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Fan K, Jin H, Huang B, Duan G, Yu R, Liu ZY, Xia HN, Liu LS, Zhang Y, Xie T, Tang QY, Chen G, Zhang WH, Chen FC, Luo X, Lu WJ, Sun YP, Fu YS. Artificial superconducting Kondo lattice in a van der Waals heterostructure. Nat Commun 2024; 15:8797. [PMID: 39394191 PMCID: PMC11470022 DOI: 10.1038/s41467-024-53166-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2024] [Accepted: 10/02/2024] [Indexed: 10/13/2024] Open
Abstract
Engineering Kondo lattice with tailored functionality is desirable for elucidating the heavy fermion physics. We realize the construction of an artificial Kondo lattice/superconductor heterojunction by growing monolayer VSe2 on bulk 2H-NbSe2 with molecular beam epitaxy. Spectroscopic imaging scanning tunneling microscopy measurements show the emergence of a new charge density wave (CDW) phase with3 × 3 periodicity on the monolayer VSe2. Unexpectedly, a pronounced Kondo resonance appears around the Fermi level, and distributes uniformly over the entire film, evidencing the formation of Kondo lattice. Density functional theory calculations suggest the existence of magnetic interstitial V atoms in VSe2/NbSe2, which play a key role in forming the CDW phase along with the Kondo lattice observed in VSe2. The Kondo origin is verified from both the magnetic field and temperature dependences of the resonance peak, yielding a Kondo temperature of ~ 44 K. Moreover, a superconducting proximity gap opens on monolayer VSe2, whose shape deviates from the function of one-band BCS superconductor, but is reproduced by model calculations with heavy electrons participating the pairing condensate. Our work lays the experimental foundation for studying interactions between the heavy fermion liquids and the superconducting condensate.
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Affiliation(s)
- Kai Fan
- School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Heng Jin
- School of Physics and Astronomy, Beijing Normal University, Beijing, 100875, China
- Beijing Computational Science Research Center, Beijing, 100093, China
| | - Bing Huang
- School of Physics and Astronomy, Beijing Normal University, Beijing, 100875, China
- Beijing Computational Science Research Center, Beijing, 100093, China
| | - Guijing Duan
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing, 100872, China
| | - Rong Yu
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing, 100872, China
| | - Zhen-Yu Liu
- School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Hui-Nan Xia
- School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Li-Si Liu
- School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Yao Zhang
- School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Tao Xie
- School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Qiao-Yin Tang
- School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Gang Chen
- School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Wen-Hao Zhang
- School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - F C Chen
- Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei, 230031, China
| | - X Luo
- Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei, 230031, China
| | - W J Lu
- Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei, 230031, China
| | - Y P Sun
- Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei, 230031, China
- High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei, 230031, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China
| | - Ying-Shuang Fu
- School of Physics and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, 430074, China.
- Wuhan Institute of Quantum Technology, Wuhan, 430206, China.
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2
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Ayani CG, Bosnar M, Calleja F, Solé AP, Stetsovych O, Ibarburu IM, Rebanal C, Garnica M, Miranda R, Otrokov MM, Ondráček M, Jelínek P, Arnau A, Vázquez de Parga AL. Unveiling the Interlayer Interaction in a 1H/1T TaS 2 van der Waals Heterostructure. NANO LETTERS 2024; 24:10805-10812. [PMID: 39038223 DOI: 10.1021/acs.nanolett.4c02068] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/24/2024]
Abstract
This study delves into the intriguing properties of the 1H/1T-TaS2 van der Waals heterostructure, focusing on the transparency of the 1H layer to the charge density wave of the underlying 1T layer. Despite the sizable interlayer separation and metallic nature of the 1H layer, positive bias voltages result in a pronounced superposition of the 1T charge density wave structure on the 1H layer. The conventional explanation relying on tunneling effects proves insufficient. Through a comprehensive investigation combining low-temperature scanning tunneling microscopy, scanning tunneling spectroscopy, non-contact atomic force microscopy, and first-principles calculations, we propose an alternative interpretation. The transparency effect arises from a weak yet substantial electronic coupling between the 1H and 1T layers, challenging prior understanding of the system. Our results highlight the critical role played by interlayer electronic interactions in van der Waals heterostructures to determine the final ground states of the systems.
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Affiliation(s)
- Cosme G Ayani
- Departamento de Física de la Materia Condensada, Universidad Autónoma de Madrid - Cantoblanco Campus, 28049 Madrid, Spain
- IMDEA Nanociencia, Calle Faraday 9, 28049 Cantoblanco, Madrid, Spain
| | - Mihovil Bosnar
- Departamento de Polímeros y Materiales Avanzados: Física, Química y Tecnología, Facultad de Ciencias Químicas, Universidad del País Vasco UPV/EHU, 20018 Donostia-San Sebastián, Spain
- Donostia International Physics Center (DIPC), 20018 Donostia-San Sebastián, Spain
| | - Fabian Calleja
- IMDEA Nanociencia, Calle Faraday 9, 28049 Cantoblanco, Madrid, Spain
| | - Andrés Pinar Solé
- FZU - Institute of Physics of the Czech Academy of Sciences, Cukrovarnicka 10, 16200 Prague 6, Czech Republic
| | - Oleksandr Stetsovych
- FZU - Institute of Physics of the Czech Academy of Sciences, Cukrovarnicka 10, 16200 Prague 6, Czech Republic
| | - Iván M Ibarburu
- Departamento de Física de la Materia Condensada, Universidad Autónoma de Madrid - Cantoblanco Campus, 28049 Madrid, Spain
- IMDEA Nanociencia, Calle Faraday 9, 28049 Cantoblanco, Madrid, Spain
| | - Clara Rebanal
- Departamento de Física de la Materia Condensada, Universidad Autónoma de Madrid - Cantoblanco Campus, 28049 Madrid, Spain
- IMDEA Nanociencia, Calle Faraday 9, 28049 Cantoblanco, Madrid, Spain
| | - Manuela Garnica
- IMDEA Nanociencia, Calle Faraday 9, 28049 Cantoblanco, Madrid, Spain
- Instituto Nicolás Cabrera (INC), Universidad Autónoma de Madrid - Cantoblanco Campus, 28049 Madrid, Spain
| | - Rodolfo Miranda
- Departamento de Física de la Materia Condensada, Universidad Autónoma de Madrid - Cantoblanco Campus, 28049 Madrid, Spain
- IMDEA Nanociencia, Calle Faraday 9, 28049 Cantoblanco, Madrid, Spain
- Instituto Nicolás Cabrera (INC), Universidad Autónoma de Madrid - Cantoblanco Campus, 28049 Madrid, Spain
- Condensed Matter Physics center (IFIMAC), Universidad Autónoma de Madrid - Cantoblanco Campus, 28049 Madrid, Spain
| | - Mikhail M Otrokov
- Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC-Universidad de Zaragoza, 50009 Zaragoza, Spain
| | - Martin Ondráček
- FZU - Institute of Physics of the Czech Academy of Sciences, Cukrovarnicka 10, 16200 Prague 6, Czech Republic
| | - Pavel Jelínek
- FZU - Institute of Physics of the Czech Academy of Sciences, Cukrovarnicka 10, 16200 Prague 6, Czech Republic
| | - Andrés Arnau
- Departamento de Polímeros y Materiales Avanzados: Física, Química y Tecnología, Facultad de Ciencias Químicas, Universidad del País Vasco UPV/EHU, 20018 Donostia-San Sebastián, Spain
- Donostia International Physics Center (DIPC), 20018 Donostia-San Sebastián, Spain
- Centro de Física de Materiales CSIC/UPV-EHU-Materials Physics Center, Manuel Lardizabal 5, E-20018 San Sebastián, Spain
| | - Amadeo L Vázquez de Parga
- Departamento de Física de la Materia Condensada, Universidad Autónoma de Madrid - Cantoblanco Campus, 28049 Madrid, Spain
- IMDEA Nanociencia, Calle Faraday 9, 28049 Cantoblanco, Madrid, Spain
- Instituto Nicolás Cabrera (INC), Universidad Autónoma de Madrid - Cantoblanco Campus, 28049 Madrid, Spain
- Condensed Matter Physics center (IFIMAC), Universidad Autónoma de Madrid - Cantoblanco Campus, 28049 Madrid, Spain
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Mahatha SK, Phillips J, Corral-Sertal J, Subires D, Korshunov A, Kar A, Buck J, Diekmann F, Garbarino G, Ivanov YP, Chuvilin A, Mondal D, Vobornik I, Bosak A, Rossnagel K, Pardo V, Fumega AO, Blanco-Canosa S. Self-Stacked 1T-1H Layers in 6R-NbSeTe and the Emergence of Charge and Magnetic Correlations Due to Ligand Disorder. ACS NANO 2024. [PMID: 39086092 DOI: 10.1021/acsnano.4c02005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/02/2024]
Abstract
The emergence of correlated phenomena arising from the combination of 1T and 1H van der Waals layers is the focus of intense research. Here, we synthesize a self-stacked 6R phase in NbSeTe, showing perfect alternating 1T and 1H layers that grow coherently along the c-direction, as revealed by scanning transmission electron microscopy. Angle-resolved photoemission spectroscopy shows a mixed contribution of the trigonal and octahedral Nb bands to the Fermi level. Diffuse scattering reveals temperature-independent short-range charge fluctuations with propagation vector qCO = (0.25 0), derived from the condensation of a longitudinal mode in the 1T layer, while the long-range charge density wave is quenched by ligand disorder. Magnetization measurements suggest the presence of an inhomogeneous, short-range magnetic order, further supported by the absence of a clear phase transition in the specific heat. These experimental analyses in combination with ab initio calculations indicate that the ground state of 6R-NbSeTe is described by a statistical distribution of short-range charge-modulated and spin-correlated regions driven by ligand disorder. Our results demonstrate how natural 1T-1H self-stacked bulk heterostructures can be used to engineer emergent phases of matter.
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Affiliation(s)
- Sanjoy K Mahatha
- UGC-DAE Consortium for Scientific Research, University Campus, Khandwa Road, Indore 452001, India
- Ruprecht Haensel Laboratory, Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
| | - Jan Phillips
- Departamento de Física Aplicada, Universidade de Santiago de Compostela, Campus Sur s/n, E-15782 Santiago de Compostela, Spain
- Instituto de Materiais iMATUS, Universidade de Santiago de Compostela, Campus Sur s/n, E-15782 Santiago de Compostela, Spain
| | - Javier Corral-Sertal
- Departamento de Física Aplicada, Universidade de Santiago de Compostela, Campus Sur s/n, E-15782 Santiago de Compostela, Spain
- CiQUS, Centro Singular de Investigacion en Quimica Biolóxica e Materiais Moleculares, Departamento de Quimica-Fisica, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain
| | - David Subires
- Donostia International Physics Center (DIPC), E-20018 San Sebastián, Spain
- University of the Basque Country (UPV/EHU), Basque Country, Bilbao 48080 Spain
| | - Artem Korshunov
- European Synchrotron Radiation Facility (ESRF), BP 220, F-38043 Grenoble Cedex, France
| | - Arunava Kar
- Donostia International Physics Center (DIPC), E-20018 San Sebastián, Spain
| | - Jens Buck
- Ruprecht Haensel Laboratory, Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
- Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - Florian Diekmann
- Ruprecht Haensel Laboratory, Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
- Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - Gaston Garbarino
- European Synchrotron Radiation Facility (ESRF), BP 220, F-38043 Grenoble Cedex 9, France
| | - Yurii P Ivanov
- Electron Spectroscopy and Nanoscopy, Istituto Italiano di Tecnologia, Via Morego 30, 16163 Genova, Italy
| | - Andrey Chuvilin
- CIC Nanogune, E-20018 San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Spain
| | - Debashis Mondal
- Consiglio Nazionale delle Ricerche (CNR)- Istituto Officina dei Materiali (IOM), Laboratorio TASC in Area Science, 34149 Trieste, Italy
- Sovarani Memorial College, Jagatballavpur, Howrah 711408, India
| | - Ivana Vobornik
- Consiglio Nazionale delle Ricerche (CNR)- Istituto Officina dei Materiali (IOM), Laboratorio TASC in Area Science, 34149 Trieste, Italy
| | - Alexei Bosak
- European Synchrotron Radiation Facility (ESRF), BP 220, F-38043 Grenoble Cedex, France
| | - Kai Rossnagel
- Ruprecht Haensel Laboratory, Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
- Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität zu Kiel, 24098 Kiel, Germany
| | - Victor Pardo
- Departamento de Física Aplicada, Universidade de Santiago de Compostela, Campus Sur s/n, E-15782 Santiago de Compostela, Spain
- Instituto de Materiais iMATUS, Universidade de Santiago de Compostela, Campus Sur s/n, E-15782 Santiago de Compostela, Spain
| | - Adolfo O Fumega
- Department of Applied Physics, Aalto University, 02150 Espoo, Finland
| | - Santiago Blanco-Canosa
- Donostia International Physics Center (DIPC), E-20018 San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Spain
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4
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Akif Keskiner M, Ghaemi P, Oktel MÖ, Erten O. Theory of Moiré Magnetism and Multidomain Spin Textures in Twisted Mott Insulator-Semimetal Heterobilayers. NANO LETTERS 2024; 24:8575-8579. [PMID: 38976398 DOI: 10.1021/acs.nanolett.4c01574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/10/2024]
Abstract
Motivated by the recent experimental developments in van der Waals heterostructures, we investigate the emergent magnetism in Mott insulator-semimetal moiré superlattices by deriving effective spin models and exploring their phase diagram by Monte Carlo simulations. Our analysis indicates that the stacking-dependent interlayer Kondo interaction can give rise to different types of magnetic order, forming domains within the moiré unit cell. In particular, we find that the AB (AA) stacking regions tend to order (anti)ferromagnetically for an extended range of parameters. The remaining parts of the moiré unit cell form ferromagnetic chains that are coupled antiferromagnetically. We show that the decay length of the Kondo interaction can control the extent of these phases. Our results highlight the importance of stacking-dependent interlayer exchange and the rich magnetic spin textures that can be obtained in van der Waals heterostructures.
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Affiliation(s)
| | - Pouyan Ghaemi
- Physics Department, City College of the City University of New York, New York, New York 10031, United States
- Physics Program, Graduate Center of City University of New York, New York, New York 10031, United States
| | | | - Onur Erten
- Department of Physics, Arizona State University, Tempe, Arizona 85287, United States
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5
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Lee H, Im H, Choi BK, Park K, Chen Y, Ruan W, Zhong Y, Lee JE, Ryu H, Crommie MF, Shen ZX, Hwang C, Mo SK, Hwang J. Controlling structure and interfacial interaction of monolayer TaSe 2 on bilayer graphene. NANO CONVERGENCE 2024; 11:14. [PMID: 38622355 PMCID: PMC11018566 DOI: 10.1186/s40580-024-00422-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2024] [Accepted: 04/01/2024] [Indexed: 04/17/2024]
Abstract
Tunability of interfacial effects between two-dimensional (2D) crystals is crucial not only for understanding the intrinsic properties of each system, but also for designing electronic devices based on ultra-thin heterostructures. A prerequisite of such heterostructure engineering is the availability of 2D crystals with different degrees of interfacial interactions. In this work, we report a controlled epitaxial growth of monolayer TaSe2 with different structural phases, 1H and 1 T, on a bilayer graphene (BLG) substrate using molecular beam epitaxy, and its impact on the electronic properties of the heterostructures using angle-resolved photoemission spectroscopy. 1H-TaSe2 exhibits significant charge transfer and band hybridization at the interface, whereas 1 T-TaSe2 shows weak interactions with the substrate. The distinct interfacial interactions are attributed to the dual effects from the differences of the work functions as well as the relative interlayer distance between TaSe2 films and BLG substrate. The method demonstrated here provides a viable route towards interface engineering in a variety of transition-metal dichalcogenides that can be applied to future nano-devices with designed electronic properties.
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Affiliation(s)
- Hyobeom Lee
- Department of Physics and Institute of Quantum Convergence Technology, Kangwon National University, Chuncheon, South Korea
| | - Hayoon Im
- Department of Physics, Pusan National University, Busan, South Korea
| | - Byoung Ki Choi
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Kyoungree Park
- Department of Physics and Institute of Quantum Convergence Technology, Kangwon National University, Chuncheon, South Korea
| | - Yi Chen
- Department of Physics, University of California, Berkeley, CA, USA
- International Center for Quantum Materials, School of Physics, Peking University, Beijing, 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing, 100871, China
- Interdisciplinary Institute of Light-Element Quantum Materials and Research Center for Light-Element Advanced Materials, Peking University, Beijing, 100871, China
| | - Wei Ruan
- Department of Physics, University of California, Berkeley, CA, USA
- State Key Laboratory of Surface Physics, New Cornerstone Science Laboratory, and Department of Physics, Fudan University, Shanghai, China
| | - Yong Zhong
- Geballe Laboratory for Advanced Materials, Department of Physics and Applied Physics, Stanford University, Stanford, CA, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - Ji-Eun Lee
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Max Planck POSTECH Center for Complex Phase Materials, Pohang University of Science and Technology, Pohang, South Korea
| | - Hyejin Ryu
- Center for Spintronics, Korea Institute of Science and Technology, Seoul, South Korea
| | - Michael F Crommie
- Department of Physics, University of California, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Zhi-Xun Shen
- Geballe Laboratory for Advanced Materials, Department of Physics and Applied Physics, Stanford University, Stanford, CA, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA, USA
| | - Choongyu Hwang
- Department of Physics, Pusan National University, Busan, South Korea.
| | - Sung-Kwan Mo
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA, USA.
| | - Jinwoong Hwang
- Department of Physics and Institute of Quantum Convergence Technology, Kangwon National University, Chuncheon, South Korea.
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6
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Crippa L, Bae H, Wunderlich P, Mazin II, Yan B, Sangiovanni G, Wehling T, Valentí R. Heavy fermions vs doped Mott physics in heterogeneous Ta-dichalcogenide bilayers. Nat Commun 2024; 15:1357. [PMID: 38355694 PMCID: PMC10866876 DOI: 10.1038/s41467-024-45392-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2023] [Accepted: 01/19/2024] [Indexed: 02/16/2024] Open
Abstract
Controlling and understanding electron correlations in quantum matter is one of the most challenging tasks in materials engineering. In the past years a plethora of new puzzling correlated states have been found by carefully stacking and twisting two-dimensional van der Waals materials of different kind. Unique to these stacked structures is the emergence of correlated phases not foreseeable from the single layers alone. In Ta-dichalcogenide heterostructures made of a good metallic "1H"- and a Mott insulating "1T"-layer, recent reports have evidenced a cross-breed itinerant and localized nature of the electronic excitations, similar to what is typically found in heavy fermion systems. Here, we put forward a new interpretation based on first-principles calculations which indicates a sizeable charge transfer of electrons (0.4-0.6 e) from 1T to 1H layers at an elevated interlayer distance. We accurately quantify the strength of the interlayer hybridization which allows us to unambiguously determine that the system is much closer to a doped Mott insulator than to a heavy fermion scenario. Ta-based heterolayers provide therefore a new ground for quantum-materials engineering in the regime of heavily doped Mott insulators hybridized with metallic states at a van der Waals distance.
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Affiliation(s)
- Lorenzo Crippa
- Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074, Würzburg, Germany.
| | - Hyeonhu Bae
- Department of Condensed Matter Physics, Weizmann Institute of Science, 7610001, Rehovot, Israel
| | - Paul Wunderlich
- Institut für Theoretische Physik, Goethe Universität Frankfurt, am Main, Germany
| | - Igor I Mazin
- Department of Physics and Astronomy, George Mason University, Fairfax, VA, 22030, USA
- Quantum Science and Engineering Center, George Mason University, Fairfax, VA, 22030, USA
| | - Binghai Yan
- Department of Condensed Matter Physics, Weizmann Institute of Science, 7610001, Rehovot, Israel
| | - Giorgio Sangiovanni
- Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, 97074, Würzburg, Germany
| | - Tim Wehling
- I. Institute of Theoretical Physics, University of Hamburg, Notkestrasse 9, 22607, Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, D-22761, Hamburg, Germany
| | - Roser Valentí
- Institut für Theoretische Physik, Goethe Universität Frankfurt, am Main, Germany.
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