds. A charge stripe scenario is evidenced by (polarized) neutron diffraction measurements and also corroborated by spin wave simulations. Our results indicate that charge stripes are the origin of the anisotropic stripe- or diamond-shaped high-energy part of the hour-glass spectrum. A link between hour-glass spectra and charge stripes could be of relevance for the physics in HTSC cuprates. The hour-glass magnetic excitation spectrum is a universal feature of most cuprate high-temperature superconductors, yet the exact origins are still debated. Here, using inelastic neutron scattering techniques, the authors report hour-glass magnetic spectra in an oxygen-doped cobaltate La2CoO4+δ and discuss the potential link with charge stripes and the “diamond-shaped” high energy part of the hour-glass spectrum of this system.
大多数高温超导(HTSC)铜氧化物的磁激发光谱呈小时玻璃状。在等结构掺杂锶的钴酸盐 La2-xSrxCoO4 中观察到小时玻璃光谱,有助于加深对这些光谱的理解。迄今为止,人们只在那些从不相称磁峰演化而来的系统中观察到小时玻璃光谱。在此,我们报告了掺氧钴酸盐 La2CoO4+δ 中出现的小时玻璃光谱。掺氧钴酸盐小时玻璃光谱的高能量部分极度各向异性,具有非常明显的条纹状外观,这在纯掺锶化合物中并不明显。偏振)中子衍射测量证明了电荷条纹的存在,自旋波模拟也证实了这一点。我们的研究结果表明,电荷条纹是小时玻璃光谱中各向异性条纹或菱形高能部分的起源。小时玻璃光谱与电荷条纹之间的联系可能与 HTSC 铜氧化物的物理学有关。小时玻璃磁激发光谱是大多数杯状高温超导体的普遍特征,但其确切起源仍存在争议。在此,作者利用非弹性中子散射技术,报告了掺氧钴酸盐 La2CoO4+δ 中的小时玻璃磁谱,并讨论了与电荷条纹和该系统小时玻璃谱中 "菱形 "高能量部分的潜在联系。
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引用次数: 0
Automatic extraction of fine structural information in angle-resolved photoemission spectroscopy by multi-stage clustering algorithm 基于多阶段聚类算法的角分辨光谱学精细结构信息自动提取
IF 5.4 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-12-06 DOI: 10.1038/s42005-024-01878-1
Lingzhu Bian, Chen Liu, Zhen Zhang, Yingke Huang, Xinyu Pan, Yi Zhang, Jiaou Wang, Pavel Dudin, Jose Avila, Zhesheng Chen, Yuhui Dong
Unsupervised clustering method has shown strong capabilities in automatically categorizing the ARPES (ARPES: angle-resolved photoemission spectroscopy) spatial mapping dataset. However, there is still room for improvement in distinguishing subtle differences caused by different layers and substrates. Here, we propose a method called Multi-Stage Clustering Algorithm (MSCA). Using the K-means clustering results/metrics for real space in different energy-momentum windows as the input of the second round K-means clustering for momentum space, the energy-momentum windows that exhibit subtle inhomogeneity in real space will be highlighted. It recognizes different types of electronic structures both in real space and momentum space in spatially resolved ARPES dataset. This method can be used to capture the areas of interest, and is especially suitable for samples with complex band dispersions, and can be a practical tool to any high dimensional scientific data analysis. A bottleneck for the analysis of data produced by angle-resolved photoemission spectroscopy (ARPES) is the size of the data related to spatial resolution. Building on earlier work, the authors present a data processing method that adopts unsupervised machine learning-based tools to improve the accuracy and efficiency when analysing data produced by nano-ARPES measurements.
无监督聚类方法在ARPES(角分辨光谱学)空间制图数据的自动分类中显示出强大的能力。然而,在区分不同层和基材引起的细微差异方面仍有改进的余地。在这里,我们提出了一种称为多阶段聚类算法(MSCA)的方法。使用不同能量-动量窗口的真实空间K-means聚类结果/指标作为第二轮动量空间K-means聚类的输入,将突出真实空间中表现出微妙非均匀性的能量-动量窗口。在空间分辨的ARPES数据集中,它可以识别实空间和动量空间中不同类型的电子结构。该方法可用于捕获感兴趣的区域,特别适用于具有复杂波段色散的样品,并且可以成为任何高维科学数据分析的实用工具。角分辨光谱学(ARPES)产生的数据分析的瓶颈是与空间分辨率相关的数据的大小。在早期工作的基础上,作者提出了一种数据处理方法,该方法采用基于无监督机器学习的工具,以提高分析纳米arpes测量产生的数据时的准确性和效率。
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引用次数: 0
Community detection and anomaly prediction in dynamic networks 动态网络中的社团检测与异常预测
IF 5.4 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-12-05 DOI: 10.1038/s42005-024-01889-y
Hadiseh Safdari, Caterina De Bacco
Anomaly detection is an essential task in the analysis of dynamic networks, offering early warnings of abnormal behavior. We present a principled approach to detect anomalies in dynamic networks that integrates community structure as a foundational model for regular behavior. Our model identifies anomalies as irregular edges while capturing structural changes. Our approach leverages a Markovian framework for temporal transitions and latent variables for community and anomaly detection, inferring hidden parameters to detect unusual interactions. Evaluations on synthetic and real-world datasets show strong anomaly detection across various scenarios. In a case study on professional football player transfers, we detect patterns influenced by club wealth and country, as well as unexpected transactions both within and across community boundaries. This work provides a framework for adaptable anomaly detection, highlighting the value of integrating domain knowledge with data-driven techniques for improved interpretability and robustness in complex networks. The authors propose a method to detect anomalies in dynamic networks by using community structure as a baseline for normal behavior: the model flags anomalies as irregular connections while tracking structural changes. In football player transfers, it reveals patterns tied to club wealth, nationality, and unexpected transactions across communities.
异常检测是动态网络分析中的一项重要任务,为异常行为提供早期预警。我们提出了一种有原则的方法来检测动态网络中的异常,该网络将社区结构作为常规行为的基础模型。我们的模型将异常识别为不规则边缘,同时捕捉结构变化。我们的方法利用马尔可夫框架进行时间转换和潜在变量进行社区和异常检测,推断隐藏参数以检测异常相互作用。对合成数据集和真实世界数据集的评估显示,在各种场景中都有很强的异常检测能力。在一个关于职业足球运动员转会的案例研究中,我们发现了受俱乐部财富和国家影响的模式,以及社区内和社区外的意外交易。这项工作为适应性异常检测提供了一个框架,突出了将领域知识与数据驱动技术相结合的价值,以提高复杂网络中的可解释性和鲁棒性。作者提出了一种方法,通过使用社区结构作为正常行为的基线来检测动态网络中的异常:该模型在跟踪结构变化时将异常标记为不规则连接。在足球运动员转会中,它揭示了与俱乐部财富、国籍和社区间意外交易相关的模式。
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引用次数: 0
Topological superconductivity in monolayer Td−MoTe2 单层Td−MoTe2的拓扑超导性
IF 5.4 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-12-05 DOI: 10.1038/s42005-024-01881-6
Xin-Zhi Li, Zhen-Bo Qi, Quansheng Wu, Wen-Yu He
Topological superconductivity has attracted significant attention due to its potential applications in quantum computation, but its experimental realization remains challenging. Recently, monolayer Td−MoTe2 was observed to exhibit gate tunable superconductivity, and its in-plane upper critical field exceeds the Pauli limit. Here, we show that an in-plane magnetic field beyond the Pauli limit can drive the superconducting monolayer Td−MoTe2 into a topological superconductor. The topological superconductivity arises from the interplay between the in-plane Zeeman coupling and the unique Ising plus in-plane spin-orbit coupling (SOC) in the monolayer Td−MoTe2. The Ising plus in-plane SOC plays the essential role to enable the effective px + ipy pairing. As the essential Ising plus in-plane SOC in the monolayer Td−MoTe2 is generated by an in-plane polar field, our proposal demonstrates that applying an in-plane magnetic field to a gate tunable 2D superconductor with an in-plane polar axis is a feasible way to realize topological superconductivity. Topological superconductivity is the holy grail for implementing fault-tolerant quantum computation. Here, the authors show that for a superconducting monolayer Td−MoTe2 characterized by the Ising plus in-plane spin-orbit coupling, applying an in-plane magnetic field can drive it to a topological superconductor.
拓扑超导由于其在量子计算中的潜在应用而备受关注,但其实验实现仍然具有挑战性。最近,单层Td−MoTe2被观察到表现出栅极可调超导性,其面内上临界场超过泡利极限。在这里,我们证明了超过泡利极限的面内磁场可以驱动超导单层Td−MoTe2成为拓扑超导体。拓扑超导性是由单层Td−MoTe2的面内塞曼耦合和独特的Ising +面内自旋轨道耦合(SOC)相互作用产生的。isingplus平面内SOC对于实现有效的px  + ; y配对起着至关重要的作用。由于单层Td−MoTe2中必不可少的Ising +面内SOC是由面内极性场产生的,因此我们的研究表明,在具有面内极性轴的栅极可调谐二维超导体上施加面内磁场是实现拓扑超导的可行方法。拓扑超导性是实现容错量子计算的圣杯。在这里,作者证明了以Ising +面内自旋轨道耦合为特征的超导单层Td−MoTe2,施加一个面内磁场可以驱动它成为拓扑超导体。
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引用次数: 0
Probing chiral-symmetric higher-order topological insulators with multipole winding number 探测具有多极圈数的手性对称高阶拓扑绝缘子
IF 5.4 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-12-04 DOI: 10.1038/s42005-024-01884-3
Ling Lin, Chaohong Lee
The interplay between crystalline symmetry and band topology gives rise to unprecedented lower-dimensional boundary states in higher-order topological insulators (HOTIs). However, the measurement of the topological invariants of HOTIs remains a significant challenge. Here, we define a multipole winding number (MWN) for chiral-symmetric HOTIs by applying a corner twisted boundary condition. The MWN, arising from both bulk and boundary states, accurately captures the bulk-corner correspondence including boundary-obstructed topological phases. To address the measurement challenge, we leverage the perturbative nature of the corner twisted boundary condition and develop a real-space approach for determining the MWN in both two-dimensional and three-dimensional systems. The real-space formula provides an experimentally viable strategy for directly probing the topology of chiral-symmetric HOTIs through dynamical evolution. Our findings not only highlight the twisted boundary condition as a powerful tool for investigating HOTIs, but also establish a paradigm for exploring real-space formulas for the topological invariants of HOTIs. Topological invariants are critical in characterizing higher-order topological insulators. In this work, the authors show how to define a multipole winding number that can capture the bulk-corner correspondence, including boundary obstructed topological phases. An experimental proposal complements the theoretical one.
在高阶拓扑绝缘体(HOTIs)中,晶体对称性和带拓扑结构之间的相互作用产生了前所未有的低维边界态。然而,测量HOTIs的拓扑不变量仍然是一个重大的挑战。本文应用角扭边界条件,定义了手性对称hoti的多极圈数。由体态和边界态产生的MWN准确地捕获了包括边界阻塞拓扑相位在内的体角对应。为了解决测量挑战,我们利用角扭曲边界条件的微扰性质,并开发了一种用于确定二维和三维系统中的MWN的实空间方法。实空间公式为通过动态演化直接探测手性对称HOTIs的拓扑结构提供了一种实验上可行的策略。我们的发现不仅突出了扭曲边界条件作为研究hoti的有力工具,而且为探索hoti的拓扑不变量的实空间公式建立了一个范式。拓扑不变量是表征高阶拓扑绝缘子的关键。在这项工作中,作者展示了如何定义一个多极绕组数,可以捕获体角对应,包括边界受阻的拓扑相。一个实验方案补充了理论方案。
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引用次数: 0
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Communications Physics
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