1
|
Kamra LJ, Lu B, Linder J, Tanaka Y, Nagaosa N. Optical conductivity of the Majorana mode at the s- and d-wave topological superconductor edge. Proc Natl Acad Sci U S A 2024; 121:e2404009121. [PMID: 39320921 DOI: 10.1073/pnas.2404009121] [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: 02/26/2024] [Accepted: 08/21/2024] [Indexed: 09/26/2024] Open
Abstract
The Majorana fermion offers fascinating possibilities such as non-Abelian statistics and nonlocal robust qubits, and hunting it is one of the most important topics in current condensed matter physics. Most of the efforts have been focused on the Majorana bound state at zero energy in terms of scanning tunneling spectroscopy searching for the quantized conductance. On the other hand, a chiral Majorana edge channel appears at the surface of a three-dimensional topological insulator when engineering an interface between proximity-induced superconductivity and ferromagnetism. Recent advances in microwave spectroscopy of topological edge states open a new avenue for observing signatures of such Majorana edge states through the local optical conductivity. As a guide to future experiments, we show how the local optical conductivity and density of states present distinct qualitative features depending on the symmetry of the superconductivity, that can be tuned via the magnetization and temperature. In particular, the presence of the Majorana edge state leads to a characteristic nonmonotonic temperature dependence achieved by tuning the magnetization.
Collapse
Affiliation(s)
- Lina Johnsen Kamra
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, Trondheim NO-7491, Norway
- Condensed Matter Physics Center and Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Madrid E-28049, Spain
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139
| | - Bo Lu
- Center for Joint Quantum Studies, Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Department of Physics, Tianjin University, Tianjin 300354, China
| | - Jacob Linder
- Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology, Trondheim NO-7491, Norway
| | - Yukio Tanaka
- Department of Applied Physics, Nagoya University, Nagoya 464-8603, Japan
- Research Center for Crystalline Materials Engineering, Nagoya University, Nagoya 464-8603, Japan
| | - Naoto Nagaosa
- RIKEN Center for Emergent Matter Science, Wako, Saitama 351-0198, Japan
- Fundamental Quantum Science Program, Transformative Research Innovation Platform (TRIP) Headquarters, RIKEN, Wako 351-0198, Japan
| |
Collapse
|
2
|
Sun ZT, Hu JX, Xie YM, Law KT. Anomalous h/2e Periodicity and Majorana Zero Modes in Chiral Josephson Junctions. PHYSICAL REVIEW LETTERS 2024; 133:056601. [PMID: 39159079 DOI: 10.1103/physrevlett.133.056601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2023] [Revised: 04/24/2024] [Accepted: 06/26/2024] [Indexed: 08/21/2024]
Abstract
Recent experiments reported that quantum Hall chiral edge state-mediated Josephson junctions (chiral Josephson junctions) could exhibit Fraunhofer oscillations with a periodicity of either h/e [Vignaud et al., Nature (London) 624, 545 (2023)NATUAS0028-083610.1038/s41586-023-06764-4] or h/2e [Amet et al., Science 352, 966 (2016)SCIEAS0036-807510.1126/science.aad6203]. While the h/e-periodic component of the supercurrent had been anticipated theoretically before, the emergence of the h/2e periodicity is still not fully understood. In this Letter, we systematically study the Fraunhofer oscillations of chiral Josephson junctions. In chiral Josephson junctions, the chiral edge states coupled to the superconductors become chiral Andreev edge states. We find that in short junctions, the coupling of the chiral Andreev edge states can trigger the h/2e-magnetic flux periodicity. Our theory resolves the important puzzle concerning the appearance of the h/2e periodicity in chiral Josephson junctions. Furthermore, we explain that when the chiral Andreev edge states couple, a pair of localized Majorana zero modes appear at the ends of the Josephson junction, which are robust and independent of the phase difference between the two superconductors. As the h/2e periodicity and the Majorana zero modes have the same physical origin in the wide junction limit, the Fraunhofer oscillation period could be useful in identifying the regime with Majorana zero modes.
Collapse
|
3
|
Yu H, Yan D, Guo Z, Zhou Y, Yang X, Li P, Wang Z, Xiang X, Li J, Ma X, Zhou R, Hong F, Wuli Y, Shi Y, Wang JT, Yu X. Observation of Emergent Superconductivity in the Topological Insulator Ta 2Pd 3Te 5 via Pressure Manipulation. J Am Chem Soc 2024; 146:3890-3899. [PMID: 38294957 DOI: 10.1021/jacs.3c11364] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2024]
Abstract
Topological insulators offer significant potential to revolutionize diverse fields driven by nontrivial manifestations of their topological electronic band structures. However, the realization of superior integration between exotic topological states and superconductivity for practical applications remains a challenge, necessitating a profound understanding of intricate mechanisms. Here, we report experimental observations for a novel superconducting phase in the pressurized second-order topological insulator candidate Ta2Pd3Te5, and the high-pressure phase maintains its original ambient pressure lattice symmetry up to 45 GPa. Our in situ high-pressure synchrotron X-ray diffraction, electrical transport, infrared reflectance, and Raman spectroscopy measurements, in combination with rigorous theoretical calculations, provide compelling evidence for the association between the superconducting behavior and the densified phase. The electronic state change around 20 GPa was found to modify the topology of the Fermi surface directly, which synergistically fosters the emergence of robust superconductivity. In-depth comprehension of the fascinating properties exhibited by the compressed Ta2Pd3Te5 phase is achieved, highlighting the extraordinary potential of topological insulators for exploring and investigating high-performance electronic advanced devices under extreme conditions.
Collapse
Affiliation(s)
- Hui Yu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Dayu Yan
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Zhaopeng Guo
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yizhou Zhou
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Xue Yang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Peiling Li
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Zhijun Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Xiaojun Xiang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Junkai Li
- Center for High Pressure Science and Technology Advanced Research, Beijing 100094, P. R. China
| | - Xiaoli Ma
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Rui Zhou
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan523808, Guangdong, China
| | - Fang Hong
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yunxiao Wuli
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Youguo Shi
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan523808, Guangdong, China
| | - Jian-Tao Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan523808, Guangdong, China
| | - Xiaohui Yu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
- Songshan Lake Materials Laboratory, Dongguan523808, Guangdong, China
| |
Collapse
|
4
|
Xiang F, Gupta A, Chaves A, Krix ZE, Watanabe K, Taniguchi T, Fuhrer MS, Peeters FM, Neilson D, Milošević MV, Hamilton AR. Intra-Zero-Energy Landau Level Crossings in Bilayer Graphene at High Electric Fields. NANO LETTERS 2023; 23:9683-9689. [PMID: 37883804 DOI: 10.1021/acs.nanolett.3c01456] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/28/2023]
Abstract
The highly tunable band structure of the zero-energy Landau level (zLL) of bilayer graphene makes it an ideal platform for engineering novel quantum states. However, the zero-energy Landau level at high electric fields has remained largely unexplored. Here we present magnetotransport measurements of bilayer graphene in high transverse electric fields. We observe previously undetected Landau level crossings at filling factors ν = -2, 1, and 3 at high electric fields. These crossings provide constraints for theoretical models of the zero-energy Landau level and show that the orbital, valley, and spin character of the quantum Hall states at high electric fields is very different from low electric fields. At high E, new transitions between states at ν = -2 with different orbital and spin polarization can be controlled by the gate bias, while the transitions between ν = 0 → 1 and ν = 2 → 3 show anomalous behavior.
Collapse
Affiliation(s)
- Feixiang Xiang
- School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Abhay Gupta
- School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Andrey Chaves
- Universidade Federal do Ceará, Departamento de Física, Caixa Postal 6030, 60455-760 Fortaleza, Ceará Brazil
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium
| | - Zeb E Krix
- School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, University of New South Wales, Sydney, New South Wales 2052, Australia
| | - Kenji Watanabe
- National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan
| | - Michael S Fuhrer
- School of Physics and Astronomy and ARC Centre of Excellence in Future Low-Energy Electronics Technologies (FLEET), Monash University, Clayton, Victoria 3800, Australia
| | - François M Peeters
- Universidade Federal do Ceará, Departamento de Física, Caixa Postal 6030, 60455-760 Fortaleza, Ceará Brazil
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium
| | - David Neilson
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, University of New South Wales, Sydney, New South Wales 2052, Australia
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium
| | - Milorad V Milošević
- Department of Physics, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium
- NANOlab Center of Excellence, University of Antwerp, B-2020 Antwerp, Belgium
| | - Alexander R Hamilton
- School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia
- ARC Centre of Excellence in Future Low-Energy Electronics Technologies, University of New South Wales, Sydney, New South Wales 2052, Australia
| |
Collapse
|