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Giant paramagnetic Meissner effect in multiband superconductors.

da Silva RM, Milošević MV, Shanenko AA, Peeters FM, Aguiar JA - Sci Rep (2015)

Bottom Line: Superconductors, ideally diamagnetic when in the Meissner state, can also exhibit paramagnetic behavior due to trapped magnetic flux.Here we show that in multiband superconductors paramagnetic response can be observed even in slab geometries, and can be far larger than any previous estimate - even multiply larger than the diamagnetic Meissner response for the same applied magnetic field.We link the appearance of this giant paramagnetic response to the broad crossover between conventional Type-I and Type-II superconductors, where Abrikosov vortices interact non-monotonically and multibody effects become important, causing unique flux configurations and their locking in the presence of surfaces.

View Article: PubMed Central - PubMed

Affiliation: Programa de Pós-Graduação em Ciência dos Materiais, Universidade Federal de Pernambuco, Av. Jorn. Aníbal Fernandes, s/n, 50670-901 Recife-PE, Brazil.

ABSTRACT
Superconductors, ideally diamagnetic when in the Meissner state, can also exhibit paramagnetic behavior due to trapped magnetic flux. In the absence of pinning such paramagnetic response is weak, and ceases with increasing sample thickness. Here we show that in multiband superconductors paramagnetic response can be observed even in slab geometries, and can be far larger than any previous estimate - even multiply larger than the diamagnetic Meissner response for the same applied magnetic field. We link the appearance of this giant paramagnetic response to the broad crossover between conventional Type-I and Type-II superconductors, where Abrikosov vortices interact non-monotonically and multibody effects become important, causing unique flux configurations and their locking in the presence of surfaces.

No MeSH data available.


Related in: MedlinePlus

The number of vortices Nv in the sample in decreasing magnetic field (below H = Hd) at T = 0.94Tc(a), and the average distance between vortices (dv), for two values of v1/v2 ratio that provide different sign of the superconducting-normal state interface energy (σSN). Insets show cumulative Cooper-pair density plots  of vortex states obtained in two considered cases for the same magnetic field H = 0.563Hc.
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f5: The number of vortices Nv in the sample in decreasing magnetic field (below H = Hd) at T = 0.94Tc(a), and the average distance between vortices (dv), for two values of v1/v2 ratio that provide different sign of the superconducting-normal state interface energy (σSN). Insets show cumulative Cooper-pair density plots of vortex states obtained in two considered cases for the same magnetic field H = 0.563Hc.

Mentions: What is the underlying mechanism for the giant paramagnetic response? In simple terms, it is the facilitated trapping of magnetic flux in the crossover domain between Type-I and Type-II superconductivity, since vortices attract in the entire range of parameters where GPR is observed. However, GPR is found to be particularly large for σSN > 0, where vortex-vortex interaction is purely attractive and vortices should coalesce into larger normal domains. On the contrary, we observe that in decreasing field separate vortex cores are still visible, though strongly overlapping (see inset in Fig. 5). To clarify the dense vortex packing observed in Fig. 5, we calculate the multibody vortex-vortex interaction shown for several vortex clusters in Fig. 6. As a major surprise, we found that in this regime multibody vortex interactions become short-range repulsive and cause the formation of a vortex lattice. This is illustrated in Fig. 6(a) (for v1/v2 = 0.47 and T = 0.94Tc, i.e. σSN > 0), where we show the calculated vortex-vortex interaction as a function of the distance between vortices (labelled d), for a vortex pair, a vortex trimer, a vortex diamond-like cluster and a hexagonal vortex cluster. The pairwise vortex interaction is purely attractive, as expected, but in the other cases the short-range repulsion arises so that energetically favorable vortex-vortex distance arises in mid-range (note that this favorable distance closely corresponds to the average vortex distance observed in Fig. 5(b)). An insight into the physics of this short-range repulsive interaction can be achieved by analysing the superconducting state inside, for example, the hexagonal vortex cluster shown in Fig. 6. With this aim, we computed the maximum of the Cooper-pair density, nmax, inside that cluster for each band-condensate separately, shown as a function of vortex distance d in Fig. 6(b). We reveal that the Cooper-pair density in the second condensate vanishes inside the vortex cluster at the vortex distance where short-range repulsion arises. Hence we can conclude that inside the vortex cluster the physics is driven by the other condensate, which has Type-II character, hence the repulsive interaction of vortices prevails at short distances. It is known that multibody vortex interactions are more complex than a simple superposition of pairwise interactions (see Refs. [50, 51, 52, 53]), but it has never been found before that multibody interactions can change the polarity of the vortex-vortex interaction. This is a key feature of the found mixed state for parameters of the system between σSN = 0 and Hc(T) = Hc2(T) lines in Fig. 4. In addition, we have plotted in Fig. 5(a) the number of vortices in the sample Nv as a function of H in the downward branch of M(H) in Fig. 2 for v1/v2 = 0.65 (in the Type-II limit) and v1/v2 = 0.47 (inside the crossover region). The high retention of flux is clearly seen as a nonlinear behavior for v1/v2 = 0.47 which contrasts the Type-II case in which Nv is linearly decreasing towards the origin. We find that although the number of vortices in the states between σSN = 0 and Hc(T) = Hc2(T) lines slowly decreases with decreasing magnetic field, their favorable distance is approximately independent of field [see Fig. 5(b)]. This unconventional vortex state allows the penetration of the magnetic field in larger portions of the sample (inhomogeneous penetration, within but also between vortices), and clearly traps more flux than an ordinary vortex lattice, down to very low field - resulting in a more pronounced GPR. Due to the interlocking of vortices in this regime, the barrier for the expulsion of the entire vortex cluster in decreasing field corresponds to the Bean-Livingston barrier for a single vortex, which we confirmed by an independent calculation. Notice that as soon as the S-N surface energy changes sign, the barrier for single-vortex expulsion becomes nonzero at all fields. However, we have the simultaneous appearance of short-range vortex repulsion, which in effect diminishes the Bean-Livingston barrier and vortices are gradually expelled from the sample depending on their density and applied magnetic field. This manifests in the magnetization curves as a gradual decrease of the paramagnetic effect in decreasing field, down to zero for zero field. As the v1/v2 ratio or temperature are further increased, vortices become increasingly repulsive and the paramagnetic response decreases to its conventional behavior for Type-II superconductors.


Giant paramagnetic Meissner effect in multiband superconductors.

da Silva RM, Milošević MV, Shanenko AA, Peeters FM, Aguiar JA - Sci Rep (2015)

The number of vortices Nv in the sample in decreasing magnetic field (below H = Hd) at T = 0.94Tc(a), and the average distance between vortices (dv), for two values of v1/v2 ratio that provide different sign of the superconducting-normal state interface energy (σSN). Insets show cumulative Cooper-pair density plots  of vortex states obtained in two considered cases for the same magnetic field H = 0.563Hc.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4525483&req=5

f5: The number of vortices Nv in the sample in decreasing magnetic field (below H = Hd) at T = 0.94Tc(a), and the average distance between vortices (dv), for two values of v1/v2 ratio that provide different sign of the superconducting-normal state interface energy (σSN). Insets show cumulative Cooper-pair density plots of vortex states obtained in two considered cases for the same magnetic field H = 0.563Hc.
Mentions: What is the underlying mechanism for the giant paramagnetic response? In simple terms, it is the facilitated trapping of magnetic flux in the crossover domain between Type-I and Type-II superconductivity, since vortices attract in the entire range of parameters where GPR is observed. However, GPR is found to be particularly large for σSN > 0, where vortex-vortex interaction is purely attractive and vortices should coalesce into larger normal domains. On the contrary, we observe that in decreasing field separate vortex cores are still visible, though strongly overlapping (see inset in Fig. 5). To clarify the dense vortex packing observed in Fig. 5, we calculate the multibody vortex-vortex interaction shown for several vortex clusters in Fig. 6. As a major surprise, we found that in this regime multibody vortex interactions become short-range repulsive and cause the formation of a vortex lattice. This is illustrated in Fig. 6(a) (for v1/v2 = 0.47 and T = 0.94Tc, i.e. σSN > 0), where we show the calculated vortex-vortex interaction as a function of the distance between vortices (labelled d), for a vortex pair, a vortex trimer, a vortex diamond-like cluster and a hexagonal vortex cluster. The pairwise vortex interaction is purely attractive, as expected, but in the other cases the short-range repulsion arises so that energetically favorable vortex-vortex distance arises in mid-range (note that this favorable distance closely corresponds to the average vortex distance observed in Fig. 5(b)). An insight into the physics of this short-range repulsive interaction can be achieved by analysing the superconducting state inside, for example, the hexagonal vortex cluster shown in Fig. 6. With this aim, we computed the maximum of the Cooper-pair density, nmax, inside that cluster for each band-condensate separately, shown as a function of vortex distance d in Fig. 6(b). We reveal that the Cooper-pair density in the second condensate vanishes inside the vortex cluster at the vortex distance where short-range repulsion arises. Hence we can conclude that inside the vortex cluster the physics is driven by the other condensate, which has Type-II character, hence the repulsive interaction of vortices prevails at short distances. It is known that multibody vortex interactions are more complex than a simple superposition of pairwise interactions (see Refs. [50, 51, 52, 53]), but it has never been found before that multibody interactions can change the polarity of the vortex-vortex interaction. This is a key feature of the found mixed state for parameters of the system between σSN = 0 and Hc(T) = Hc2(T) lines in Fig. 4. In addition, we have plotted in Fig. 5(a) the number of vortices in the sample Nv as a function of H in the downward branch of M(H) in Fig. 2 for v1/v2 = 0.65 (in the Type-II limit) and v1/v2 = 0.47 (inside the crossover region). The high retention of flux is clearly seen as a nonlinear behavior for v1/v2 = 0.47 which contrasts the Type-II case in which Nv is linearly decreasing towards the origin. We find that although the number of vortices in the states between σSN = 0 and Hc(T) = Hc2(T) lines slowly decreases with decreasing magnetic field, their favorable distance is approximately independent of field [see Fig. 5(b)]. This unconventional vortex state allows the penetration of the magnetic field in larger portions of the sample (inhomogeneous penetration, within but also between vortices), and clearly traps more flux than an ordinary vortex lattice, down to very low field - resulting in a more pronounced GPR. Due to the interlocking of vortices in this regime, the barrier for the expulsion of the entire vortex cluster in decreasing field corresponds to the Bean-Livingston barrier for a single vortex, which we confirmed by an independent calculation. Notice that as soon as the S-N surface energy changes sign, the barrier for single-vortex expulsion becomes nonzero at all fields. However, we have the simultaneous appearance of short-range vortex repulsion, which in effect diminishes the Bean-Livingston barrier and vortices are gradually expelled from the sample depending on their density and applied magnetic field. This manifests in the magnetization curves as a gradual decrease of the paramagnetic effect in decreasing field, down to zero for zero field. As the v1/v2 ratio or temperature are further increased, vortices become increasingly repulsive and the paramagnetic response decreases to its conventional behavior for Type-II superconductors.

Bottom Line: Superconductors, ideally diamagnetic when in the Meissner state, can also exhibit paramagnetic behavior due to trapped magnetic flux.Here we show that in multiband superconductors paramagnetic response can be observed even in slab geometries, and can be far larger than any previous estimate - even multiply larger than the diamagnetic Meissner response for the same applied magnetic field.We link the appearance of this giant paramagnetic response to the broad crossover between conventional Type-I and Type-II superconductors, where Abrikosov vortices interact non-monotonically and multibody effects become important, causing unique flux configurations and their locking in the presence of surfaces.

View Article: PubMed Central - PubMed

Affiliation: Programa de Pós-Graduação em Ciência dos Materiais, Universidade Federal de Pernambuco, Av. Jorn. Aníbal Fernandes, s/n, 50670-901 Recife-PE, Brazil.

ABSTRACT
Superconductors, ideally diamagnetic when in the Meissner state, can also exhibit paramagnetic behavior due to trapped magnetic flux. In the absence of pinning such paramagnetic response is weak, and ceases with increasing sample thickness. Here we show that in multiband superconductors paramagnetic response can be observed even in slab geometries, and can be far larger than any previous estimate - even multiply larger than the diamagnetic Meissner response for the same applied magnetic field. We link the appearance of this giant paramagnetic response to the broad crossover between conventional Type-I and Type-II superconductors, where Abrikosov vortices interact non-monotonically and multibody effects become important, causing unique flux configurations and their locking in the presence of surfaces.

No MeSH data available.


Related in: MedlinePlus