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Liu T, Wan CY, Yang H, Zhao Y, Xie B, Zheng W, Yi Z, Guan D, Wang S, Zheng H, Liu C, Fu L, Liu J, Li Y, Jia J. Signatures of hybridization of multiple Majorana zero modes in a vortex. Nature 2024:10.1038/s41586-024-07857-4. [PMID: 39198651 DOI: 10.1038/s41586-024-07857-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2024] [Accepted: 07/19/2024] [Indexed: 09/01/2024]
Abstract
Majorana zero modes (MZMs) are emergent zero-energy topological quasiparticles that are their own antiparticles1,2. Detected MZMs are spatially separated and electrically neutral, so producing hybridization between MZMs is extremely challenging in superconductors3,4. Here, we report the magnetic field response of vortex bound states in superconducting topological crystalline insulator SnTe (001) films. Several MZMs were predicted to coexist in a single vortex due to magnetic mirror symmetry. Using a scanning tunnelling microscope equipped with a three-axis vector magnet, we found that the zero-bias peak (ZBP) in a single vortex exhibits an apparent anisotropic response even though the magnetic field is weak. The ZBP can robustly extend a long distance of up to approximately 100 nm at the (001) surface when the magnetic field is parallel to the ( 1 1 ¯ 0 )-type mirror plane, otherwise it displays an asymmetric splitting. Our systematic simulations demonstrate that the anisotropic response cannot be reproduced with trivial ZBPs. Although the different MZMs cannot be directly distinguished due to the limited energy resolution in our experiments, our comparisons between experimental measurements and theoretical simulations strongly support the existence and hybridization of symmetry-protected multiple MZMs. Our work demonstrates a way to hybridize different MZMs by controlling the orientation of the magnetic field and expands the types of MZM available for tuning topological states.
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Affiliation(s)
- Tengteng Liu
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Chun Yu Wan
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
| | - Hao Yang
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Yujun Zhao
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
| | - Bangjin Xie
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Weiyan Zheng
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Zhaoxia Yi
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
| | - Dandan Guan
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
- Shanghai Research Center for Quantum Sciences, Shanghai, China
- Hefei National Laboratory, Hefei, China
| | - Shiyong Wang
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
- Shanghai Research Center for Quantum Sciences, Shanghai, China
- Hefei National Laboratory, Hefei, China
| | - Hao Zheng
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
- Shanghai Research Center for Quantum Sciences, Shanghai, China
- Hefei National Laboratory, Hefei, China
| | - Canhua Liu
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China
- Shanghai Research Center for Quantum Sciences, Shanghai, China
- Hefei National Laboratory, Hefei, China
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Junwei Liu
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China.
| | - Yaoyi Li
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China.
- Shanghai Research Center for Quantum Sciences, Shanghai, China.
- Hefei National Laboratory, Hefei, China.
| | - Jinfeng Jia
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China.
- Shanghai Research Center for Quantum Sciences, Shanghai, China.
- Hefei National Laboratory, Hefei, China.
- Department of Physics, Southern University of Science and Technology, Shenzhen, China.
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Ibabe Á, Steffensen GO, Casal I, Gómez M, Kanne T, Nygård J, Levy Yeyati A, Lee EJH. Heat Dissipation Mechanisms in Hybrid Superconductor-Semiconductor Devices Revealed by Joule Spectroscopy. NANO LETTERS 2024; 24:6488-6495. [PMID: 38771151 PMCID: PMC11157656 DOI: 10.1021/acs.nanolett.4c00574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2024] [Revised: 05/17/2024] [Accepted: 05/17/2024] [Indexed: 05/22/2024]
Abstract
Understanding heating and cooling mechanisms in mesoscopic superconductor-semiconductor devices is crucial for their application in quantum technologies. Owing to their poor thermal conductivity, heating effects can drive superconducting-to-normal transitions even at low bias, observed as sharp conductance dips through the loss of Andreev excess currents. Tracking such dips across magnetic field, cryostat temperature, and applied microwave power allows us to uncover cooling bottlenecks in different parts of a device. By applying this "Joule spectroscopy" technique, we analyze heat dissipation in devices based on InAs-Al nanowires and reveal that cooling of superconducting islands is limited by the rather inefficient electron-phonon coupling, as opposed to grounded superconductors that primarily cool by quasiparticle diffusion. We show that powers as low as 50-150 pW are able to suppress superconductivity on the islands. Applied microwaves lead to similar heating effects but are affected by the interplay of the microwave frequency and the effective electron-phonon relaxation time.
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Affiliation(s)
- Ángel Ibabe
- Departamento
de Física de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
- Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
| | - Gorm O. Steffensen
- Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
- Departamento
de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
| | - Ignacio Casal
- Departamento
de Física de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
- Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
| | - Mario Gómez
- Departamento
de Física de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
- Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
| | - Thomas Kanne
- Center
for Quantum Devices, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - Jesper Nygård
- Center
for Quantum Devices, Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - Alfredo Levy Yeyati
- Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
- Departamento
de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
- Instituto
Nicolás Cabrera, Universidad Autónoma
de Madrid, E-28049 Madrid, Spain
| | - Eduardo J. H. Lee
- Departamento
de Física de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain
- Condensed
Matter Physics Center (IFIMAC), Universidad
Autónoma de Madrid, E-28049 Madrid, Spain
- Instituto
Nicolás Cabrera, Universidad Autónoma
de Madrid, E-28049 Madrid, Spain
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Hirayama M, Nomoto T, Arita R. Topological band inversion and chiral Majorana mode in hcp thallium. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:275502. [PMID: 38447148 DOI: 10.1088/1361-648x/ad3093] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2023] [Accepted: 03/06/2024] [Indexed: 03/08/2024]
Abstract
The chiral Majorana fermion is an exotic particle that is its own antiparticle. It can arise in a one-dimensional edge of topological materials, and especially that in a topological superconductor can be exploited in non-Abelian quantum computation. While the chiral Majorana mode (CMM) remains elusive, a promising situation is realized when superconductivity coexists with a topologically non-trivial surface state. Here, we perform fully non-empirical calculation for the CMM considering superconductivity and surface relaxation, and show that hexagonal close-packed thallium (Tl) has an ideal electronic state that harbors the CMM. Thekz=0plane of Tl is a mirror plane, realizing a full-gap band inversion corresponding to a topological crystalline insulating phase. Its surface and hinge are stable and easy to make various structures. Another notable feature is that the surface Dirac point is very close to the Fermi level, so that a small Zeeman field can induce a topological transition. Our calculation indicates that Tl will provide a new platform of the Majorana fermion.
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Affiliation(s)
- Motoaki Hirayama
- Quantum-Phase Electronics Center, University of Tokyo, Tokyo 113-8656, Japan
- RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako 351-0198, Japan
| | - Takuya Nomoto
- Research Center for Advanced Science and Technology, University of Tokyo, Tokyo 153-8904, Japan
| | - Ryotaro Arita
- RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako 351-0198, Japan
- Research Center for Advanced Science and Technology, University of Tokyo, Tokyo 153-8904, Japan
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Pal S, Benjamin C. Honing in on a topological zero-bias conductance peak. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 36:035601. [PMID: 37813102 DOI: 10.1088/1361-648x/ad0192] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2023] [Accepted: 10/09/2023] [Indexed: 10/11/2023]
Abstract
A popular signature of Majorana bound states in topological superconductors is the quantized zero-energy conductance peak. However, a similar zero energy conductance peak can also arise due to non-topological reasons. Here we show that these trivial and topological zero energy conductance peaks can be distinguished via the zero energy local density of states (LDOSs) and local magnetization density of states (LMDOSs). We find that the zero-energy LDOSs and the LMDOSs exhibit periodic oscillations for a trivial zero-bias conductance peak (ZBCP). In contrast, these oscillations disappear for the topological ZBCP because of perfect Andreev reflection at zero energy in topological superconductor junctions. Our results suggest that the zero-energy LDOSs and the LMDOSs can be used as an experimental probe to distinguish a trivial zero-energy conductance peak from a topological zero-energy conductance peak.
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Affiliation(s)
- Subhajit Pal
- School of Physical Sciences, National Institute of Science Education & Research, Jatni 752050, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Colin Benjamin
- School of Physical Sciences, National Institute of Science Education & Research, Jatni 752050, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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Yazdani A, von Oppen F, Halperin BI, Yacoby A. Hunting for Majoranas. Science 2023; 380:eade0850. [PMID: 37347870 DOI: 10.1126/science.ade0850] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Accepted: 05/22/2023] [Indexed: 06/24/2023]
Abstract
Over the past decade, there have been considerable efforts to observe non-abelian quasiparticles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasiparticles beyond those of fermions and bosons and of establishing the underlying science for the creation of topologically protected quantum bits. In this Review, we focus on efforts to create topological superconducting phases that host Majorana zero modes. We consider the lessons learned from existing experimental efforts, which are motivating both improvements to present platforms and the exploration of new approaches. Although the experimental detection of non-abelian quasiparticles remains challenging, the knowledge gained thus far and the opportunities ahead offer high potential for discovery and advances in this exciting area of quantum physics.
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Affiliation(s)
- Ali Yazdani
- Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, NJ 08540, USA
| | - Felix von Oppen
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | | | - Amir Yacoby
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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