1
|
Kim GH, Park M, Samanta S, Choi U, Kang B, Seo U, Ji G, Noh S, Cho DY, Yoo JW, Ok JM, Kim HS, Sohn C. Suppression of antiferromagnetic order by strain-enhanced frustration in honeycomb cobaltate. SCIENCE ADVANCES 2024; 10:eadn8694. [PMID: 38968350 PMCID: PMC11225782 DOI: 10.1126/sciadv.adn8694] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2024] [Accepted: 06/04/2024] [Indexed: 07/07/2024]
Abstract
Layered honeycomb cobaltates are predicted as promising for realizing the Kitaev quantum spin liquid, a many-body quantum entangled ground state characterized by fractional excitations. However, they exhibit antiferromagnetic ordering at low temperatures, hindering the expected quantum state. We demonstrate that controlling the trigonal distortion of CoO6 octahedra is crucial to suppress antiferromagnetic order through enhancing frustration in layered honeycomb cobaltates. Using heterostructure engineering on Cu3Co2SbO6 thin films, we adjust the trigonal distortion of CoO6 octahedra and the resulting trigonal crystal field. The original Néel temperature of 16 kelvin in bulk Cu3Co2SbO6 decreases (increases) to 7.8 kelvin (22.7 kelvin) in strained Cu3Co2SbO6 films by decreasing (increasing) the magnitude of the trigonal crystal fields. The first-principles calculation suggests the enhancement of geometrical frustration as the origin of the suppression of antiferromagnetism. This finding supports the potential of layered honeycomb cobaltate heterostructures and strain engineering in realizing extremely elusive quantum phases of matter.
Collapse
Affiliation(s)
- Gye-Hyeon Kim
- Department of Physics, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| | - Miju Park
- Department of Physics, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| | - Subhasis Samanta
- Department of Semiconductor Physics and Institute of Quantum Convergence Technology, Kangwon National University, Chuncheon 24341, Republic of Korea
- Center for Extreme Quantum Matter and Functionality, Sungkyunkwan University, Suwon 16419 Republic of Korea
| | - Uksam Choi
- Department of Physics, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| | - Baekjune Kang
- Department of Physics, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| | - Uihyeon Seo
- Department of Physics, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| | - GwangCheol Ji
- Department of Physics, Pusan National University, Busan 46241, Republic of Korea
| | - Seunghyeon Noh
- Department of Materials Science and Engineering, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| | - Deok-Yong Cho
- Department of Physics, Jeonbuk National University, Jeonju 54896, Republic of Korea
| | - Jung-Woo Yoo
- Department of Materials Science and Engineering, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| | - Jong Mok Ok
- Department of Physics, Pusan National University, Busan 46241, Republic of Korea
| | - Heung-Sik Kim
- Department of Semiconductor Physics and Institute of Quantum Convergence Technology, Kangwon National University, Chuncheon 24341, Republic of Korea
| | - Changhee Sohn
- Department of Physics, Ulsan National Institute of Science and Technology, Ulsan 44919, Republic of Korea
| |
Collapse
|
2
|
Halász GB. Gate-Controlled Anyon Generation and Detection in Kitaev Spin Liquids. PHYSICAL REVIEW LETTERS 2024; 132:206501. [PMID: 38829057 DOI: 10.1103/physrevlett.132.206501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2023] [Revised: 03/25/2024] [Accepted: 04/06/2024] [Indexed: 06/05/2024]
Abstract
Reliable manipulation of non-Abelian Ising anyons supported by Kitaev spin liquids may enable intrinsically fault-tolerant quantum computation. Here, we introduce a standalone scheme for both generating and detecting individual Ising anyons using tunable gate voltages in a heterostructure containing a non-Abelian Kitaev spin liquid and a monolayer semiconductor. The key ingredients of our setup are a Kondo coupling to stabilize an Ising anyon in the spin liquid around each electron in the semiconductor, and a large charging energy to allow control over the electron numbers in distinct gate-defined regions of the semiconductor. In particular, a single Ising anyon can be generated at a disk-shaped region by gate tuning its electron number to one, while it can be interferometrically detected by measuring the electrical conductance of a ring-shaped region around it whose electron number is allowed to fluctuate between zero and one. We provide concrete experimental guidelines for implementing our proposal in promising candidate materials like α-RuCl_{3}.
Collapse
Affiliation(s)
- Gábor B Halász
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA and Quantum Science Center, Oak Ridge, Tennessee 37831, USA
| |
Collapse
|
3
|
Kao WH, Perkins NB, Halász GB. Vacancy Spectroscopy of Non-Abelian Kitaev Spin Liquids. PHYSICAL REVIEW LETTERS 2024; 132:136503. [PMID: 38613268 DOI: 10.1103/physrevlett.132.136503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Accepted: 02/16/2024] [Indexed: 04/14/2024]
Abstract
Spin vacancies in the non-Abelian Kitaev spin liquid are known to harbor Majorana zero modes, potentially enabling topological quantum computing at elevated temperatures. Here, we study the spectroscopic signatures of such Majorana zero modes in a scanning tunneling setup where a non-Abelian Kitaev spin liquid with a finite density of spin vacancies forms a tunneling barrier between a tip and a substrate. Our key result is a well-defined peak close to zero bias voltage in the derivative of the tunneling conductance whose voltage and intensity both increase with the density of vacancies. This "quasi-zero-voltage peak" is identified as the closest analog of the zero-voltage peak observed in topological superconductors that additionally reflects the fractionalized nature of spin-liquid-based Majorana zero modes. We further highlight a single-fermion Van Hove singularity at a higher voltage that reveals the energy scale of the emergent Majorana fermions in the Kitaev spin liquid. Our proposed signatures are within reach of current experiments on the candidate material α-RuCl_{3}.
Collapse
Affiliation(s)
- Wen-Han Kao
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Natalia B Perkins
- School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Gábor B Halász
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Quantum Science Center, Oak Ridge, Tennessee 37831, USA
| |
Collapse
|
4
|
Takahashi MO, Yamada MG, Udagawa M, Mizushima T, Fujimoto S. Nonlocal Spin Correlation as a Signature of Ising Anyons Trapped in Vacancies of the Kitaev Spin Liquid. PHYSICAL REVIEW LETTERS 2023; 131:236701. [PMID: 38134764 DOI: 10.1103/physrevlett.131.236701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2022] [Accepted: 11/08/2023] [Indexed: 12/24/2023]
Abstract
In the Kitaev chiral spin liquid, Ising anyons are realized as Z_{2} fluxes binding Majorana zero modes, which, however, are thermal excitations with finite decay rates. On the other hand, a lattice vacancy traps a Z_{2} flux even in the ground state, resulting in the stable realization of a Majorana zero mode in a vacancy. We demonstrate that spin-spin correlation functions between two vacancy sites exhibit long-range correlation arising from the fractionalized character of Majorana zero modes, in spite of the strong decay of bulk spin correlations. Remarkably, this nonlocal spin correlation does not decrease as the distance between two vacancy sites increases, signaling Majorana teleportation. Furthermore, we clarify that the nonlocal correlation can be detected electrically via the measurement of nonlocal conductance between two vacancy sites, which is straightforwardly utilized for the readout of Majorana qubits. These findings pave the way to the measurement-based quantum computation with Ising anyons trapped in vacancies of the Kitaev spin liquid.
Collapse
Affiliation(s)
- Masahiro O Takahashi
- Department of Materials Engineering Science, Osaka University, Toyonaka 560-8531, Japan
| | - Masahiko G Yamada
- Department of Materials Engineering Science, Osaka University, Toyonaka 560-8531, Japan
- Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan
- Department of Physics, Gakushuin University, Mejiro, Toshima-ku 171-8588, Japan
| | - Masafumi Udagawa
- Department of Physics, Gakushuin University, Mejiro, Toshima-ku 171-8588, Japan
| | - Takeshi Mizushima
- Department of Materials Engineering Science, Osaka University, Toyonaka 560-8531, Japan
| | - Satoshi Fujimoto
- Department of Materials Engineering Science, Osaka University, Toyonaka 560-8531, Japan
- Center for Quantum Information and Quantum Biology, Osaka University, Toyonaka 560-8531, Japan
| |
Collapse
|
5
|
Cassella G, d'Ornellas P, Hodson T, Natori WMH, Knolle J. An exact chiral amorphous spin liquid. Nat Commun 2023; 14:6663. [PMID: 37863892 PMCID: PMC10589230 DOI: 10.1038/s41467-023-42105-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2023] [Accepted: 09/26/2023] [Indexed: 10/22/2023] Open
Abstract
Topological insulator phases of non-interacting particles have been generalized from periodic crystals to amorphous lattices, which raises the question whether topologically ordered quantum many-body phases may similarly exist in amorphous systems? Here we construct a soluble chiral amorphous quantum spin liquid by extending the Kitaev honeycomb model to random lattices with fixed coordination number three. The model retains its exact solubility but the presence of plaquettes with an odd number of sides leads to a spontaneous breaking of time reversal symmetry. We unearth a rich phase diagram displaying Abelian as well as a non-Abelian quantum spin liquid phases with a remarkably simple ground state flux pattern. Furthermore, we show that the system undergoes a finite-temperature phase transition to a conducting thermal metal state and discuss possible experimental realisations.
Collapse
Affiliation(s)
- G Cassella
- Blackett Laboratory, Imperial College London, London, SW7 2AZ, United Kingdom
| | - P d'Ornellas
- Blackett Laboratory, Imperial College London, London, SW7 2AZ, United Kingdom.
| | - T Hodson
- Blackett Laboratory, Imperial College London, London, SW7 2AZ, United Kingdom
| | - W M H Natori
- Institut Laue-Langevin, BP 156, 41 Avenue des Martyrs, 38042, Grenoble Cedex 9, France
| | - J Knolle
- Blackett Laboratory, Imperial College London, London, SW7 2AZ, United Kingdom.
- Department of Physics TQM, Technische Universität München, James-Franck-Straße 1, D-85748, Garching, Germany.
- Munich Center for Quantum Science and Technology (MCQST), 80799, Munich, Germany.
| |
Collapse
|
6
|
Wang Z, Liu L, Zheng H, Zhao M, Yang K, Wang C, Yang F, Wu H, Gao C. Direct observation of the Mottness and p-d orbital hybridization in the epitaxial monolayer α-RuCl 3. NANOSCALE 2022; 14:11745-11749. [PMID: 35917194 DOI: 10.1039/d2nr02827a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
α-RuCl3, a promising material to accomplish the Kitaev honeycomb model, has attracted enormous interest recently. Mottness and p-d bonds play vital roles in generating Kitaev interactions and underpinning the potential exotic states of quantum magnets, and the van der Waals monolayer is considered to be a better platform to approach a two-dimensional Kitaev model than the bulk. Here, we worked out the growth art of an α-RuCl3 monolayer on a graphite substrate and studied its electronic structure, particularly the delicate orbital occupations, through scanning tunneling microscopy and spectroscopy. An in-plane lattice expansion of 2.67 ± 0.83% is observed and the pronounced t2g-pπ and eg-pσ hybridization are visualized. The Mott nature is unveiled by an ∼0.6 eV full gap at the Fermi level located inside the t2g-pπ manifold which is further verified by the density functional theory calculations. The monolayer phase of α-RuCl3 fulfills the a priori criteria of recent theoretical predictions of tuning the relevant properties in this material and provides a novel platform to explore the Kitaev physics.
Collapse
Affiliation(s)
- Zhongjie Wang
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200438, China.
| | - Lu Liu
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200438, China.
- Laboratory for Computational Physical Sciences (MOE), Fudan University, Shanghai 200438, China
| | - Haoran Zheng
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200438, China.
| | - Meng Zhao
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200438, China.
| | - Ke Yang
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200438, China.
- Laboratory for Computational Physical Sciences (MOE), Fudan University, Shanghai 200438, China
| | - Chunzheng Wang
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200438, China.
| | - Fang Yang
- Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Songhu Rd. 2005, Shanghai 200438, China
- Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai 201210, China
| | - Hua Wu
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200438, China.
- Laboratory for Computational Physical Sciences (MOE), Fudan University, Shanghai 200438, China
- Shanghai Qi Zhi Institute, Shanghai 200232, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Chunlei Gao
- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200438, China.
- Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Songhu Rd. 2005, Shanghai 200438, China
- Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai 201210, China
- Shanghai Qi Zhi Institute, Shanghai 200232, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| |
Collapse
|
7
|
Liu Y, Slagle K, Burch KS, Alicea J. Dynamical Anyon Generation in Kitaev Honeycomb Non-Abelian Spin Liquids. PHYSICAL REVIEW LETTERS 2022; 129:037201. [PMID: 35905346 DOI: 10.1103/physrevlett.129.037201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2021] [Accepted: 06/22/2022] [Indexed: 06/15/2023]
Abstract
Relativistic Mott insulators known as "Kitaev materials" potentially realize spin liquids hosting non-Abelian anyons. Motivated by fault-tolerant quantum-computing applications in this setting, we introduce a dynamical anyon-generation protocol that exploits universal edge physics. The setup features holes in the spin liquid, which define energetically cheap locations for non-Abelian anyons, connected by a narrow bridge that can be tuned between spin liquid and topologically trivial phases. We show that modulating the bridge from trivial to spin liquid over intermediate time scales-quantified by analytics and extensive simulations-deposits non-Abelian anyons into the holes with O(1) probability. The required bridge manipulations can be implemented by integrating the Kitaev material into magnetic tunnel junction arrays that engender locally tunable exchange fields. Combined with existing readout strategies, our protocol reveals a path to topological qubit experiments in Kitaev materials at zero applied magnetic field.
Collapse
Affiliation(s)
- Yue Liu
- Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Kevin Slagle
- Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Kenneth S Burch
- Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA
| | - Jason Alicea
- Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
| |
Collapse
|
8
|
Persky E, Bjørlig AV, Feldman I, Almoalem A, Altman E, Berg E, Kimchi I, Ruhman J, Kanigel A, Kalisky B. Magnetic memory and spontaneous vortices in a van der Waals superconductor. Nature 2022; 607:692-696. [PMID: 35896649 DOI: 10.1038/s41586-022-04855-2] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2021] [Accepted: 05/11/2022] [Indexed: 11/09/2022]
Abstract
Doped Mott insulators exhibit some of the most intriguing quantum phases of matter, including quantum spin liquids, unconventional superconductors and non-Fermi liquid metals1-3. Such phases often arise when itinerant electrons are close to a Mott insulating state, and thus experience strong spatial correlations. Proximity between different layers of van der Waals heterostructures naturally realizes a platform for experimentally studying the relationship between localized, correlated electrons and itinerant electrons. Here we explore this relationship by studying the magnetic landscape of tantalum disulfide 4Hb-TaS2, which realizes an alternating stacking of a candidate spin liquid and a superconductor4. We report on a spontaneous vortex phase whose vortex density can be trained in the normal state. We show that time-reversal symmetry is broken in the normal state, indicating the presence of a magnetic phase independent of the superconductor. Notably, this phase does not generate ferromagnetic signals that are detectable using conventional techniques. We use scanning superconducting quantum interference device microscopy to show that it is incompatible with ferromagnetic ordering. The discovery of this unusual magnetic phase illustrates how combining superconductivity with a strongly correlated system can lead to unexpected physics.
Collapse
Affiliation(s)
- Eylon Persky
- Department of Physics, Bar Ilan University, Ramat Gan, Israel. .,Bar Ilan Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat Gan, Israel.
| | - Anders V Bjørlig
- Department of Physics, Bar Ilan University, Ramat Gan, Israel.,Bar Ilan Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat Gan, Israel
| | - Irena Feldman
- Department of Physics, Technion-Israel Institute of Technology, Haifa, Israel
| | - Avior Almoalem
- Department of Physics, Technion-Israel Institute of Technology, Haifa, Israel
| | - Ehud Altman
- Department of Physics, University of California, Berkeley, Berkeley, CA, USA.,Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Erez Berg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel
| | - Itamar Kimchi
- School of Physics, Georgia Institute of Technology, Atlanta, GA, USA
| | - Jonathan Ruhman
- Department of Physics, Bar Ilan University, Ramat Gan, Israel
| | - Amit Kanigel
- Department of Physics, Technion-Israel Institute of Technology, Haifa, Israel
| | - Beena Kalisky
- Department of Physics, Bar Ilan University, Ramat Gan, Israel. .,Bar Ilan Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat Gan, Israel.
| |
Collapse
|
9
|
Klocke K, Aasen D, Mong RSK, Demler EA, Alicea J. Time-Domain Anyon Interferometry in Kitaev Honeycomb Spin Liquids and Beyond. PHYSICAL REVIEW LETTERS 2021; 126:177204. [PMID: 33988434 DOI: 10.1103/physrevlett.126.177204] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2020] [Accepted: 03/30/2021] [Indexed: 06/12/2023]
Abstract
Motivated by recent experiments on the Kitaev honeycomb magnet α-RuCl_{3}, we introduce time-domain probes of the edge and quasiparticle content of non-Abelian spin liquids. Our scheme exploits ancillary quantum spins that communicate via time-dependent tunneling of energy into and out of the spin liquid's chiral Majorana edge state. We show that the ancillary-spin dynamics reveals the edge-state velocity and, in suitable geometries, detects individual non-Abelian anyons and emergent fermions via a time-domain counterpart of quantum-Hall anyon interferometry. We anticipate applications to a wide variety of topological phases in solid-state and cold-atoms settings.
Collapse
Affiliation(s)
- Kai Klocke
- Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - David Aasen
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
- Microsoft Quantum, Microsoft Station Q, University of California, Santa Barbara, California 93106-6105, USA
| | - Roger S K Mong
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
- Pittsburgh Quantum Institute, Pittsburgh, Pennsylvania 15260, USA
| | - Eugene A Demler
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA
| | - Jason Alicea
- Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
- Walker Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
| |
Collapse
|