1
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Posey VA, Turkel S, Rezaee M, Devarakonda A, Kundu AK, Ong CS, Thinel M, Chica DG, Vitalone RA, Jing R, Xu S, Needell DR, Meirzadeh E, Feuer ML, Jindal A, Cui X, Valla T, Thunström P, Yilmaz T, Vescovo E, Graf D, Zhu X, Scheie A, May AF, Eriksson O, Basov DN, Dean CR, Rubio A, Kim P, Ziebel ME, Millis AJ, Pasupathy AN, Roy X. Two-dimensional heavy fermions in the van der Waals metal CeSiI. Nature 2024; 625:483-488. [PMID: 38233620 DOI: 10.1038/s41586-023-06868-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2023] [Accepted: 11/14/2023] [Indexed: 01/19/2024]
Abstract
Heavy-fermion metals are prototype systems for observing emergent quantum phases driven by electronic interactions1-6. A long-standing aspiration is the dimensional reduction of these materials to exert control over their quantum phases7-11, which remains a significant challenge because traditional intermetallic heavy-fermion compounds have three-dimensional atomic and electronic structures. Here we report comprehensive thermodynamic and spectroscopic evidence of an antiferromagnetically ordered heavy-fermion ground state in CeSiI, an intermetallic comprising two-dimensional (2D) metallic sheets held together by weak interlayer van der Waals (vdW) interactions. Owing to its vdW nature, CeSiI has a quasi-2D electronic structure, and we can control its physical dimension through exfoliation. The emergence of coherent hybridization of f and conduction electrons at low temperature is supported by the temperature evolution of angle-resolved photoemission and scanning tunnelling spectra near the Fermi level and by heat capacity measurements. Electrical transport measurements on few-layer flakes reveal heavy-fermion behaviour and magnetic order down to the ultra-thin regime. Our work establishes CeSiI and related materials as a unique platform for studying dimensionally confined heavy fermions in bulk crystals and employing 2D device fabrication techniques and vdW heterostructures12 to manipulate the interplay between Kondo screening, magnetic order and proximity effects.
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Affiliation(s)
| | - Simon Turkel
- Physics Department, Columbia University, New York, NY, USA
- Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, NY, USA
| | - Mehdi Rezaee
- Physics Department, Harvard University, Cambridge, MA, USA
| | | | - Asish K Kundu
- Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, NY, USA
| | - Chin Shen Ong
- Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden
| | - Morgan Thinel
- Chemistry Department, Columbia University, New York, NY, USA
- Physics Department, Columbia University, New York, NY, USA
| | - Daniel G Chica
- Chemistry Department, Columbia University, New York, NY, USA
| | | | - Ran Jing
- Physics Department, Columbia University, New York, NY, USA
| | - Suheng Xu
- Physics Department, Columbia University, New York, NY, USA
| | - David R Needell
- Chemistry Department, Columbia University, New York, NY, USA
| | - Elena Meirzadeh
- Chemistry Department, Columbia University, New York, NY, USA
| | | | - Apoorv Jindal
- Physics Department, Columbia University, New York, NY, USA
| | - Xiaomeng Cui
- Physics Department, Harvard University, Cambridge, MA, USA
| | - Tonica Valla
- Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, NY, USA
- Donostia International Physics Center (DIPC), Donostia-San Sebastián, Spain
| | - Patrik Thunström
- Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden
| | - Turgut Yilmaz
- National Synchrotron Light Source II, Brookhaven National Lab, Upton, NY, USA
| | - Elio Vescovo
- National Synchrotron Light Source II, Brookhaven National Lab, Upton, NY, USA
| | - David Graf
- National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL, USA
| | - Xiaoyang Zhu
- Chemistry Department, Columbia University, New York, NY, USA
| | - Allen Scheie
- Neutron Scattering Division, Oak Ridge National Lab, Oak Ridge, TN, USA
- MPA-Q, Los Alamos National Lab, Los Alamos, NM, USA
| | - Andrew F May
- Materials Science and Technology Division, Oak Ridge National Lab, Oak Ridge, TN, USA
| | - Olle Eriksson
- Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden
- Wallenberg Initiative Materials Science for Sustainability, Uppsala University, Uppsala, Sweden
| | - D N Basov
- Physics Department, Columbia University, New York, NY, USA
| | - Cory R Dean
- Physics Department, Columbia University, New York, NY, USA
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free-Electron Laser Science and Department of Physics, Hamburg, Germany.
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Departmento de Polímeros y Materiales Avanzados: Física, Química y Tecnología, Universidad del País Vasco (UPV/EHU), San Sebastián, Spain.
- Center for Computational Quantum Physics, Flatiron Institute, New York, NY, USA.
| | - Philip Kim
- Physics Department, Harvard University, Cambridge, MA, USA
| | | | - Andrew J Millis
- Physics Department, Columbia University, New York, NY, USA.
- Center for Computational Quantum Physics, Flatiron Institute, New York, NY, USA.
| | - Abhay N Pasupathy
- Physics Department, Columbia University, New York, NY, USA.
- Condensed Matter Physics and Materials Science Division, Brookhaven National Laboratory, Upton, NY, USA.
| | - Xavier Roy
- Chemistry Department, Columbia University, New York, NY, USA.
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2
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Yang CJ, Kliemt K, Krellner C, Kroha J, Fiebig M, Pal S. Critical slowing down near a magnetic quantum phase transition with fermionic breakdown. NATURE PHYSICS 2023; 19:1605-1610. [PMID: 37970535 PMCID: PMC10635820 DOI: 10.1038/s41567-023-02156-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/13/2022] [Accepted: 06/23/2023] [Indexed: 11/17/2023]
Abstract
When a system close to a continuous phase transition is subjected to perturbations, it takes an exceptionally long time to return to equilibrium. This critical slowing down is observed universally in the dynamics of bosonic excitations, such as order-parameter collective modes, but it is not generally expected to occur for fermionic excitations. Here using terahertz time-domain spectroscopy, we find evidence for fermionic critical slowing down in YbRh2Si2 close to a quantum phase transition between an antiferromagnetic phase and a heavy Fermi liquid. In the latter phase, the relevant quasiparticles are a quantum superposition of itinerant and localized electronic states with a strongly enhanced effective mass. As the temperature is lowered on the heavy-Fermi-liquid side of the transition, the heavy-fermion spectral weight builds up until the Kondo temperature TK ≈ 25 K, then decays towards the quantum phase transition and is, thereafter, followed by a logarithmic rise of the quasiparticle excitation rate below 10 K. A two-band heavy-Fermi-liquid theory shows that this is indicative of the fermionic critical slowing down associated with heavy-fermion breakdown near the quantum phase transition. The critical exponent of this breakdown could be used to classify this system among a wider family of fermionic quantum phase transitions that is yet to be fully explored.
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Affiliation(s)
- Chia-Jung Yang
- Department of Materials, ETH Zurich, Zurich, Switzerland
| | - Kristin Kliemt
- Physikalisches Institut, Goethe-Universität Frankfurt, Frankfurt, Germany
| | - Cornelius Krellner
- Physikalisches Institut, Goethe-Universität Frankfurt, Frankfurt, Germany
| | - Johann Kroha
- Physikalisches Institut and Bethe Center for Theoretical Physics, Universität Bonn, Bonn, Germany
| | - Manfred Fiebig
- Department of Materials, ETH Zurich, Zurich, Switzerland
| | - Shovon Pal
- Department of Materials, ETH Zurich, Zurich, Switzerland
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Jatni, India
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3
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Peculiar Physics of Heavy-Fermion Metals: Theory versus Experiment. ATOMS 2022. [DOI: 10.3390/atoms10030067] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Abstract
This review considers the topological fermion condensation quantum phase transition (FCQPT) that leads to flat bands and allows the elucidation of the special behavior of heavy-fermion (HF) metals that is not exhibited by common metals described within the framework of the Landau Fermi liquid (LFL) theory. We bring together theoretical consideration within the framework of the fermion condensation theory based on the FCQPT with experimental data collected on HF metals. We show that very different HF metals demonstrate universal behavior induced by the FCQPT and demonstrate that Fermi systems near the FCQPT are controlled by the Fermi quasiparticles with the effective mass M* strongly depending on temperature T, magnetic field B, pressure P, etc. Within the framework of our analysis, the experimental data regarding the thermodynamic, transport and relaxation properties of HF metal are naturally described. Based on the theory, we explain a number of experimental data and show that the considered HF metals exhibit peculiar properties such as: (1) the universal T/B scaling behavior; (2) the linear dependence of the resistivity on T, ρ(T)∝A1T (with A1 is a temperature-independent coefficient), and the negative magnetoresistance; (3) asymmetrical dependence of the tunneling differential conductivity (resistivity) on the bias voltage; (4) in the case of a flat band, the superconducting critical temperature Tc∝g with g being the coupling constant, while the M* becomes finite; (5) we show that the so called Planckian limit exhibited by HF metals with ρ(T)∝T is defined by the presence of flat bands.
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4
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Shen S, Wen C, Kong P, Gao J, Si J, Luo X, Lu W, Sun Y, Chen G, Yan S. Inducing and tuning Kondo screening in a narrow-electronic-band system. Nat Commun 2022; 13:2156. [PMID: 35444181 PMCID: PMC9021272 DOI: 10.1038/s41467-022-29891-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2021] [Accepted: 04/04/2022] [Indexed: 11/09/2022] Open
Abstract
Although the single-impurity Kondo physics has already been well understood, the understanding of the Kondo lattice where a dense array of local moments couples to the conduction electrons is still far from complete. The ability of creating and tuning the Kondo lattice in non-f-electron systems will be great helpful for further understanding the Kondo lattice behavior. Here we show that the Pb intercalation in the charge-density-wave-driven narrow-electronic-band system 1T-TaS2 induces a transition from the insulating gap to a sharp Kondo resonance in the scanning tunneling microscopy measurements. It results from the Kondo screening of the localized moments in the 13-site Star-of-David clusters of 1T-TaS2. As increasing the Pb concentration, the narrow electronic band derived from the localized electrons shifts away from the Fermi level and the Kondo resonance peak is gradually suppressed. Our results pave the way for creating and tuning many-body electronic states in layered narrow-electronic-band materials.
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Affiliation(s)
- Shiwei Shen
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, China
| | - Chenhaoping Wen
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, China
| | - Pengfei Kong
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, China
| | - Jingjing Gao
- Key Laboratory of Materials Physics, Institute of Solid State Physics, HFIPS, Chinese Academy of Sciences, Hefei, 230031, China.,University of Science and Technology of China, Hefei, 230026, China
| | - Jianguo Si
- Key Laboratory of Materials Physics, Institute of Solid State Physics, HFIPS, Chinese Academy of Sciences, Hefei, 230031, China
| | - Xuan Luo
- Key Laboratory of Materials Physics, Institute of Solid State Physics, HFIPS, Chinese Academy of Sciences, Hefei, 230031, China
| | - Wenjian Lu
- Key Laboratory of Materials Physics, Institute of Solid State Physics, HFIPS, Chinese Academy of Sciences, Hefei, 230031, China
| | - Yuping Sun
- Key Laboratory of Materials Physics, Institute of Solid State Physics, HFIPS, Chinese Academy of Sciences, Hefei, 230031, China.,High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences, Hefei, 230031, China.,Collaborative Innovation Centre of Advanced Microstructures, Nanjing University, Nanjing, 210093, China
| | - Gang Chen
- Department of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics at Hong Kong, The University of Hong Kong, Hong Kong, China
| | - Shichao Yan
- School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, China. .,ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University, Shanghai, 201210, China.
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5
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Artificial heavy fermions in a van der Waals heterostructure. Nature 2021; 599:582-586. [PMID: 34819682 DOI: 10.1038/s41586-021-04021-0] [Citation(s) in RCA: 45] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2021] [Accepted: 09/14/2021] [Indexed: 11/08/2022]
Abstract
Heavy-fermion systems represent one of the paradigmatic strongly correlated states of matter1-5. They have been used as a platform for investigating exotic behaviour ranging from quantum criticality and non-Fermi liquid behaviour to unconventional topological superconductivity4-12. The heavy-fermion phenomenon arises from the exchange interaction between localized magnetic moments and conduction electrons leading to Kondo lattice physics, and represents one of the long-standing open problems in quantum materials3. In a Kondo lattice, the exchange interaction gives rise to a band with heavy effective mass. This intriguing phenomenology has so far been realized only in compounds containing rare-earth elements with 4f or 5f electrons1,4,13,14. Here we realize a designer van der Waals heterostructure where artificial heavy fermions emerge from the Kondo coupling between a lattice of localized magnetic moments and itinerant electrons in a 1T/1H-TaS2 heterostructure. We study the heterostructure using scanning tunnelling microscopy and spectroscopy and show that depending on the stacking order of the monolayers, we can reveal either the localized magnetic moments and the associated Kondo effect, or the conduction electrons with a heavy-fermion hybridization gap. Our experiments realize an ultimately tunable platform for future experiments probing enhanced many-body correlations, dimensional tuning of quantum criticality and unconventional superconductivity in two-dimensional artificial heavy-fermion systems15-17.
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6
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Nguyen DH, Sidorenko A, Taupin M, Knebel G, Lapertot G, Schuberth E, Paschen S. Superconductivity in an extreme strange metal. Nat Commun 2021; 12:4341. [PMID: 34290244 PMCID: PMC8295387 DOI: 10.1038/s41467-021-24670-z] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2020] [Accepted: 06/28/2021] [Indexed: 11/09/2022] Open
Abstract
Some of the highest-transition-temperature superconductors across various materials classes exhibit linear-in-temperature 'strange metal' or 'Planckian' electrical resistivities in their normal state. It is thus believed by many that this behavior holds the key to unlock the secrets of high-temperature superconductivity. However, these materials typically display complex phase diagrams governed by various competing energy scales, making an unambiguous identification of the physics at play difficult. Here we use electrical resistivity measurements into the micro-Kelvin regime to discover superconductivity condensing out of an extreme strange metal state-with linear resistivity over 3.5 orders of magnitude in temperature. We propose that the Cooper pairing is mediated by the modes associated with a recently evidenced dynamical charge localization-delocalization transition, a mechanism that may well be pertinent also in other strange metal superconductors.
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Affiliation(s)
- D H Nguyen
- Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstr. 8-10, Vienna, Austria
| | - A Sidorenko
- Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstr. 8-10, Vienna, Austria
| | - M Taupin
- Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstr. 8-10, Vienna, Austria
| | - G Knebel
- Université Grenoble Alpes, CEA, Grenoble INP, IRIG, PHELIQS, Grenoble, France
| | - G Lapertot
- Université Grenoble Alpes, CEA, Grenoble INP, IRIG, PHELIQS, Grenoble, France
| | - E Schuberth
- Technische Universität München, Garching, Germany
| | - S Paschen
- Institute of Solid State Physics, Vienna University of Technology, Wiedner Hauptstr. 8-10, Vienna, Austria.
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7
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Agustsson SY, Chernov SV, Medjanik K, Babenkov S, Fedchenko O, Vasilyev D, Schlueter C, Gloskovskii A, Matveyev Y, Kliemt K, Krellner C, Demsar J, Schönhense G, Elmers HJ. Temperature-dependent change of the electronic structure in the Kondo lattice system YbRh 2Si 2. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:205601. [PMID: 33561846 DOI: 10.1088/1361-648x/abe479] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2020] [Accepted: 02/09/2021] [Indexed: 06/12/2023]
Abstract
The heavy-fermion behavior in intermetallic compounds manifests itself in a quenching of local magnetic moments by developing Kondo spin-singlet many-body states combined with a drastic increase of the effective mass of conduction electrons, which occurs below the lattice Kondo temperatureTK. This behavior is caused by interactions between the strongly localized 4felectrons and itinerant electrons. A controversially discussed question in this context is how the localized electronic states contribute to the Fermi surface upon changing the temperature. One expects that hybridization between the local moments and the itinerant electrons leads to a transition from a small Fermi surface in a non-coherent regime at high temperatures to a large Fermi surface once the coherent Kondo lattice regime is realized belowTK. We demonstrate, using hard x-ray angle-resolved photoemission spectroscopy that the electronic structure of the prototypical heavy fermion compound YbRh2Si2changes with temperature between 100 and 200 K, i.e. far above the Kondo temperature,TK= 25 K, of this system. Our results suggest a transition from a small to a large Fermi surface with decreasing temperature. This result is inconsistent with the prediction of the dynamical mean-field periodic Anderson model and supports the idea of an independent energy scale governing the change of band dispersion.
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Affiliation(s)
- S Y Agustsson
- Institut für Physik, Johannes Gutenberg-Universität, Staudingerweg 7, 55128 Mainz, Germany
| | - S V Chernov
- Institut für Physik, Johannes Gutenberg-Universität, Staudingerweg 7, 55128 Mainz, Germany
| | - K Medjanik
- Institut für Physik, Johannes Gutenberg-Universität, Staudingerweg 7, 55128 Mainz, Germany
| | - S Babenkov
- Institut für Physik, Johannes Gutenberg-Universität, Staudingerweg 7, 55128 Mainz, Germany
| | - O Fedchenko
- Institut für Physik, Johannes Gutenberg-Universität, Staudingerweg 7, 55128 Mainz, Germany
| | - D Vasilyev
- Institut für Physik, Johannes Gutenberg-Universität, Staudingerweg 7, 55128 Mainz, Germany
| | - C Schlueter
- Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
| | - A Gloskovskii
- Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
| | - Yu Matveyev
- Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany
| | - K Kliemt
- Physikalisches Institut, Goethe Universität Frankfurt, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
| | - C Krellner
- Physikalisches Institut, Goethe Universität Frankfurt, Max-von-Laue-Strasse 1, 60438 Frankfurt am Main, Germany
| | - J Demsar
- Institut für Physik, Johannes Gutenberg-Universität, Staudingerweg 7, 55128 Mainz, Germany
| | - G Schönhense
- Institut für Physik, Johannes Gutenberg-Universität, Staudingerweg 7, 55128 Mainz, Germany
| | - H-J Elmers
- Institut für Physik, Johannes Gutenberg-Universität, Staudingerweg 7, 55128 Mainz, Germany
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8
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Violation of the Time-Reversal and Particle-Hole Symmetries in Strongly Correlated Fermi Systems: A Review. Symmetry (Basel) 2020. [DOI: 10.3390/sym12101596] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In this review, we consider the time reversal T and particle-antiparticle C symmetries that, being most fundamental, can be violated at microscopic level by a weak interaction. The notable example here is from condensed matter, where strongly correlated Fermi systems like heavy-fermion metals and high Tc superconductors exhibit C and T symmetries violation due to so-called non-Fermi liquid (NFL) behavior. In these systems, tunneling differential conductivity (or resistivity) is a very sensitive tool to experimentally test the above symmetry break. When a strongly correlated Fermi system turns out to be near the topological fermion condensation quantum phase transition (FCQPT), it exhibits the NFL properties, so that the C symmetry breaks down, making the differential tunneling conductivity to be an asymmetric function of the bias voltage V. This asymmetry does not take place in normal metals, where Landau Fermi liquid (LFL) theory holds. Under the application of magnetic field, a heavy fermion metal transits to the LFL state, and σ(V) becomes symmetric function of V. These findings are in good agreement with experimental observations. We suggest that the same topological FCQPT underlies the baryon asymmetry in the Universe. We demonstrate that the most fundamental features of the nature are defined by its topological and symmetry properties.
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9
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Zhang SS, Yin JX, Ikhlas M, Tien HJ, Wang R, Shumiya N, Chang G, Tsirkin SS, Shi Y, Yi C, Guguchia Z, Li H, Wang W, Chang TR, Wang Z, Yang YF, Neupert T, Nakatsuji S, Hasan MZ. Many-Body Resonance in a Correlated Topological Kagome Antiferromagnet. PHYSICAL REVIEW LETTERS 2020; 125:046401. [PMID: 32794798 DOI: 10.1103/physrevlett.125.046401] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2020] [Accepted: 06/26/2020] [Indexed: 06/11/2023]
Abstract
We use scanning tunneling microscopy to elucidate the atomically resolved electronic structure in the strongly correlated kagome Weyl antiferromagnet Mn_{3}Sn. In stark contrast to its broad single-particle electronic structure, we observe a pronounced resonance with a Fano line shape at the Fermi level resembling the many-body Kondo resonance. We find that this resonance does not arise from the step edges or atomic impurities but the intrinsic kagome lattice. Moreover, the resonance is robust against the perturbation of a vector magnetic field, but broadens substantially with increasing temperature, signaling strongly interacting physics. We show that this resonance can be understood as the result of geometrical frustration and strong correlation based on the kagome lattice Hubbard model. Our results point to the emergent many-body resonance behavior in a topological kagome magnet.
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Affiliation(s)
- Songtian Sonia Zhang
- Laboratory for Topological Quantum Matter and Advanced Spectroscopy, Department of Physics, Princeton University, Princeton 08544, New Jersey, USA
| | - Jia-Xin Yin
- Laboratory for Topological Quantum Matter and Advanced Spectroscopy, Department of Physics, Princeton University, Princeton 08544, New Jersey, USA
| | - Muhammad Ikhlas
- Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
| | - Hung-Ju Tien
- Department of Physics, National Cheng Kung University, Tainan 701, Taiwan
| | - Rui Wang
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
| | - Nana Shumiya
- Laboratory for Topological Quantum Matter and Advanced Spectroscopy, Department of Physics, Princeton University, Princeton 08544, New Jersey, USA
| | - Guoqing Chang
- Laboratory for Topological Quantum Matter and Advanced Spectroscopy, Department of Physics, Princeton University, Princeton 08544, New Jersey, USA
| | - Stepan S Tsirkin
- Department of Physics, University of Zurich, Zurich 8057, Switzerland
| | - Youguo Shi
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Changjiang Yi
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Zurab Guguchia
- Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, Villigen PSI CH-5232, Switzerland
| | - Hang Li
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Wenhong Wang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Tay-Rong Chang
- Department of Physics, National Cheng Kung University, Tainan 701, Taiwan
| | - Ziqiang Wang
- Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA
| | - Yi-Feng Yang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Titus Neupert
- Department of Physics, University of Zurich, Zurich 8057, Switzerland
| | - Satoru Nakatsuji
- Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
- Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
- CREST, Japan Science and Technology Agency (JST), 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan
| | - M Zahid Hasan
- Laboratory for Topological Quantum Matter and Advanced Spectroscopy, Department of Physics, Princeton University, Princeton 08544, New Jersey, USA
- Material Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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