Physical Review B最新文献

{"title":"Locality, correlations, information, and non-Hermitian quantum systems","authors":"Brian Barch","doi":"10.1103/physrevb.110.094307","DOIUrl":"https://doi.org/10.1103/physrevb.110.094307","url":null,"abstract":"Local non-Hermitian (NH) quantum systems generically exhibit breakdown of Lieb-Robinson (LR) bounds, motivating study of whether new locality measures might shed light not seen by existing measures. In this paper we discuss extensions of the connected correlation function (CC) as measures of locality and information spreading in both Hermitian and NH systems. We find that in Hermitian systems, <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>δ</mi><mi>ρ</mi><mo>=</mo><mi>ρ</mi><mo>−</mo><msub><mi>ρ</mi><mi>A</mi></msub><mo>⊗</mo><msub><mi>ρ</mi><mi>B</mi></msub></mrow></math> can be written as a linear combination of CCs, allowing placement of an LR bound on <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mrow><mo>∥</mo><mi>δ</mi><mi>ρ</mi><mo>∥</mo></mrow><mn>2</mn></msub></math>, which we show generically extends to an LR bound on mutual information. Additionally, we extend the CC to NH systems in a form that recovers locality, and use the metric formalism to derive a modified CC which recovers not just locality but even LR bounds in local <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>P</mi><mi>T</mi></mrow></math>-Symmetric systems. We find that even with these CCs, the bound on <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mrow><mo>∥</mo><mi>δ</mi><mi>ρ</mi><mo>∥</mo></mrow><mn>2</mn></msub></math> breaks down in certain NH cases, which can be used to place a necessary condition on which local NH Hamiltonians are capable of nonlocal entanglement generation. Numerical simulations are provided by means of exact diagonalization for the NH Transverse-Field Ising Model, demonstrating both breakdown and recovery of LR bounds.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142142543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}

{"title":"Optimized effective potential forces with the plane-wave and pseudopotential method","authors":"Damian Contant, Maria Hellgren","doi":"10.1103/physrevb.110.125110","DOIUrl":"https://doi.org/10.1103/physrevb.110.125110","url":null,"abstract":"The optimized effective potential (OEP) approach has so far mainly been used in benchmark studies and for the evaluation of band gaps. In this work, we extend the application of the OEP by determining the analytical ionic forces within the plane-wave and pseudopotential framework. It is first shown that, due to the constrained optimization inherent to the OEP approach, an extra term needs to be added to the standard Hellmann-Feynman expression for the forces, whenever nonlocal pseudopotentials are employed. Computing this term for functionals based on Hartree-Fock and the hybrid PBE0 functional yields forces with excellent numerical accuracy. Furthermore, results for equilibrium geometries and vibrational frequencies on a set of molecules and solids confirm that the local exchange OEP is able to reproduce results obtained with the nonlocal exchange potential. Our work opens up the possibility to study lattice dynamics using advanced orbital functionals for describing exchange and correlation effects.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142142547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}

{"title":"Attractive Haldane bilayers for trapping non-Abelian anyons","authors":"Valentin Crépel, Nicolas Regnault","doi":"10.1103/physrevb.110.115109","DOIUrl":"https://doi.org/10.1103/physrevb.110.115109","url":null,"abstract":"We study the interplay between intrinsic topological order and superconductivity in a two-component Haldane bilayer, where the two layers are coupled by an attractive force. We obtain the phase diagram of the model with exact diagonalization in finite size, and develop arguments to assess the stability of the observed phases in the thermodynamic limit. Our main result is that a finite critical attraction strength is needed to pair fermions forming a fractional topological order. This behavior can be harnessed to create clean interfaces between a fractional topological insulator and a superconductor by gating, wherein non-Abelian parafermionic modes are trapped. We discuss realization of such interfaces in the bulk of double bilayers of transition metal dichalcogenides by inhomogenous electrostatic gating, which should mitigate the spurious effects of disorder and crystalline defects present on physical edges.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142144411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}

{"title":"Anisotropy-induced spin parity effects","authors":"Shuntaro Sumita, Akihiro Tanaka, Yusuke Kato","doi":"10.1103/physrevb.110.l100403","DOIUrl":"https://doi.org/10.1103/physrevb.110.l100403","url":null,"abstract":"Spin parity effects refer to those special situations where a dichotomy in the physical behavior of a system arises, solely depending on whether the relevant spin quantum number is integral or half-odd integral. As is the case with the Haldane conjecture in antiferromagnetic spin chains, their pursuit often derives deep insights and invokes new developments in quantum condensed matter physics. Here, we put forth a simple and general scheme for generating such effects in any spatial dimension through the use of anisotropic interactions, and a setup within reasonable reach of state-of-the-art cold-atom implementations. We demonstrate its utility through a detailed analysis of the magnetization behavior of a specific one-dimensional spin chain model, an anisotropic antiferromagnet in a transverse magnetic field, unraveling along the way the quantum origin of finite-size effects observed in the magnetization curve that had previously been noted but not clearly understood.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142144414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}

{"title":"High harmonic generation from electrons moving in topological spin textures","authors":"Atsushi Ono, Shun Okumura, Shohei Imai, Yutaka Akagi","doi":"10.1103/physrevb.110.125111","DOIUrl":"https://doi.org/10.1103/physrevb.110.125111","url":null,"abstract":"High harmonic generation (HHG) is a striking phenomenon, which reflects the ultrafast dynamics of electrons. Recently, it has been demonstrated that HHG can be used to reconstruct not only the energy band structure but also the geometric structure characterized by the Berry curvature. Here, we numerically investigate HHG arising from electrons coupled with a topological spin texture in a spin scalar chiral state where time reversal symmetry is broken. In this system, a sign change in scalar chirality alters the sign of the Berry curvature while keeping the energy band structure unchanged, allowing us to discuss purely geometrical effects on HHG. Notably, we found that, when the optical frequency is significantly lower than the energy gap, the sign of scalar chirality largely affects the longitudinal response parallel to the optical field rather than the transverse response. Our analysis suggests that this can be attributed to interband currents induced by the recombination of electron-hole pairs whose real-space trajectories are modulated by the anomalous velocity term.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142142548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}

{"title":"Uncovering gauge-dependent critical order-parameter correlations by a stochastic gauge fixing at O(N)* and Ising* continuous transitions","authors":"Claudio Bonati, Andrea Pelissetto, Ettore Vicari","doi":"10.1103/physrevb.110.125109","DOIUrl":"https://doi.org/10.1103/physrevb.110.125109","url":null,"abstract":"We study the &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mrow&gt;&lt;mi mathvariant=\"normal\"&gt;O&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt; transitions that occur in the 3D &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;msub&gt;&lt;mi mathvariant=\"double-struck\"&gt;Z&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;/math&gt;-gauge &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/math&gt;-vector model and the analogous &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;Ising&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msup&gt;&lt;/math&gt; transitions occurring in the 3D &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;msub&gt;&lt;mi mathvariant=\"double-struck\"&gt;Z&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;/math&gt;-gauge Higgs model, corresponding to the &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;msub&gt;&lt;mi mathvariant=\"double-struck\"&gt;Z&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;/math&gt;-gauge &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/math&gt;-vector model with &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;. At these transitions, gauge-invariant correlations behave as in the usual &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/math&gt;-vector (Ising for &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;) model. Instead, the non-gauge-invariant spin correlations are trivial and therefore the spin order parameter that characterizes the spontaneous breaking of the &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mrow&gt;&lt;mi mathvariant=\"normal\"&gt;O&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt; symmetry in standard &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/math&gt;-vector (Ising) systems is apparently absent. We define a gauge fixing procedure—we name it stochastic gauge fixing—that allows us to define a gauge-dependent vector field that orders at the transition and is therefore the appropriate order parameter for the &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mrow&gt;&lt;mi mathvariant=\"normal\"&gt;O&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt; symmetry breaking. To substantiate this approach, we perform numerical simulations for &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt; and &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;. A finite-size scaling analysis of the numerical data allows us to confirm the general scenario: the gauge-fixed spin correlation functions behave as the corresponding functions computed in the usual &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/math&gt;-vector (Ising) model. The emergence of a critical vector order parameter in the gauge model shows the complete equivalence of the &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mrow&gt;&lt;mi mathvariant=\"normal\"&gt;O&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt; (&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;Ising&lt;/mi","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142142546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}

{"title":"Spin supercurrent in superconductor/ferromagnet van der Waals heterostructures","authors":"G. A. Bobkov, A. M. Bobkov, I. V. Bobkova","doi":"10.1103/physrevb.110.104506","DOIUrl":"https://doi.org/10.1103/physrevb.110.104506","url":null,"abstract":"We study dissipationless spin transport induced by a charge supercurrent in a monolayer van der Waals superconductor under the applied magnetic field and in a bilayer superconductor/ferromagnet (S/F) heterostructure with no external field. It is shown that in both cases a combined action of the Ising-type spin-orbit coupling and the Zeeman field results in the appearance of nonunitary superconducting triplet correlations with nonzero average Cooper pair spin, which carry spin current in the presence of a condensate motion. Properties of this dissipationless spin current are investigated. In particular, it is shown that it manifests a rectification effect. In addition, in S/F heterostructures the amplitude and the sign of the spin current are controlled by gating.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142144402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}

{"title":"Enantioselective optical forces and size-dependent sorting of single chiral particles using vortex beams","authors":"R. Ali, F. A. Pinheiro, R. S. Dutra, T. P. Mayer Alegre, G. S. Wiederhecker","doi":"10.1103/physrevb.110.115412","DOIUrl":"https://doi.org/10.1103/physrevb.110.115412","url":null,"abstract":"We put forward an approach to manipulate and enantioselect chiral microspheres using vortex beams that encode topological charges. Vortex beams with different topological charges transfer angular momentum to chiral particles with opposite handedness in a different way. This process also depends on the incident polarization, in a rich interplay that ultimately leads to enantioselective optical forces acting on single chiral particles with selected, arbitrary sizes. Besides this scheme also depends on the order of the topological charge, which can also be controlled experimentally. The resulting enantioselective optical forces are up to two orders of magnitude larger than the existing chiral resolution methods based on optical forces, further demonstrating the unique functionalities and applicability of the method.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142144413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}

{"title":"Diffusion constants from the recursion method","authors":"Jiaozi Wang, Mats H. Lamann, Robin Steinigeweg, Jochen Gemmer","doi":"10.1103/physrevb.110.104413","DOIUrl":"https://doi.org/10.1103/physrevb.110.104413","url":null,"abstract":"Understanding the transport behavior of quantum many-body systems constitutes an important physical endeavor, both experimentally and theoretically. While a reliable classification into normal and anomalous dynamics is known to be notoriously difficult for a given microscopic model, even the seemingly simpler evaluation of transport coefficients in diffusive systems continues to be a hard task in practice. This fact has motivated the development and application of various sophisticated methods and is also the main issue of this paper. We particularly take a barely used strategy, which is based on the recursion method, and demonstrate that this strategy allows for accurate calculation of diffusion constants for different paradigmatic examples, including magnetization transport in nonintegrable spin-<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math> chains and ladders as well as energy transport in the mixed-field Ising model in one dimension.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142144401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}

{"title":"Electronic band structure of high-symmetry homobilayers of transition metal dichalcogenides","authors":"Heng Zhang, Wen Xu, Yiming Xiao, Francois M. Peeters, Milorad V. Milošević","doi":"10.1103/physrevb.110.115410","DOIUrl":"https://doi.org/10.1103/physrevb.110.115410","url":null,"abstract":"High-symmetric homobilayer transition metal dichalcogenides (TMDs) are important members of the bilayer (BL) van der Waals material family. Here we present a systematic study of the electronic band structure in low-energy regime in homo-BL TMD structures by using the standard &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;·&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt; method. Six types of BL TMD stacking configurations, which satisfy the &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;msub&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msub&gt;&lt;/math&gt; symmetry are considered and they are &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;msubsup&gt;&lt;mi mathvariant=\"normal\"&gt;H&lt;/mi&gt;&lt;mi mathvariant=\"normal\"&gt;M&lt;/mi&gt;&lt;mi mathvariant=\"normal\"&gt;M&lt;/mi&gt;&lt;/msubsup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt; &lt;/mo&gt;&lt;msubsup&gt;&lt;mi mathvariant=\"normal\"&gt;H&lt;/mi&gt;&lt;mi mathvariant=\"normal\"&gt;X&lt;/mi&gt;&lt;mi mathvariant=\"normal\"&gt;M&lt;/mi&gt;&lt;/msubsup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt; &lt;/mo&gt;&lt;msubsup&gt;&lt;mi mathvariant=\"normal\"&gt;H&lt;/mi&gt;&lt;mi mathvariant=\"normal\"&gt;X&lt;/mi&gt;&lt;mi mathvariant=\"normal\"&gt;X&lt;/mi&gt;&lt;/msubsup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt; &lt;/mo&gt;&lt;msubsup&gt;&lt;mi mathvariant=\"normal\"&gt;R&lt;/mi&gt;&lt;mi mathvariant=\"normal\"&gt;M&lt;/mi&gt;&lt;mi mathvariant=\"normal\"&gt;M&lt;/mi&gt;&lt;/msubsup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt; &lt;/mo&gt;&lt;msubsup&gt;&lt;mi mathvariant=\"normal\"&gt;R&lt;/mi&gt;&lt;mi mathvariant=\"normal\"&gt;X&lt;/mi&gt;&lt;mi mathvariant=\"normal\"&gt;M&lt;/mi&gt;&lt;/msubsup&gt;&lt;/math&gt;, and &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;msubsup&gt;&lt;mi mathvariant=\"normal\"&gt;R&lt;/mi&gt;&lt;mi mathvariant=\"normal\"&gt;M&lt;/mi&gt;&lt;mi mathvariant=\"normal\"&gt;X&lt;/mi&gt;&lt;/msubsup&gt;&lt;/math&gt;. The intrinsic spin-orbit coupling (SOC) in the conduction and valence bands and the phase of interlayer hopping matrix elements are included in our investigation. Taking BL &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;msub&gt;&lt;mi&gt;MoS&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;/math&gt; as an example, we examine the electronic energy spectra, the electron density of states, and the Fermi energies in these BL structures. We find that the electron energy dispersions in high-symmetric BL TMDs are not parabolic-like, where the band parameters (such as the energy gap, the effective electron band mass and the fourth-order correction coefficient in different subbands) depend markedly on the stacking configurations. Interestingly, the spin splitting in &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi mathvariant=\"normal\"&gt;H&lt;/mi&gt;&lt;/math&gt;-stacked BL TMDs is suppressed because of center-inversion symmetry and time-reversal symmetry. Importantly, the phase of the interlayer hopping matrix element affects significantly the electronic properties of &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;msubsup&gt;&lt;mi mathvariant=\"normal\"&gt;H&lt;/mi&gt;&lt;mi mathvariant=\"normal\"&gt;X&lt;/mi&gt;&lt;mi mathvariant=\"normal\"&gt;X&lt;/mi&gt;&lt;/msubsup&gt;&lt;/math&gt; and &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;msubsup&gt;&lt;mi mathvariant=\"normal\"&gt;R&lt;/mi&gt;&lt;mi mathvariant=\"normal\"&gt;M&lt;/mi&gt;&lt;mi mathvariant=\"normal\"&gt;M&lt;/mi&gt;&lt;/msubsup&gt;&lt;/math&gt; stacked BL TMDs. The methodology and the results presented in this study can foster further exploration of the basic physical properties of BL TMDs for potential applications in ele","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142142545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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}