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Chin. Phys. B, 2021, Vol. 30(10): 106802    DOI: 10.1088/1674-1056/ac0903

Direct observation of the scaling relation between density of states and pairing gap in a dirty superconductor

Chang-Jiang Zhu(朱长江)1,2,†, Limin Liu(刘立民)1,2,†, Peng-Bo Song(宋鹏博)1,2,†, Han-Bin Deng(邓翰宾)1,2, Chang-Jiang Yi(伊长江)1, Ying-Kai Sun(孙英开)1,2, R Wu(武睿)1,5, Jia-Xin Yin(殷嘉鑫)4, Youguo Shi(石友国)1,‡, Ziqiang Wang(汪自强)6,§, and Shuheng H. Pan(潘庶亨)1,2,3,5,¶
1 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
2 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
3 CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China;
4 Laboratory for Topological Quantum Matter and Advanced Spectroscopy(B7), Department of Physics, Princeton University, Princeton, NJ, USA;
5 Songshan Lake Materials Laboratory, Dongguan 523808, China;
6 Department of Physics, Boston College, Chestnut Hill, MA, USA
Abstract  Theories and experiments on dirty superconductors are complex but important in terms of both theoretical fundamentals and practical applications. These activities are even more challenging when magnetic fields are present because the field distribution, electron density of states, and superconducting pairing potentials become nonuniform. Here, we present tunneling microspectroscopic experiments on NbC single crystals and demonstrate that NbC is a homogeneous dirty superconductor. When applying magnetic fields to the samples, we found that the zero-energy local density of states and the pairing energy gap followed the explicit scaling relation proposed by de Gennes for homogeneous dirty superconductors in high magnetic fields. More significantly, our experimental findings indicate that the validity of the scaling relation extends to magnetic field strengths far below the upper critical field, calling for a new nonperturbative understanding of this fundamental property in dirty superconductors. On the practical side, we used the observed scaling relation to derive a simple and straightforward experimental scheme for estimating the superconducting coherence length of a dirty superconductor in magnetic fields.
Keywords:  NbC      dirty superconductor      de Gennes theory      scanning tunneling microscope  
Received:  01 June 2021      Revised:  02 June 2021      Accepted manuscript online:  08 June 2021
PACS:  68.37.Ef (Scanning tunneling microscopy (including chemistry induced with STM))  
  74.25.Ha (Magnetic properties including vortex structures and related phenomena)  
  74.62.-c (Transition temperature variations, phase diagrams)  
  74.70.Ad (Metals; alloys and binary compounds)  
Fund: Project supported by the National Key Research and Development Program of the Ministry of Science and Technology of China (Grant Nos. 2017YFA0302903, 2016YFA0300602, 2016YFA0300604, and 2016YFJC010282), the National Natural Science Foundation of China (Grant Nos. 11227903, 12004416, and U2032204), the Beijing Municipal Science and Technology Commission, China (Grant Nos. Z181100004218007 and Z191100007219011), the National Basic Research Program of China (Grant No. 2015CB921304), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos. XDB07000000, XDB28000000 and XDB33000000). Z.W. was supported by the US Department of Energy (Basic Energy Sciences Grant No. DE-FG02-99ER45747).
Corresponding Authors:  Youguo Shi, Ziqiang Wang, Shuheng H. Pan     E-mail:;;

Cite this article: 

Chang-Jiang Zhu(朱长江), Limin Liu(刘立民), Peng-Bo Song(宋鹏博), Han-Bin Deng(邓翰宾), Chang-Jiang Yi(伊长江), Ying-Kai Sun(孙英开), R Wu(武睿), Jia-Xin Yin(殷嘉鑫), Youguo Shi(石友国), Ziqiang Wang(汪自强), and Shuheng H. Pan(潘庶亨) Direct observation of the scaling relation between density of states and pairing gap in a dirty superconductor 2021 Chin. Phys. B 30 106802

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