Last updated: ; sokuma@o.cc.titech.ac.jp

We measure the detailed electronic transport properties in disordered superconductors at low temperatures. We primarily study conventional (low-T_C ) superconductors (LTSC's) whose dimensionality and disorder are well controlled, while we are aware of the extensive literature of the high-T_C superconductors (HTSC's) and concerned with whether the phenomena found in HTSC's are also observed in LTSC's. The purpose of our study is to explore the dynamic as well as static vortex states in both two (2D) and three (3D) dimensional superconductors.

It is of great interest how the elastic media respond to an external shearing force and are driven over a random pinning potential. This study will lead to new insights into friction at a solid-solid interface and plastic motion of solids, which are widely observed in nature [1]. It is also interesting to investigate how the driven particles interacting with quenched disorder escape from the pinning potential and self-organize into ordered structures [2]. We show that a vortex system in type-II superconductors is a suitable model system to study such phenomena. In recent years, we have experimentally studied the dynamics of vortices driven by dc and/or ac currents in amorphous films with weak random pinning.

In the high velocity region, we are able to study the melting of moving lattices decoupled from the underlying pinning potential [3] by a mode-locking resonance [4]. We particularly focus on (i) the quantum melting induced by magnetic field near zero temperature [5] and (ii) the thermal melting of highly anisotropic lattices formed in tilted fields [6], which are difficult to study using conventional crystals. By lowering the velocity, i.e., increasing the effective pinning, we are able to explore how the elastic objects (i.e., vortex lattices) flowing over the random substrate transform into a plastic flow. Specifically, (iii) by using a Corbino-disk sample, we have observed rotating vortex-lattice rings [7], whose width decreases with decreasing the velocity [8]. At much lower velocities, we explore novel non-equilibrium phase transitions in interacting many-particle systems, which include (iv) a reversible to irreversible flow transition [9] first reported in a colloidal system [10] and a plastic depinning transition [9,11].

For detail, please see:

1. G. W. Crabtree, Nat Mat. 2, 435 (2003): M. C. Miguel and S. Zapperi, Nat. Mat. 2 (2003) 477.
2. N. Mangan, C. Reichhardt, and C. J. Olson Reichhardt, Phys. Rev. Lett. 100 (2008) 187002: 103 (2009) 168301: PNAS 108 (2011) 19099 .
3. A. E. Koshelev and V. M. Vinokur, Phys. Rev. Lett. 73 (1994) 3580.
4. S. Okuma, J. Inoue, and N. Kokubo, Phys. Rev. B 76 (2007) 172503: S. Okuma, H. Imaizumi, D. Shimamoto, and N. Kokubo, Phys. Rev. B 83 (2011) 064520: S. Okuma, D. Shimamoto, and N. Kokubo, Phys. Rev. B 85 (2012) 064508.
5. S. Okuma, H. Imaizumi, and K. Kokubo, Phys. Rev. B 80 (2009) 132503: A. Ochi, N. Sohara, S. Kaneko, N. Kokubo, and S. Okuma, J. Phys. Soc. Jpn. 85 (2016) 0447001.
6. A. Ochi et al., J. Phys. Soc. Jpn. 85 (2016) 034712.
7. S. Okuma, Y. Yamazaki, and K. Kokubo, Phys. Rev. B 80 (2009) 220501(R).
8. Y. Kawamura et al., Supercond. Sci. Technol. 28 (2015) 045002.
9. S. Okuma, Y. Yamazaki, and K. Kokubo, Phys. Rev. B 80 (2009) 220501(R).
10. S. Okuma, Y. Tsugawa, and A. Motohashi, Phys. Rev. B 83 (2011) 012503: J. Phys. Soc. Jpn. 81 (2012) 114718 .
11. L. Corte, P.M. Chaikin, J.P. Gollub, and D.J. Pine: Nature Phys. 4 (2008) 420.
12. S. Okuma and A. Motohashi, New. J. Phys. 14 (2012) 123021.

It is well known that the discovery of the HTSC's has triggered off the intensive investigations about the vortex states in the mixed state of the type-II superconductors. Much studies, both experimentally and theoretically, have revealed that the mean-field (B-T) phase diagram is drastically altered in HTSC's that have strong thermal fluctuations and the extreme type-II nature. In a conventional picture of the type-II superconductors, an application of the magnetic field to superconductors results in depairing of Cooper pairs as the field exceeds an upper critical field B_C2. In a recent picture, however, the crossover from the vortex-liquid state to the normal state is not a sharp phase transition: i.e., B_C2 has lost its clear physical meaning as a phase transition. In the systems with moderate disorder (such as random pinning), which we concentrate on in the recent studies, the stable superconducting state is a vortex-glass state and the true phase transition occurs between the vortex-glass phase and vortex-liquid phase (thus it is called the vortex-glass [VG] transition). This phase transition is second-order and expected to occur at locations far below B_C2 in HTSC's.

The presence of the VG transition has been supported by a number of experimental work for HTSC's. Nevertheless, studies using LTSC's have not been performed except for quite limited systems. In the recent work, we have made careful dc and ac complex resistivity measurements for granular indium films with T_C〜3-4 K and obtained first convincing evidence for the second-order transition in LTSC's [1,2]. This result, together with the finding that VG transition also exists in uniformly disordered a-MoxSi1-x films with microscopic pinning [3], indicates that the VG transition is universal in type-II superconductors. Quite recently, we have found for thick a-MoxSi1-x films that the VG transition persists down to very low temperatures (T→0) and up to high fields near B_C2(T=0) [4]. The vortex phase diagram [the VG transition line B_g(T)] is constructed in the B-T plane over the broad T range. Interestingly, there is a finite field region B_g < B < B_C2 at T→0, indicating the presence of the (T=0) quantum-vortex-liquid phase [4-7].

For detail, please see:

1. S. Okuma and N. Kokubo, Phys. Rev. B 56, 14138 (1997).
2. S. Okuma and H. Hirai, Physica B 228, 272 (1996).
3. S. Okuma and M. Arai, J. Phys. Soc. Jpn. 69 (2000) 2747.
4. S. Okuma, Y. Imamoto, and M. Morita, Phys. Rev. Lett.,86 (2001) 3136.
5. S. Okuma, M. Morita, and Y. Imamoto, Phys. Rev. B 66 (2002) 104506.
6. S. Okuma, S. Togo, and M. Morita, Phys. Rev. Lett. 91 (2003) 067001.
7. S. Okuma, M. Kobayashi, and M. Kamada, Phys. Rev. Lett. 94 (2005) 047003.

When the finite dc current I (or static Lorentz force) is applied to the vortex solid, the pinned vortex solid is depinned and flows, producing finite dc voltage. As long as the current is low, the vortex motion is dominated by the random pinning potential. This is called the plastic-flow state, where the voltage produced by the moving soft vortex solid strongly fluctuates. As the current I increases, the plastic-flow state is changed to the elastic-flow state where the vortex motion is free from the random pinning potential and is dominated by the interaction between vortices: Coherent motion just like a moving vortex lattice is expected to occur and the fluctuation of the voltage becomes diminishingly small. Theoretically, such a change in the dynamical vortex state has attracted much attention and has been interpreted in terms of the dynamical phase transition driven by the current. Experimentally, this type of the dynamical transition is difficult to detect using usual static transport measurements alone, while voltage (flux) noise measurements are very useful to study such phenomena related to fluctuations of vortex motion.

We have made the voltage noise measurements of amorphous Mo_xSi_1-x films over the broad frequency range spanning six decades (f = 0.1 Hz-100 kHz) in magnetic fields, as a function of a steady current and studied the dynamical (fluctuating) properties of the vortex motion in both 2D and 3D superconductors. The origin of the low-frequency (f〜0.1-10Hz) noise observed near the zero-resistance region is mainly due to temperature fluctuations and the contribution due to flux motion is very small. In contrast, S_V(f) at higher frequencies (f〜10 Hz-100 kHz) appears to be dominated by the flux motion [1]. Comparing the results in 3D with those in 2D, we have found that the voltage noise in 3D at low I is consistent with the plastic-flow picture. We have found for both 2D and 3D films that there is the largest noise at B=0 (or Meissner phase). As the field exceeds the lower critical field H_c1, noise S_V decreases drastically and falls down to the background level at B well below the VG transition field B_g. The large noise at and near B=0 is due to large density fluctuations associated with unbinding of vortex-antivortex pairs and nucleated and subsequently grown vortex loops for 2D and 3D, respectively [2]. For 3D films, with further increasing B, S_V again appears and broad peak occurs in the VG phase. The origin of this peak is due to the plastic-flow motion of VG. In contrast, for 2D films such a peak in S_V is not observed [2], consistent with the 2D VG theory that there is no VG phase except at T=0.

For detail, please see:

1. N. Kokubo, T. Terashima, and S. Okuma, J. Phys. Soc. Jpn. 67, 725 (1998).
2. S. Okuma and N. Kokubo, Phys. Rev. B 61, 671 (2000).

We have examined the superconductor-insulator (S-I) transition in 2D, focusing on the quantum fluctuation effects, which occur at low temperatures. Despite numerous experimental [1] and theoretical effort to understand the physics on the S-I transition, there remain basic and interesting problems to be settled. The existence of the universal critical resistance for the S-I transition and that of the Bose-insulator phase are most interesting problems which have been actively discussed.

According to the VG theory for 2D, when the finite field smaller than B_C2 (but larger than B_C1) is applied, vortex creep occurs at any finite temperatures. This destroys the phase coherence and leads to a finite resistance. Therefore, the true superconducting vortex-glass state is attained only at T = 0, where vortices are localized; i.e., the vortex-glass transition occurs at T = 0 in 2D. As the field is increased at T = 0, an interesting possibility arises: field-induced vortices Bose condense and Cooper pairs localized at a critical field B_C before Cooper pairs disappear around B_C2. Thus the transition from the vortex-glass to Bose-glass phase takes places at B_C. Right at the transition, the system is metallic with a finite resistance close to h/4e².

We have studied the S-I transition driven by disorder and field in thin (2D) indium films based on simultaneous measurements of the Hall R_xy and longitudinal R_xxC resistances at low temperatures [2]. By increasing field B at fixed disorder, we have found, in addition to a usual critical field B_xxC where R_xx(T→0)→∞, another critical field B_xyC (>B_xxC) where R_xy(T→0) diverges. This unusual insulating region B_xxC<B<B_xyC is similar to that which has been reported by Paalanen, Hebard and Ruel [1]. We have found that this region tends to increase with increasing disorder and/or decreasing film thickness [3]. From these results, we propose the possibility that the insulating region corresponds to the Bose-glass insulator where quantum fluctuations of the phase enhanced in 2D play an essential role.

Recently, we have made systematic studies for both the zero-field and field-driven S-I transitions in a series of 4 nm-thick films [4] of amorphous Mo_xSi_1-x at even lower temperatures T down to〜0.05 K and higher fields B up to 15 T. For superconducting films, we have observed an anomalous peak in the magnetoresistance R(B) and a subsequent decrease in R(B) with increasing B at low temperatures in fields higher than the critical field B_xxC. In contrast, the magnetoresistance for insulating films is always monotonic and positive irrespective of the temperature, consistent with the 2D weak-localization theory for fermions in the presence of strong spin-orbit interaction. From these results, we suggest the possibility that the localized Cooper pairs may exist even on the insulating side of the field-driven S-I transition (B > B_xxC) in the limit of T→0 [5]. On the basis of the data, including R(B) for thick films and that in parallel fields, we have constructed the T=0 vortex phase diagram for the field and disorder-driven S-I transitions [6,7].

For detail, please see:

1. M. A. Paalanen, A. F. Hebard, and R. R. Ruel, Phys. Rev.Lett. 69, 1604 (1992).
2. S. Okuma and N. Kokubo, Phys. Rev. B 51, 15415 (1995).
3. S. Okuma and N. Kokubo, Phys. Rev. B 56, 410 (1997).
4. S. Okuma, T. Terashima, and N. Kokubo, Solid State Commun. 106, 529 (1998).
5. S. Okuma, T. Terashima, and N. Kokubo, Phys. Rev. B 58 ,2816 (1998).
6. S. Okuma, S. Shinozali, and M. Morita, Phys. Rev. B 63, 54523 (2001).
7. S. Okuma, M. Morita, and Y. Imamoto, Phys. Rev. B 66 (2002) 104506