{"title":"Magnon-mediated quantum gates for superconducting qubits","authors":"Martijn Dols, Sanchar Sharma, Lenos Bechara, Yaroslav M. Blanter, Marios Kounalakis, Silvia Viola Kusminskiy","doi":"10.1103/physrevb.110.104416","DOIUrl":"https://doi.org/10.1103/physrevb.110.104416","url":null,"abstract":"We propose a hybrid quantum system consisting of a magnetic particle inductively coupled to two superconducting transmon qubits, where qubit-qubit interactions are mediated via magnons. We show that the system can be tuned into three different regimes of effective qubit-qubit interactions, namely, a transverse (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>X</mi><mi>X</mi><mo>+</mo><mi>Y</mi><mi>Y</mi></mrow></math>), a longitudinal (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>Z</mi><mi>Z</mi></mrow></math>), and a nontrivial <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>Z</mi><mi>X</mi></mrow></math> interaction. In addition, we show that an enhanced coupling can be achieved by employing an ellipsoidal magnet, carrying anisotropic magnetic fluctuations. We propose a scheme for realizing two-qubit gates, and simulate their performance under realistic experimental conditions. We find that i<span>swap</span> and <span>cz</span> gates can be performed in this setup with an average fidelity <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo>≳</mo><mn>99</mn><mo>%</mo></mrow></math>, while an i<span>cnot</span> gate can be applied with an average fidelity <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo>≳</mo><mn>88</mn><mo>%</mo></mrow></math>. Our proposed hybrid circuit architecture offers an alternative platform for realizing two-qubit gates between superconducting qubits and could be employed for constructing qubit networks using magnons as mediators.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158906","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}
Physical Review BPub Date : 2024-09-09DOI: 10.1103/physrevb.110.125117
Sumit Ghosh, Yuriy Mokrousov, Stefan Blügel
{"title":"Microscopic origin of scalar potential induced topological transition in massive Dirac fermions and scalar Hall effect","authors":"Sumit Ghosh, Yuriy Mokrousov, Stefan Blügel","doi":"10.1103/physrevb.110.125117","DOIUrl":"https://doi.org/10.1103/physrevb.110.125117","url":null,"abstract":"We present a systematic study of scalar potential induced topological transition in massive Dirac fermions. We show how a distribution of scalar potential can manipulate the signature of the gap or the <i>mass</i>, as well as the dispersion leading to a band inversion. This is mediated by the <i>Klein tunneling</i> as well as <i>inverse Klein tunneling</i>, which makes it inherently different from the mechanism leading to topological Anderson insulator. In one dimension it can lead to the formation of edge localization. In two dimensions this can give rise to the quantized Hall effect. Unlike conventional Hall effects, this is induced by a scalar interaction and is intrinsic in nature. Therefore, we call it a <i>scalar Hall effect</i>. This can facilitate direct manipulation of topological invariants, e.g., the Chern number, as well as the manipulation of the edge states locally in a trivial insulator and thus opens new possibilities for tuning physical observables which originate from the nontrivial topology.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158677","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}
Physical Review BPub Date : 2024-09-09DOI: 10.1103/physrevb.110.104414
Daniel Qvarngård, P. Henelius
{"title":"Classical spin models and basic magnetic interactions on 1/1-approximant crystals","authors":"Daniel Qvarngård, P. Henelius","doi":"10.1103/physrevb.110.104414","DOIUrl":"https://doi.org/10.1103/physrevb.110.104414","url":null,"abstract":"We study classical spin models on the 1/1 Tsai-type approximant lattice using Monte Carlo and mean-field methods. Our aim is to understand whether the phase diagram differences between Gd- and Tb-based approximants can be attributed to anisotropy induced by the crystal-electric field. To address this question, we treat Gd ions as Heisenberg spins and Tb ions as Ising spins. Additionally, we consider the presence of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction to replicate the experimentally observed correlation between magnetic properties and electron concentration. Surprisingly, our findings show that the transition between ferromagnetic and antiferromagnetic order remains unaltered by the anisotropy, even when accounting for the dipole interaction. We conclude that a more comprehensive model, extending beyond the free-electron gas RKKY interaction, is likely required to fully understand the distinctions between Gd- and Tb-based approximants. Our work represents a systematic exploration of the impact of anisotropy on the ground-state properties of classical spin models in quasicrystal approximants.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158904","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}
Physical Review BPub Date : 2024-09-09DOI: 10.1103/physrevb.110.125118
Lucas Z. Brito, Stephen Carr, J. Alexander Jacoby, J. B. Marston
{"title":"Hamiltonian reconstruction: The correlation matrix and incomplete operator bases","authors":"Lucas Z. Brito, Stephen Carr, J. Alexander Jacoby, J. B. Marston","doi":"10.1103/physrevb.110.125118","DOIUrl":"https://doi.org/10.1103/physrevb.110.125118","url":null,"abstract":"We explore the robustness of the correlation matrix Hamiltonian reconstruction technique with respect to the choice of operator basis, studying the effects of bases that are <i>undercomplete</i> and <i>overcomplete</i>—too few or too many operators, respectively. An approximation scheme for reconstruction using an undercomplete basis is proposed and tested numerically on select models. We discuss the confounding effects of conserved quantities and symmetries on reconstruction attempts. We apply these considerations to a variety of one-dimensional systems at zero and nonzero temperature.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158678","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}
Physical Review BPub Date : 2024-09-09DOI: 10.1103/physrevb.110.104415
Emily Z. Zhang, Ciarán Hickey, Yong Baek Kim
{"title":"Disentangling spin excitation continua in classical and quantum magnets using two-dimensional nonlinear spectroscopy","authors":"Emily Z. Zhang, Ciarán Hickey, Yong Baek Kim","doi":"10.1103/physrevb.110.104415","DOIUrl":"https://doi.org/10.1103/physrevb.110.104415","url":null,"abstract":"Inelastic neutron scattering (INS) has traditionally been one of the primary methods for investigating quantum magnets, particularly in identifying a continuum of excitations as a hallmark of spin fractionalization in quantum spin liquids (QSLs). However, INS faces severe limitations due to its inability to distinguish between such QSL signatures and similar excitation continua arising from highly frustrated magnetic orders with large unit cells or classical spin liquids. In contrast, two-dimensional coherent spectroscopy (2DCS) has emerged as a powerful tool to probe nonlinear excitation dynamics, offering insights into the underlying mechanisms behind these broad spectral features. In this paper, we utilize classical molecular dynamics techniques to explore the 2DCS responses of frustrated magnets with dominant Kitaev interactions. Comparing the classical and quantum versions of the pure Kitaev model, our results indicate both clear similarities, in the form of sharp line features, and clear distinctions, in the locations of these features and in selection rules. Moreover, in the extended <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>K</mi><mi mathvariant=\"normal\">Γ</mi><msup><mi mathvariant=\"normal\">Γ</mi><mo>′</mo></msup></mrow></math> model, we show that the 2DCS response of the Kitaev spin liquid is completely distinct from that of large unit cell magnetic orders, despite both generating a broad continuum in INS. Additionally, we demonstrate the extreme sensitivity of classical 2DCS to thermal fluctuations and discuss the potential significance of quantum coherence in experimental settings. Overall, our paper illustrates the potential of 2DCS in resolving the complex physics underlying ambiguous spin excitation continua, thereby enhancing our understanding of the dynamics in these frustrated systems.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158905","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":"Investigating the cause of crossover from charge/spin-stripe insulator to correlated metallic phase in layered T′ nickelates R4Ni3O8 (R=La,Pr,orNd)","authors":"Dibyata Rout, Sanchayeta Ranajit Mudi, Suman Karmakar, Rajeev Rawat, Surjeet Singh","doi":"10.1103/physrevb.110.094412","DOIUrl":"https://doi.org/10.1103/physrevb.110.094412","url":null,"abstract":"The infinite layered (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>T</mi><mo>′</mo></msup></math>) nickelates have recently garnered significant attention due to the discovery of superconductivity in hole-doped <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mrow><mi>R</mi><mtext>NiO</mtext></mrow><mn>2</mn></msub></math> (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>R</mi><mo>=</mo><mi mathvariant=\"normal\">La</mi><mo>,</mo><mi mathvariant=\"normal\">Pr</mi><mo>,</mo><mtext>or</mtext><mi mathvariant=\"normal\">Nd</mi></mrow></math>), which is the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>n</mi><mo>=</mo><mi>∞</mi></mrow></math> member of the series <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>R</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><msub><mi>Ni</mi><mi>n</mi></msub><msub><mi mathvariant=\"normal\">O</mi><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>2</mn></mrow></msub></mrow></math>. Here, we investigate the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>n</mi><mo>=</mo><mn>3</mn></mrow></math> member, namely <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>R</mi><mn>4</mn></msub><msub><mi>Ni</mi><mn>3</mn></msub><msub><mi mathvariant=\"normal\">O</mi><mn>8</mn></msub></mrow></math> (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>R</mi><mo>=</mo><mi mathvariant=\"normal\">La</mi><mo>,</mo><mi mathvariant=\"normal\">Pr</mi><mo>,</mo><mtext>or</mtext><mi mathvariant=\"normal\">Nd</mi></mrow></math>), of this family. The compound <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"normal\">La</mi><mn>4</mn></msub><msub><mi mathvariant=\"normal\">Ni</mi><mn>3</mn></msub><msub><mi mathvariant=\"normal\">O</mi><mn>8</mn></msub></math> exhibits simultaneous charge/spin-stripe ordering at <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mi>T</mi><mi>N</mi><mo>*</mo></msubsup></math> = 105 K, which occurs concomitantly with the onset of the metal-to-insulator (MIT) transition below <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mi>T</mi><mi>N</mi><mo>*</mo></msubsup></math>. We investigate the conspicuous absence of this transition in the Pr and Nd analogs of <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"normal\">La</mi><mn>4</mn></msub><msub><mi mathvariant=\"normal\">Ni</mi><mn>3</mn></msub><msub><mi mathvariant=\"normal\">O</mi><mn>8</mn></msub></math>. For this purpose, we synthesized solid solutions of the form <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo>(</mo><mi mathvariant=\"normal\">La</mi><mo>,</mo><msub><mrow><mi>Pr</mi><mo>)</mo></mrow><mn>4</mn></msub><msub><mi>Ni</mi><mn>3</mn></msub><msub><mi mathvariant=\"normal\">O</mi><mn>8</mn></msub></mrow></math> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo>(</mo><mi mathvariant=\"normal\">La</mi><mo>,</mo><msub><mrow><mi>Nd</mi><mo>)</mo></mrow><mn>4</mn></msub><msub><mi>Ni</mi><mn>3</mn></msub><msub><mi mathv","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158883","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}
Physical Review BPub Date : 2024-09-09DOI: 10.1103/physrevb.110.104303
Taiki Haga
{"title":"Oscillating-mode gap: An indicator of phase transitions in open quantum many-body systems","authors":"Taiki Haga","doi":"10.1103/physrevb.110.104303","DOIUrl":"https://doi.org/10.1103/physrevb.110.104303","url":null,"abstract":"It presents a significant challenge to elucidate the relationship between the phases of open quantum many-body systems and the spectral structure of their governing Liouvillian, which determines how the density matrix evolves. Previous studies have focused on the Liouvillian gap, defined as the decay rate of the most slowly decaying mode, as a key indicator of dissipative phase transition, noting its closure in symmetry-broken phases and opening in disordered phases. In this work, we propose an additional spectral gap, termed the oscillating-mode gap, defined as the decay rate of the most slowly decaying oscillating mode. Through the analysis of a prototype dissipative boson system, we demonstrate the necessity of both the Liouvillian gap and the oscillating-mode gap for the comprehensive characterization of the system's phases and the transitions between them.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158887","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":"Circularly polarized light irradiated ferromagnetic MnBi2Te4: A possible ideal Weyl semimetal","authors":"Shuai Fan, Shengpu Huang, Zhuo Chen, Fangyang Zhan, Xian-Yong Ding, Da-Shuai Ma, Rui Wang","doi":"10.1103/physrevb.110.125204","DOIUrl":"https://doi.org/10.1103/physrevb.110.125204","url":null,"abstract":"The interaction between light and nontrivial energy band topology allows for the precise manipulation of topological quantum states, which has attracted intensive interest in condensed-matter physics. In this work, using first-principles calculations, we studied the topological transition of ferromagnetic (FM) <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>MnBi</mi><mn>2</mn></msub><msub><mi>Te</mi><mn>4</mn></msub></mrow></math> upon irradiation with circularly polarized light (CPL). We revealed that the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>MnBi</mi><mn>2</mn></msub><msub><mi>Te</mi><mn>4</mn></msub></mrow></math> can be driven from an FM insulator to a Weyl semimetal with a minimum number of Weyl points, i.e., two Weyl points (WPs) in systems without time-reversal symmetry. More importantly, in FM <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>MnBi</mi><mn>2</mn></msub><msub><mi>Te</mi><mn>4</mn></msub></mrow></math> with an out-of-plane easy magnetization axis, we found that the band dispersion of the WP evolves from type-II to type-III and finally to type-I when the light intensity increases. Moreover, we show that the profile of the characteristic Fermi arc of the Weyl semimetal phase is sensitive to changes in light intensity, which enables efficient manipulation of the Fermi arc length of FM <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>MnBi</mi><mn>2</mn></msub><msub><mi>Te</mi><mn>4</mn></msub></mrow></math> in experiments. In addition, for FM <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>MnBi</mi><mn>2</mn></msub><msub><mi>Te</mi><mn>4</mn></msub></mrow></math> with an in-plane easy magnetization axis, the system becomes a type-I Weyl semimetal under CPL irradiation. With controllable band dispersion, the length of the Fermi arc, and a minimum number of WPs, our results indicate that CPL-irradiated FM <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>MnBi</mi><mn>2</mn></msub><msub><mi>Te</mi><mn>4</mn></msub></mrow></math> is an ideal platform for the study of novel transport phenomena in Weyl semimetals with distinct band dispersion.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158679","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}
Physical Review BPub Date : 2024-09-09DOI: 10.1103/physrevb.110.125114
Robert Peters, Tsuneya Yoshida
{"title":"Hinge non-Hermitian skin effect in the single-particle properties of a strongly correlated f-electron system","authors":"Robert Peters, Tsuneya Yoshida","doi":"10.1103/physrevb.110.125114","DOIUrl":"https://doi.org/10.1103/physrevb.110.125114","url":null,"abstract":"Non-Hermitian systems exhibit novel phenomena without Hermitian counterparts, such as exceptional points and the non-Hermitian skin effect. These non-Hermitian topological phenomena are observable in single-particle excitations of correlated systems in equilibrium, which are described by Green's functions. In this paper we demonstrate the appearance of the hinge non-Hermitian skin effect in the effective Hamiltonian that describes the single-particle properties of an <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>f</mi></math>-electron system. Skin effects result in a strong sensitivity to boundary conditions, and a large number of eigenstates localize at one boundary when open boundary conditions are applied. Our system exhibits such sensitivity and hosts skin modes localized around hinges. This hinge skin effect is induced by a non-Hermitian topology of the surface Brillouin zone. The hinge skin modes are observed for one-dimensional subsystems located between one pair of exceptional points in the surface Brillouin zone. This paper highlights that correlated materials are an exciting platform for analyzing non-Hermitian phenomena.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158916","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}
Physical Review BPub Date : 2024-09-09DOI: 10.1103/physrevb.110.094103
Bogdan Guster, Miguel Pruneda, Pablo Ordejón, Enric Canadell, Jean-Paul Pouget
{"title":"Charge density waves and electron-hole instabilities of the hidden-nesting materials P4W12O44, γ- and η−Mo4O11","authors":"Bogdan Guster, Miguel Pruneda, Pablo Ordejón, Enric Canadell, Jean-Paul Pouget","doi":"10.1103/physrevb.110.094103","DOIUrl":"https://doi.org/10.1103/physrevb.110.094103","url":null,"abstract":"The origin of the charge density wave (CDW) instabilities in the isostructural but not isoelectronic octahedral layers of the three-dimensional solids <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>γ</mi><mtext>−</mtext><msub><mi>Mo</mi><mn>4</mn></msub><msub><mi mathvariant=\"normal\">O</mi><mn>11</mn></msub></mrow></math> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi mathvariant=\"normal\">P</mi><mn>4</mn></msub><msub><mi mathvariant=\"normal\">W</mi><mn>12</mn></msub><msub><mi mathvariant=\"normal\">O</mi><mn>44</mn></msub></mrow></math> is discussed on the basis of first-principles density functional theory calculations. These layers contain three different and superposed one-dimensional (1D) systems (two diagonal and one horizontal) associated with the three <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>t</mi><mrow><mn>2</mn><mi>g</mi></mrow></msub></math> orbitals of the transition metal in octahedral coordination. Because of the special topology of the layers the three 1D systems are practically independent (hidden nesting) and the Lindhard function contains three different lines of intensity maxima associated with each of them. Clear cusps (six for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi mathvariant=\"normal\">P</mi><mn>4</mn></msub><msub><mi mathvariant=\"normal\">W</mi><mn>12</mn></msub><msub><mi mathvariant=\"normal\">O</mi><mn>44</mn></msub></mrow></math> and four for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>γ</mi><mtext>−</mtext><msub><mi>Mo</mi><mn>4</mn></msub><msub><mi mathvariant=\"normal\">O</mi><mn>11</mn></msub></mrow></math>) occur at the intersections of these intensity lines. The wave vector of the structural modulations associated with some of these cusps from our calculations is in good agreement with the observed CDW wave vectors. The nature of the different modulations is analyzed on the basis of the calculated thermal dependence of intrachain and interchain coherence lengths of the diffuse lines associated with the diagonal and horizontal chains. Modulation in the diagonal chains is found to be more favorable than in the horizontal chain. The same type of wave vector is selected for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>γ</mi><mtext>−</mtext><msub><mi>Mo</mi><mn>4</mn></msub><msub><mi mathvariant=\"normal\">O</mi><mn>11</mn></msub></mrow></math> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi mathvariant=\"normal\">P</mi><mn>4</mn></msub><msub><mi mathvariant=\"normal\">W</mi><mn>12</mn></msub><msub><mi mathvariant=\"normal\">O</mi><mn>44</mn></msub></mrow></math> despite having a different band filling. The coupling of the electronic instability to the phonon spectra and the relationship between the nature of the high-temperature modulation with the width of the octahedral layers is discussed. Among the two Magnéli phases the interlayer coupling is found to be somewhat stronger in <math xmlns=\"http://www.w3.org","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158881","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}