Nearly Isotropic Vortex Solid in (La,Pr)₃Ni₂O₇ Thin Films

Summary

By simultaneously measuring the resistance and diamagnetism of (La,Pr)₃Ni₂O₇ thin films and mapping the vortex-melting phase diagram under in-plane and out-of-plane magnetic fields, we investigated the anisotropy of superconductivity in bilayer nickelates. For H ∥ c, geometric confinement in ultrathin films leads to pancake vortices; the vortex-melting-field anisotropy parameter γ_Hm = H_m^ab/H_m^c decreases monotonically with decreasing temperature and approaches 1 at low temperatures, indicating the formation of a nearly isotropic vortex solid. Within anisotropic Ginzburg-Landau scaling, this ratio reflects the anisotropy of the superfluid density, and the results therefore point to a nearly isotropic superfluid response; this is incompatible with a contribution solely from the strictly two-dimensional Ni 3d_x²-y² band, but is naturally explained by a significant interlayer superfluid weight provided by the Ni 3d_z²-derived γ band. This work provides thermodynamic evidence that superconductivity in bilayer nickelate thin films includes a substantial contribution from the γ band.

Materials

• (La,Pr)₃Ni₂O₇

Methods

• simultaneous resistance and diamagnetism measurements
• tunnel diode oscillator (TDO) setup
• ac lock-in transport measurements
• high magnetic field measurements up to 34 T using a resistive water-cooled magnet
• HAADF imaging
• anisotropic Ginzburg-Landau scaling
• 2D Tinkham model analysis
• 2D-GL model fitting
• vortex melting phase diagram mapping
• ARPES

Keywords

• vortex solid
• vortex melting phase diagram
• pancake vortices
• josephson vortices
• anisotropy parameter of vortex melting field
• nearly isotropic superfluid density
• interlayer superfluid contribution
• ni 3d_z2 derived gamma band
• ni 3d_x2 y2 derived bands
• multiorbital superconductivity
• geometric confinement
• quasi 2d superconductivity
• thermal fluctuations
• pauli paramagnetic effect
• orbital depairing
• superfluid density anisotropy

Highlights

• The Meissner transition temperature T_m of the sample is significantly higher than in previous studies and nearly coincides with the zero-resistance temperature, demonstrating high quality and good superconducting homogeneity.
• The angular dependence of the superconducting transition temperature near T_c displays a sharp cusp-like feature that conforms to the two-dimensional Tinkham model, establishing the quasi-2D nature of the superconductivity.
• The vortex melting exponent for H parallel to c falls in the characteristic range of 1.5-2.0 for pancake vortices in cuprates.
• The same near-isotropic behavior at low temperatures is also observed in samples with broader vortex liquid regions, confirming that this isotropy is a generic feature of the bilayer nickelate system.
• The data establish the Ni 3d_z2-derived gamma band as a non-negligible component of the superconducting state and provide essential constraints for theoretical models.
• Disorder suppresses the vortex solid phase and broadens the vortex liquid regime.
• Zero-temperature critical fields are estimated as 90.0 T for in-plane and 50.5 T for out-of-plane, and the effective superconducting thickness is close to the film thickness, confirming the intrinsic bulk nature of superconductivity in the film.

Conclusions

• For H applied along c, geometric confinement of the ultrathin film gives rise to pancake vortex behavior in the vortex melting response.
• The anisotropy parameter of the vortex melting field, gamma_Hm = H_m^ab/H_m^c, decreases monotonically with decreasing temperature and approaches unity at low temperatures, indicating a nearly isotropic vortex solid.
• Within anisotropic Ginzburg-Landau scaling, H_m^ab/H_m^c tracks the superfluid-density anisotropy, so the nearly isotropic vortex solid implies a nearly isotropic superfluid density.
• The nearly isotropic superfluid density is irreconcilable with the strictly two-dimensional 3d_x2-y2-derived bands, but naturally explained by a substantial interlayer superfluid contribution from the Ni 3d_z2-derived gamma band.
• The results provide thermodynamic evidence for a substantial contribution of the gamma band to superconductivity in bilayer nickelate thin films.
• The observed anisotropy near T_c is governed by competing depairing channels rather than intrinsic electronic structure.

Main claims

• The vortex melting field anisotropy gamma_Hm decreases monotonically with decreasing temperature and approaches unity at low temperatures, indicating a nearly isotropic vortex solid.
  • Evidence: simultaneous resistance and diamagnetism measurements on (La,Pr)₃Ni₂O₇ thin films,mapping of vortex melting phase diagram for H parallel c and H parallel ab,gamma_Hm = H_m^ab/H_m^c decreases monotonically and extrapolates to 1 at zero temperature
• Within anisotropic Ginzburg-Landau scaling, the observed melting-field ratio tracks superfluid-density anisotropy, so the nearly isotropic vortex solid implies a nearly isotropic superfluid density.
  • Evidence: H_m^ab/H_m^c = sqrt(rho_s^ab/rho_s^c),Lindemann criterion and anisotropic Ginzburg-Landau theory relate melting-field anisotropy to superfluid density
• The nearly isotropic superfluid density is incompatible with a contribution solely from strictly two-dimensional Ni 3d_x2-y2-derived bands.
  • Evidence: 3d_x2-y2 bands confined to NiO₂ planes predict predominantly in-plane superfluid contribution,nearly isotropic vortex solid observed at low temperatures
• A substantial interlayer superfluid contribution from the Ni 3d_z2-derived gamma band naturally explains the nearly isotropic superfluid density.
  • Evidence: gamma band provides interlayer coupling via apical oxygen atoms,ARPES measurements on the same films resolve a superconducting gap on the gamma band,thermodynamic vortex melting evidence for nearly isotropic superfluid response
• Superconductivity in ultrathin (La,Pr)₃Ni₂O₇ films is quasi-2D near T_c and shows pancake vortex behavior for H parallel c.
  • Evidence: angular dependence of superconducting transition temperature conforms to the 2D Tinkham model and deviates from 3D Ginzburg-Landau description,2D Ginzburg-Landau fits give in-plane critical field 90.0 T and out-of-plane critical field 50.5 T,coherence lengths and effective superconducting thickness confirm a geometrically confined 2D regime

Workflow

• sample_growth — The studied (La,Pr)₃Ni₂O₇ films were high-quality, phase-pure, compressively strained thin films.
  • Materials: (La,Pr)₃Ni₂O₇ thin films; (001)-oriented SrLaAlO₄ substrates
  • Methods: gigantic-oxidative atomic layer-by-layer epitaxy
  • Observations: films are phase pure with uniform, well-defined interfaces over extended regions; no observable intergrowths of adjacent Ruddlesden-Popper phases
• sample_characterization — The films show high superconducting homogeneity and a clear Meissner response.
  • Materials: 3UC(La,Pr)₃Ni₂O₇/SrLaAlO₄ thin film
  • Methods: HAADF imaging; zero-field resistance measurement; zero-field diamagnetism measurement
  • Observations: metallic normal state over a wide temperature range; superconducting resistance onset at 40.7 K and midpoint at 37.8 K; zero resistance at 29.5 K; Meissner effect observed and vortex melting temperature nearly coincides with zero-resistance temperature
• simultaneous_transport_and_diamagnetism_measurement — Simultaneous transport and diamagnetism allow mapping of the vortex melting field.
  • Materials: (La,Pr)₃Ni₂O₇ thin film; top-surface electrodes; home-made tunnel diode oscillator setup with a small disk-shaped coil attached to the bottom surface
  • Methods: ac lock-in resistance measurement; tunnel diode oscillator diamagnetism measurement
  • Observations: frequency shift as a function of magnetic field at selected temperatures; frequency shift increases with magnetic field and converges to the normal-state background; vortex melting field determined where frequency shift intersects the normal-state background
• vortex_phase_diagram_mapping — The out-of-plane vortex melting behavior is consistent with pancake vortices in a quasi-2D superconductor.
  • Materials: (La,Pr)₃Ni₂O₇ thin film
  • Methods: field-dependent resistance and diamagnetism; 2D Tinkham model; 2D Ginzburg-Landau model; empirical vortex melting formula
  • Observations: for H parallel c, geometric confinement gives pancake vortices; melting line exponent falls in the 1.5-2.0 range characteristic of pancake vortices; vortex liquid region shrinks with decreasing temperature; disorder broadens the vortex liquid region in another sample
• anisotropy_analysis — The vortex solid becomes nearly isotropic at low temperature, implying a nearly isotropic superfluid density.
  • Materials: vortex melting field data for H parallel c and H parallel ab
  • Methods: anisotropic Ginzburg-Landau scaling; Lindemann criterion; extract anisotropy parameter gamma_Hm = H_m^ab/H_m^c
  • Observations: gamma_Hm decreases monotonically with decreasing temperature; gamma_Hm extrapolates to unity at zero temperature; H_m^ab/H_m^c = sqrt(rho_s^ab/rho_s^c)
• interpretation — The nearly isotropic superfluid response points to a substantial interlayer superfluid contribution from the Ni 3d_z2-derived gamma band.
  • Materials: bilayer nickelate thin films; Ni 3d_x2-y2-derived bands; Ni 3d_z2-derived gamma band
  • Methods: comparison with anisotropic Ginzburg-Landau theory; comparison with ARPES results on same films; orbital-character reasoning
  • Observations: 3d_x2-y2 bands are confined to NiO₂ planes and expected to give mostly in-plane superfluid contribution; gamma band provides interlayer coupling via apical oxygen; ARPES resolves a superconducting gap on the gamma band