Kosterlitz–Thouless Transition in 4-nm Aluminum Nano-Film

Guan-Ming Su^1*, Bi-Yi Wu¹, Yen-Ting Fan², Ankit Kumar¹, Chau-Shing Chang¹, Ching-Chen Yeh¹, Dinesh K. Patel¹, Sheng-Di Lin², Lee Chow³, Chi-Te Liang¹

¹Department of Physics, National Taiwan University, Taipei 106, Taiwan
²Department of Electronics Engineering, National Chiao Tung University, Hsinchu 300, Taiwan
³Department of Physics, University of Central Florida, Orlando, Florida 32816, USA

* Presenter:Guan-Ming Su, email:arahaguojnestore@gmail.com

Kosterlitz–Thouless (KT) transition is known as a topological phase transition which characterized by the excitation of free vortices (anti-vortices) [1]. It is predicted to exist in 2D superconducting system, if the perpendicular penetration length λ_p=λ²/d ( λ is the bulk penetration length and d is the thickness) is comparable to the sample’s size so the vortex-anti-vortex pairs can interact logarithmically throughout the device[2, 3]. Another criterion is that the superconducting coherence length should be small enough, so the vortex core radius will be smaller than sample’s dimension and the superconductivity can be kept.
Although the bulk aluminum is well-known as a type I superconductor with long coherence length and short penetration length, we here report that by measuring the electrical properties for a MBE-grown 4-nm nano-film aluminum sample [4], whose critical temperature 2.2 K and critical field above 6671 G are both higher than the bulk value 1.2 K and 100 G, some behaviors consistent with the KT transition are observed. According to the current induced vortex-anti-vortex unbinding model, the log-to-log scale I-V curve at the KT transition temperature T_KT exhibits a slope equals to 3. By extracting the slope from our logI-logV curves at different T, T_KT =2.17 K is found. We also fit the T-R curves using the temperature induced vortex-anti-vortex unbinding model R∝e^{2(b/(T-T_KT))0.5}, we obtain that the parameter T_KT is between 2.16 to 2.2 K, with slightly current dependence which might be a consequence of Joule heating. We also utilize the dynamical scaling formula derived by Fisher, Fisher and Huse [5] to construct the scaling behavior, which gives T_KT also around 2.17 K and a dynamical exponent z=2, in agreement with the temperature induced vortex-anti-vortex unbinding model. This possible confirmation of KT transition along with the higher-than-bulk critical temperature and critical field indicate that our nano-flim may possess a different superconducting mechanism from that of the bulk.

[1] J. M. Kosterlitz and D. J. Thouless, Journal of Physics C: Solid State Physics 6, 1181 (1973)
[2] M. R. Beasley, J. E. Mooij and T. P. Orlando, Physical Review Letters 42, 1165 (1979).
[3] J. Pearl, Applied Physics Letters 5, 65-66 (1964).
[4] Y.-T. Fan, M.-C. Lo, C.-C. Wu, P.-Y. Chen, J.-S. Wu, C.-T. Liang and S.-D. Lin, AIP Advances 7, 075213 (2017).
[5] D. S. Fisher, M. P. Fisher and D. A. Huse, Physical Review B 43, 130 (1991).

Keywords: aluminum nano-film, 2D superconductivity, Kosterlitz–Thouless Transition