Abstract Body

Quantum vortices are fundamentally important for properties of superconductors. In conventional type-II superconductor they determine the magnetic response of the system and tend to form regular lattices. UTe₂ is a recently discovered heavy fermion superconductor exhibiting many anomalous macroscopic behaviors. However, the question whether it has a multicomponent order parameter remains open. Here, we study magnetic properties of UTe₂ by employing scanning superconducting quantum interference device microscopy. We find vortex behavior which is very different from that in ordinary superconductors. We imaged vortices generated by cooling in magnetic field applied along different crystalline directions. While a small out-of-plane magnetic field produces typical isolated vortices, higher field generates vortex stripe patterns which evolve with vortex density. The stripes form at different locations and along different directions in the surface plane when the vortices are crystalized along the crystalline b or c axes. The behavior is reproduced by our simulation based on an anisotropic two-component order parameter. This study shows that UTe₂ has a nontrivial disparity of multiple length scales, placing constraints on multicomponent superconductivity. The tendency of vortex stripe formation and their control by external field may be useful in fluxonics applications.

Abstract Body

Since the Ginzburg-Landau (GL) parameter k_GL of high-purity Nb is close to the critical value that separates type-I from type-II, the magnetic flux quantum (vortex) in this material has a rather unique property, i.e. non-monotonic intervortex interaction. This regime of superconductivity is often called type-II/1. Recently, the properties of vortices in this material have been reinvestigated using state-of-the-art techniques. Besides the academic interest, the understanding of the vortex dynamics in high-purity Nb is important for superconducting applications. For example, the performance of niobium superconducting radiofrequency (SRF) accelerator cavities is closely related to the behavior of remanent vortices that are not expelled during cooling. In fact, the contribution of remanent vortices is one of the factors limiting the Q-value at operating temperatures. Therefore, in order to further improve the cavity performance, it is necessary to clarify the unique vortex state of cavity-grade high-purity Nb and the behavior of the vortices during cooling.

To study the dynamic behavior of the vortices, we performed in-situ observations by magneto-optical imaging (MOI) technique during field cooling. We observed the intermediate mixed state (IMS), which is a manifestation of the attractive vortex interaction, in the cavity-grade high-purity Nb in a magnetic field of 100-400 Oe [1]. More recently, we have dynamically visualized the clustering process of a small number of vortices in lower fields by MOI with single vortex resolution [2]. In this talk, I would like to present some MOI results on the vortex behavior in high-purity Nb. The observed features can mostly be explained by the combined influence of the vortex-vortex interaction, the Lorentz force due to the screening current, and the pinning potential landscape.

References

[1] S. Ooi et al., “Observation of intermediate mixed state in high-purity cavity-grade Nb by magneto-optical imaging”, Phys. Rev. B 104, 064504 (2021).

[2] S. Ooi et al., submitted.

Keywords: Vortex cluster, Nb, Intermediate mixed state, Magneto-optical imaging

Abstract Body

Polar superconductors, in which paired electrons or quantum vortices move under the influence of electric polarization, are one of promising material platforms for searching exotic superconductivity and/or superconducting devices with new functions. Among them, the doped SrTiO₃ is an ideal candidate of the polar superconductor [1], since it easily transforms to a ferroelectric and/or a superconductor with a little perturbation, leading to the coexistence of the ferroelectricity and superconductivity [2-4]. However, the distinct nature of the polar superconductors has been vague.

In this work, we have studied transport properties, containing the liner and nonreciprocal resistance, R^ω and R^2ω, of ion-gated SrTiO₃ in an electric double layer transistor structure. In the normal state with carrier density 0.1 ~1 × 10¹⁴ cm^-2, we found the sudden occurrence of finite nonreciprocal resistance R^2ω at 30 K in the out-of-plane magnetic field B, implying the emergence of spontaneous in-plane polarization P in addition to out-of-plane P due to gating process. This leads to a unique polar superconducting state at low temperatures below 0.4 K in our systems. Indeed, in the superconducting transition region, we observed a variety of anomalous properties such as the strongly enhanced R^2ω (B) and asymmetric R^ω (B) in out-of-plane B, as well as the two-fold oscillation of R^ω (ϕ) against the in-plane ϕ rotation of B, indicating the rachet motion of pancake vortices [1,5] in anisotropic two-dimensional (quasi one-dimensional) superconducting state. To explain these anomalies, we suggest a model for the polar superconductivity with the asymmetric stripe-like modulation of order parameter along P direction. We will also discuss that the pancake vortices can be induced by in-plane B due to the antisymmetric spin-orbit interaction originating from the peculiar electric polarization in ion-gated SrTiO₃.

References

[1] Y. M. Itahashi, et al., Science Advances 6, eaay9120 (2020).

[2] C.W. Rischau et al., Nat. Phys. 13, 645 (2017). 

[3] C. W. Rischau et al., Phys. Rev. Research 4, 013019 (2022).

[4] R. Russell et al., Phys. Rev. Mater 3, 091104 (2018).

[5] Y. M. Itahashi, Y. Saito, T. Ideue, T. Nojima, Y. Iwasa, Phys. Rev. Research 2, 023127 (2020).

Acknowledgment

This work was supported by the JSPS KAKENHI (No. 20H05145).

Keywords: Polar superconductivity, 2D vortex dynamics, Nonreciprocal transport, Spin-orbit interaction

Abstract Body

Quantum vortices in type-II superconductors are known to have significant impacts on the transport properties of superconductors, thus improving the controllability of the motion of vortices has been a crucial issue. The most common method to drive vortices is the use of transport currents. In [1][2], we defined the driving force on a vortex as the sum of the magnetic and hydrodynamic forces in the framework of the time-dependent Ginzburg-Landau (TDGL) theory. We expected that the results could be extended to establish a similar picture for other driving methods, such as heat flows[3][4] and inhomogeneous spin polarization.

In [5], we investigated the dynamics of domain walls, one-dimensional topological defects, under the influence of the temperature gradient or the inhomogeneous spin polarization. The system of equations consists of the TDGL equation and the thermal / spin diffusion equation. We have shown, both analytically and numerically, that the domain walls move to the higher temperature region, where the order parameter is suppressed. This result is understood as a process reducing the loss of in the condensation energy (cf. pinning of vortices).

In this presentation, we discuss the dynamics of quantum vortices under a temperature gradient. We incorporated Ampere's law, which we did not consider in case of the dynamics of domain walls, into the system of equations.

References

[1] Y. Kato and C-K Chung, J. Phys. Soc. Jpn. 85, 033703/1-5 (2016).

[2] S. Sugai, N. Kurosawa and Y. Kato, Phys. Rev. B 104, 064516 (2021).

[3] M. J. Stephen, Phys. Rev. Lett, 16, 801 (1966).

[4] I. S. Veshchunov et al., Nat. Commun. 7, 12801 (2016).

[5] T. Kanakubo et al., Interplay between Domain Walls in Type-II Superconductors and Gradients of Temperature/Spin Density, arXiv:2405.10200 (2024).

Keywords: Type-II Superconductors, Vortex, Heat Flow, Ginzburg-Landau Theory

Abstract Body

Superconductivity in nano-size shows special properties. Previously, we investigated transition temperature of nano-sized clean and dirty superconductors [1,2]. We found that the transition temperature is increased with oscillation as size of the superconductor is decreased. This is quantum effect. Electrons are confined in small region and the energy levels become discrete. Decreasing the size, energy level distance becomes large and effective electron density within the range of the attractive interaction between electrons becomes large.

In a dirty superconductor, the transition temperature is strongly increased because of the localization of superconducting electrons and increase of local density of states [3]. In figure, we show the Tc-enhancement (a) and localized superconducting state (b). However, in such localized superconductivity, zero-resistivity may disappear because there remain normal regions. In order to obtain superconductivity in whole region, we should decrease the temperature.

Here, we investigate how localized superconductivity extend the whole region with decreasing the temperature. We solve the Bogoliubov-de Gennes equations with impurity potential using the finite element method. We have found that superconductivity extend gradually, but this behavior depends on the impurity potential.

References

[1] M. Umeda, M. Kato, and O. Sato, IEEE Trans. on Appl. Superconductivity 26 8600104 (2016).

[2] M. Umeda, M. KatoPhysica C 560 (2019).

[3] M. Umeda, M. KatoJ. Appl. Phys. 126 143905 (2019).

Acknowledgment

This work supported by the KAKENHI Grant No. 24K08236.

Figure 1. (a) Size dependence of transition temperature of a rectangular superconductor. (b)Distribution of superconducting order parameter of localized state.

Keywords: Tc enhancement, Bogoliubov-de Gennes equation, Finite element method, Localization

Abstract Body

Aiming to improve the efficiency and resolution of the scanning SQUID microscope, the present authors have fabricated a vector pickup sensor, which consists of three independent coils measuring the magnetic flux in x-, y-, and z-direction simultaneously [1]. In the previous work, to eliminate the image blur caused by the size of the pickup coil, we applied a numerical image processing method [2] to a simplified three-dimensional pickup coil model [3].

In this work, we extend the above method to analyze a more realistic pick-up coil model, taking into account the geometry and dimensions of the actual sensor (Fig.1). We have paid particular attention to the effects of the superconductivity in the sensor body, since it modifies the magnetic flux to be measured. We discuss how the magnetic flux of the sample is visualized by our system, and a numerical method for recovering the actual magnetic flux image is presented.

References

[1] T. D. Vu, T. H. Ho, S. Miyajima, M. Toji, Y. Ninomiya, H. Shishido, M. Maezawa, M. Hidaka, M. Hayashi, S. Kawamata and T. Ishida, Supercond. Sci. Technol. 32, 115006 (2019).

[2] M. Hayashi, H. Ebisawa, H. T. Huy, and T. Ishida, Appl. Phys. Lett. 100, 182601 (2012).

[3] Masahiko Hayashi, Takekazu Ishida, Hiroaki Shishido, The Dang Vu, Shuichi Kawamata J. Phys.: Conf. Ser. 2776,012001 (2024).

Acknowledgment

This work is partially supported by Grants-in-Aid for Scientific Research (JP22K04246) from JSPS.

Fig.1 Model of a vector SQUID sensor. Each pickup coil is doubly winding.

Keywords: SQUID, scanning SQUID microscopy, numerical image processing