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(Ann. Phys. 3/2024) (Ann. Phys. 3/2024)
IF 2.4 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-03-13 DOI: 10.1002/andp.202470005
{"title":"(Ann. Phys. 3/2024)","authors":"","doi":"10.1002/andp.202470005","DOIUrl":"https://doi.org/10.1002/andp.202470005","url":null,"abstract":"<p><b>Jumping Platonic Solids</b></p><p>Macroscopic objects excited mechanically by vibrating plates represent simple systems that can exhibit complex dynamics, including quasi-chaotic behavior. Bouncing spheres were investigated for decades. Such mechanical excitation provides a basis for experimental studies of granular gases. The study of bouncing Platonic solids (see article number 2300349 by Ralf Stannarius and co-workers) adds more complexity such as coupling of rotational and translational degrees of freedom. Integrated intelligent sensor chips were employed to analyze the particle trajectories and rotations.\u0000\u0000 <figure>\u0000 <div><picture>\u0000 <source></source></picture><p></p>\u0000 </div>\u0000 </figure></p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 3","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/andp.202470005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140123660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tunneling Effect of Fermions in Silicene Through Potential Barrier 硅烯中费米子通过势垒的隧道效应
IF 2.4 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-03-11 DOI: 10.1002/andp.202400002
Sanae Zriouel, Ahmed Jellal
{"title":"Tunneling Effect of Fermions in Silicene Through Potential Barrier","authors":"Sanae Zriouel,&nbsp;Ahmed Jellal","doi":"10.1002/andp.202400002","DOIUrl":"10.1002/andp.202400002","url":null,"abstract":"<p>The influence of a a rectangular potential barrier on the quantum transport of fermions in silicene is explored. Specifically, analytical solutions are presented to derive transmission and reflection probabilities together with conductance. It is shown that the transmission is highly sensitive to both the barrier height and incident energy. As a result, the occurrence of Klein and resonant tunnelings is observed, with a significant dependence on the barrier width. Notably, it is found that perfect transmission extends beyond normal incidence, occurring at various oblique angles. Moreover, the transmission pattern exhibits a more fragmented structure with increasing barrier width, reminiscent of Fabry-Pérot resonances. In contrast, the conductance displays a non-monotonic dependence on incident energy and features rapid oscillations with a rising barrier height. However, at a constant barrier height, there is a minimal disparity among conductance profiles for high incident energy values. When incident energy equals the barrier height, the conductance experiences a local minimum. For a thin barrier, a substantial reduction in conductance is observed, unlike the oscillatory behavior seen with a thicker barrier. These findings underscore the progress in silicene research and offer a fresh perspective on the relativistic applications of tunneling in this material.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140105950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Propagation Dynamics of the Symmetric Pearcey Gaussian Beam in the Kerr Medium 对称皮尔斯高斯光束在克尔介质中的传播动力学
IF 2.2 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-03-08 DOI: 10.1002/andp.202300472
Peixin Yu, Shuo Yang, Shuyu Li, Xiao Zhang, Zhongsheng Man, Xiaolu Ge, Wenfei Zhang, Chidao Chen, Dongmei Deng, Liping Zhang
{"title":"The Propagation Dynamics of the Symmetric Pearcey Gaussian Beam in the Kerr Medium","authors":"Peixin Yu,&nbsp;Shuo Yang,&nbsp;Shuyu Li,&nbsp;Xiao Zhang,&nbsp;Zhongsheng Man,&nbsp;Xiaolu Ge,&nbsp;Wenfei Zhang,&nbsp;Chidao Chen,&nbsp;Dongmei Deng,&nbsp;Liping Zhang","doi":"10.1002/andp.202300472","DOIUrl":"10.1002/andp.202300472","url":null,"abstract":"<p>In this paper, symmetric Pearcey Gaussian beams (SPGBs) are studied in a Kerr medium. By varying the initial input power, the autofocusing ability of the beams is investigated, to find a clear restrictive relationship between the breath-like structure and the initial input power. The critical collapse power is investigated when SPGBs change from discrete beams to regular breath-like structure. Finally, the transmission of SPGBs is discussed under different phase modulation when SPGBs are affected by astigmatic, the whole beam is rotated and the angle of rotation can be controlled.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 7","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140071497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cylindrically Symmetric Diffusion Model for Relativistic Heavy-Ion Collisions 相对论重离子碰撞的圆柱对称扩散模型
IF 2.4 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-03-07 DOI: 10.1002/andp.202300307
Johannes Hoelck, Georg Wolschin
{"title":"Cylindrically Symmetric Diffusion Model for Relativistic Heavy-Ion Collisions","authors":"Johannes Hoelck,&nbsp;Georg Wolschin","doi":"10.1002/andp.202300307","DOIUrl":"10.1002/andp.202300307","url":null,"abstract":"<p>A relativistic diffusion model with cylindrical symmetry, which propagates an initial state based on quantum chromodynamics in time toward a thermal equilibrium limit, is derived from nonequilibrium–statistical considerations: adapting an existing framework for Markovian stochastic processes representing relativistic phase-space trajectories, a Fokker–Planck equation is obtained for the time evolution of particle-number distribution functions with respect to transverse and longitudinal rapidity. The resulting partially-evolved distribution functions are transformed to transverse-momentum and pseudorapidity space, and compared with charged-hadron data from the CERN Large Hadron Collider.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 5","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/andp.202300307","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140071496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Wavelength Scale Singlet Achromatic Microlenses Based on High Refractive Index Materials 基于高折射率材料的波长级单色消色差微透镜
IF 2.2 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-03-06 DOI: 10.1002/andp.202300543
Xueqian Wang, Chuanbao Liu, Lijie Qiao, Ji Zhou, Yang Bai, Jingbo Sun
{"title":"Wavelength Scale Singlet Achromatic Microlenses Based on High Refractive Index Materials","authors":"Xueqian Wang,&nbsp;Chuanbao Liu,&nbsp;Lijie Qiao,&nbsp;Ji Zhou,&nbsp;Yang Bai,&nbsp;Jingbo Sun","doi":"10.1002/andp.202300543","DOIUrl":"10.1002/andp.202300543","url":null,"abstract":"<p>The common methods used for correcting chromatic aberration are typically based on multi-lens and multi-material systems, resulting in lens thicknesses that are several orders of magnitude greater than the wavelength and complex combination designs. A method to achieve the singlet achromatic microlens of the wavelength-scale thickness by utilizing high refractive index materials with an aspherical profile is proposed. A theoretical model based on the dispersion effect is developed to guide the selection of materials and the design of thicknesses for achieving chromatic aberration correction in singlet microlenses of a given diameter and numerical aperture. H-ZLaF68N (68N) glass, sapphire, and fused silica with relatively high to low refractive index are selected to prepare the singlet achromatic microlenses to verify the validity of the model. The thicknesses of three microlenses are 573, 737 nm, and 1.27 µm, respectively, and all of them have achieved achromatic correction as designed. This indicates that the high refractive index material not only achieves achromatic aberration but also reduces the thickness by ≈50% compared with the conventional low refractive index material of silica glass. The presented wavelength-scale singlet achromatic microlens hold significant promise for compact wearable devices, dynamic holography, and color projection displays.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 8","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140071493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Matrix-Product State Approach to the Generalized Nuclear Pairing Hamiltonian 广义核配对哈密顿的矩阵-乘积态方法
IF 2.4 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-03-04 DOI: 10.1002/andp.202300436
Roman Rausch, Cassian Plorin, Matthias Peschke, Christoph Karrasch
{"title":"Matrix-Product State Approach to the Generalized Nuclear Pairing Hamiltonian","authors":"Roman Rausch,&nbsp;Cassian Plorin,&nbsp;Matthias Peschke,&nbsp;Christoph Karrasch","doi":"10.1002/andp.202300436","DOIUrl":"10.1002/andp.202300436","url":null,"abstract":"&lt;p&gt;It is shown that from the point of view of the generalized pairing Hamiltonian, the atomic nucleus is a system with small entanglement and can thus be described efficiently using a 1D tensor network (matrix-product state) despite the presence of long-range interactions. The ground state can be obtained using the density-matrix renormalization group (DMRG) algorithm, which is accurate up to machine precision even for large nuclei, is numerically as cheap as the widely used Bardeen-Cooper-Schrieffer (BCS) approach, and does not suffer from any mean-field artifacts. This framework is applied to compute the even-odd mass differences of all known lead isotopes from &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;&lt;/mrow&gt;\u0000 &lt;mn&gt;178&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mtext&gt;Pb&lt;/mtext&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$^{178}text{Pb}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; to &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;&lt;/mrow&gt;\u0000 &lt;mn&gt;220&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mtext&gt;Pb&lt;/mtext&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$^{220}text{Pb}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; in a very large configuration space of 13 shells between the neutron magic numbers 82 and 184 (i.e., two major shells) and find good agreement with the experiment. Pairing with non-zero angular momentum is also considered and the lowest excited states in the full configuration space of one major shell is determined, which is demonstrated for the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;126&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$N=126$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mo&gt;≥&lt;/mo&gt;\u0000 &lt;mn&gt;82&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Zge 82$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; isotones. To demonstrate the capabilities of the method beyond low-lying excitations, the first 100 excited states of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;&lt;/mrow&gt;\u0000 &lt;mn&gt;208&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mtext&gt;Pb&lt;/mtext&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$^{208}text{Pb}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with singlet pairing and the two-neutron removal spectral function of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;&lt;/","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/andp.202300436","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140047064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inversion Symmetry Breaking in the Probability Density by Surface-Bulk Hybridization in Topological Insulators 拓扑绝缘体中表-体杂化导致的概率密度反转对称性破坏
IF 2.4 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-03-03 DOI: 10.1002/andp.202300398
Jorge David Castaño-Yepes, Enrique Muñoz
{"title":"Inversion Symmetry Breaking in the Probability Density by Surface-Bulk Hybridization in Topological Insulators","authors":"Jorge David Castaño-Yepes,&nbsp;Enrique Muñoz","doi":"10.1002/andp.202300398","DOIUrl":"10.1002/andp.202300398","url":null,"abstract":"<p>The probability density distribution is analyzed in a topological insulator (TI) slab of finite thickness, where the bulk and surface states are allowed to hybridize. By using an effective continuum Hamiltonian approach as a theoretical framework, the wave functions are analytically obtained for each state near the <span></span><math>\u0000 <semantics>\u0000 <mi>Γ</mi>\u0000 <annotation>$Gamma$</annotation>\u0000 </semantics></math>-point. The results reveal that, under particular combinations of the hybridized bulk and surface states, the spatial symmetry of the electronic probability density with respect to the center of the slab can be spontaneously broken. This symmetry breaking arises as a combination of the parity of the solutions, their spin projection, and the material constants.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Scattering of Bright Solitons Due to Defects in Binary Bose-Einstein Condensates with Nonlinear Optical Lattices 具有非线性光晶格的双玻色-爱因斯坦凝聚态中缺陷引起的亮孤子散射
IF 2.4 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-03-03 DOI: 10.1002/andp.202300522
Golam Ali Sekh
{"title":"Scattering of Bright Solitons Due to Defects in Binary Bose-Einstein Condensates with Nonlinear Optical Lattices","authors":"Golam Ali Sekh","doi":"10.1002/andp.202300522","DOIUrl":"10.1002/andp.202300522","url":null,"abstract":"<p>Spatially overlapped coupled matter-wave bright solitons are considered in binary Bose-Einstein condensates with nonlinear optical lattices(NOLs) and study the properties of scattering patterns due to a localized defect. It is shown that spatially overlapped solitons become separated and exhibit different scattering patterns with the variation of inter-species interaction. The NOL interplays with the defect and tends to influence the scattering properties. However, the effect of NOL varies with strength of inter-component interaction. It is found that, if this interaction is weak then the scattering center gets shifted outside the defect. However, for a stronger inter-component interaction, the scattering takes place from the defect and leads to different scattering patterns.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectral Determinant of the Two-Photon Quantum Rabi Model [Ann. Phys. (Berlin) 2023, 535, 2200519] 双光子量子拉比模型的光谱决定子 [Ann.
IF 2.4 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-02-27 DOI: 10.1002/andp.202400005
Daniel Braak
{"title":"Spectral Determinant of the Two-Photon Quantum Rabi Model [Ann. Phys. (Berlin) 2023, 535, 2200519]","authors":"Daniel Braak","doi":"10.1002/andp.202400005","DOIUrl":"10.1002/andp.202400005","url":null,"abstract":"<p>Contrary to the statement made in Section 2.2. and a paper by Ng et al., the Hamiltonian of the two-photon quantum Rabi model is self-adjoint for all <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ω</mi>\u0000 <mo>≥</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$omega ge 0$</annotation>\u0000 </semantics></math>. Other results of the article are not affected.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/andp.202400005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139979056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hybrid Orbital Formation and Multicenter Bonding of Hydrogen Atoms and Molecules in Ti 3 C 2 ${rm Ti}_{3}{rm C}_{2}$ MXenes Ti3C2${rm Ti}_{3}{rm C}_{2}$二茂钛中氢原子和分子的混合轨道形成与多中心结合
IF 2.4 4区 物理与天体物理
Annalen der Physik Pub Date : 2024-02-22 DOI: 10.1002/andp.202400011
Norbert H. Nickel
{"title":"Hybrid Orbital Formation and Multicenter Bonding of Hydrogen Atoms and Molecules in \u0000 \u0000 \u0000 \u0000 Ti\u0000 3\u0000 \u0000 \u0000 C\u0000 2\u0000 \u0000 \u0000 ${rm Ti}_{3}{rm C}_{2}$\u0000 MXenes","authors":"Norbert H. Nickel","doi":"10.1002/andp.202400011","DOIUrl":"10.1002/andp.202400011","url":null,"abstract":"&lt;p&gt;The formation and stability of solids and molecules is not possible without chemical bonds, which are divided into covalent, ionic, metallic, and van der Waals bonds. A special type of intermolecular bond is hydrogen bonding, which plays a crucial role for chemical, biological, and physical processes. However, hydrogen shows a far more complex behavior when it is present in solids. In this paper, it is shown that the chemical bonding of hydrogen atoms and molecules extends far beyond the simple picture of conventional, ionic, covalent, and multicenter bonds. The interaction of H with its host material is particularly important for hydrogen storage in metallic materials such as &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Ti&lt;/mi&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm Ti}_{3}{rm C}_{2}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; MXenes. Hydrogen atoms and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;${rm H}_2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; molecules form multicenter bonds in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Ti&lt;/mi&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm Ti}_{3}{rm C}_{2}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. On the surface and between two &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Ti&lt;/mi&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm Ti}_{3}{rm C}_{2}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; sheets this is limited to the formation of H–Ti bonds. However, H and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;${rm H}_2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; on interstitial sites form multicenter bonds not only with nearest neighbor Ti atoms but also with carbon atoms. Interestingly, the H–C bonds are characterized by the formation of s–p hybrid orbitals. For &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 ","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"536 6","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/andp.202400011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139956316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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