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arxiv: 2605.23567 · v1 · pith:O4UMCZMRnew · submitted 2026-05-22 · ❄️ cond-mat.supr-con · cond-mat.stat-mech

Phase diagram of the vortex state in an amorphous Re6Zr thin film exhibiting inverse melting

Pritam Das , Subhamita Sengupta , Anjan Jana , Rishabh Duhan , Sulagna Dutta , Arghya Dutta , John Jesudasan , Vivas Bagwe
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Pratap Raychaudhuri
This is my paper

Pith reviewed 2026-05-25 02:53 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con cond-mat.stat-mech
keywords inverse meltingvortex latticephase diagramthin filmsRe6Zrsuperconductivitytransport measurementsmagnetic screening
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The pith

Inverse melting of the vortex lattice in amorphous Re6Zr films is thickness-dependent.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper maps the vortex state phase diagram in magnetic field-temperature space for amorphous Re6Zr thin films by combining d.c. transport measurements, low-frequency magnetic screening, and prior scanning tunneling spectroscopy imaging. It identifies clear signatures of the inverse melting transition, in which the vortex lattice changes from a liquid at low temperature to a crystalline solid upon heating. The central finding is that this behavior changes with film thickness: 5 nm films remain in an inhomogeneous liquid state while 50 nm films stay crystalline except near the upper critical field.

Core claim

In Type II superconductors the vortex lattice can undergo inverse melting, passing from liquid to crystalline solid with increasing temperature. Using d.c. transport and low-frequency magnetic screening responses together with scanning tunneling spectroscopy, the authors construct the vortex-state phase diagram for amorphous Re6Zr thin films and show that inverse melting is thickness-dependent: a 5 nm film retains an inhomogeneous liquid state while a 50 nm film maintains a crystalline solid structure except near the upper critical field.

What carries the argument

The vortex-state phase diagram in the magnetic field-temperature plane, built from distinct signatures in d.c. transport and low-frequency magnetic screening that are cross-checked against scanning tunneling spectroscopy imaging.

If this is right

  • Transport and screening measurements can locate the inverse melting line without direct imaging.
  • Film thickness provides a practical control knob for the stability of the vortex solid versus liquid phases.
  • The 50 nm film remains solid over most of the phase diagram except close to the upper critical field.
  • The 5 nm film shows no recrystallization into a solid at any measured temperature or field.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Thickness tuning could be used to stabilize or suppress particular vortex phases in device geometries.
  • Similar thickness dependence may appear in other amorphous thin-film superconductors where inverse melting has been reported.
  • The phase boundaries identified here supply concrete targets for microscopic models of vortex pinning and dynamics.

Load-bearing premise

The signatures seen in transport and screening mark the same vortex-lattice transitions previously identified by scanning tunneling microscopy.

What would settle it

Absence of any corresponding feature in d.c. resistivity or screening response at the field and temperature values where scanning tunneling microscopy images show the liquid-to-solid transition.

Figures

Figures reproduced from arXiv: 2605.23567 by Anjan Jana, Arghya Dutta, John Jesudasan, Pratap Raychaudhuri, Pritam Das, Rishabh Duhan, Subhamita Sengupta, Sulagna Dutta, Vivas Bagwe.

Figure 1
Figure 1. Figure 1: Real-space STS conductance maps of vortex configurations (upper panels) and the corresponding two-dimensional Fourier transforms (2D-FFT) (lower panels) measured at 450 mK for 50 nm, 20 nm, and 5 nm amorphous Re6Zr films under different magnetic fields. Real space images are filtered as described in ref. 17 to reduce noise. The 2D-FFT in the 50 nm film exhibits well-defined sixfold Bragg spots over the ent… view at source ↗
Figure 2
Figure 2. Figure 2: Temperature evolution of vortex configurations (upper panels) and corresponding two￾dimensional Fourier transforms (2D-FFT) (lower panels) for the 50 nm and 20 nm amorphous Re6Zr films at representative magnetic fields obtained from STS conductance maps. Real space images are filtered as described in ref. 17 to reduce noise. The 50 nm film retains sharp sixfold Bragg spots and melts abruptly above a charac… view at source ↗
Figure 3
Figure 3. Figure 3: Magnetic-field evolution of the summed vortex images and corresponding two-dimensional Fourier transforms (2D-FFT) for the 20 nm amorphous Re₆Zr film measured at 460 mK. The system evolves from an inhomogeneous vortex liquid at low fields to an ordered hexagonal vortex lattice at intermediate fields, followed by an inhomogeneous vortex liquid at high magnetic fields. The image size scale bars and reciproca… view at source ↗
Figure 4
Figure 4. Figure 4: Temperature evolution of the summed STM vortex maps and corresponding two-dimensional Fourier transforms for the 20 nm amorphous Re₆Zr film at 3 kOe and 20 kOe. At 3 kOe, the vortex configuration evolves from a disordered state at low temperature to a more ordered hexagonal arrangement at intermediate temperatures before disordering again at higher temperatures, indicating inverse melting behaviour. In con… view at source ↗
Figure 5
Figure 5. Figure 5: Magneto-transport response of amorphous Re₆Zr films measured at 300 mK. (a) Representative current voltage ('– characteristics of the 20 nm film at different magnetic fields. The critical current, '( , is determined by extrapolating the linear flux-flow regime to the current axis, as illustrated by the black dashed line for 20 kOe. (b) Magnetic-field dependence of )( for the 5 nm film together with a fit … view at source ↗
Figure 6
Figure 6. Figure 6: Temperature-dependence of magneto-transport measurements in amorphous Re₆Zr films. (a) ^- Y curves for the 20 nm film measured at different magnetic fields with a low probing current (' = 500 nA ≪ '( ); +(6Yis determined from the points where the resistance is 90% of normal state resistance ^). (b) ^-Y curves for the 20 nm film at 20 kOe measured with different probing currents close to '( , showing the … view at source ↗
Figure 7
Figure 7. Figure 7: The AC magnetic screening response of the 20 nm amorphous Re₆Zr film. (a) Schematic of the two-coil mutual inductance measurement. Temperature dependence of the (b) real   and (c) imaginary − components of the mutual inductance measured at different magnetic fields. While  shows diamagnetic response below Y(+, the dissipative response − exhibits additional anomalies for + ≤ 25 kOe. (d) Expande… view at source ↗
Figure 8
Figure 8. Figure 8: Magnetic field–temperature (+–Y) vortex phase diagrams for a-ReZr films of different thicknesses: (a) 20 nm, (b) 5 nm, and (c) 50 nm. The orange squares show the upper critical field, Hc2, obtained from fields where the resistance is 90 % of the normal state value; the solid black lines are WHH fits to the data. The red squares show the melting line obtained from the loci of the peak effect in transport me… view at source ↗
Figure 9
Figure 9. Figure 9: Temperature dependence of resistance ^Y for the 5 nm, 20 nm, and 50 nm Re6Zr Hall bar samples with a channel width of 10 µm. All samples exhibit sharp superconducting transitions with critical temperatures Y( = 4.7 K, 5.8 K, and 6.5 K for the 5 nm, 20 nm, and 50 nm films, respectively. The inset shows the normal state resistivity as a function of film thickness [PITH_FULL_IMAGE:figures/full_fig_p027_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Representative summed raw real-space STS conductance maps of vortex configurations (top panels) and their corresponding FFTs (bottom panels) for the 5 nm a-ReZr film measured in magnetic fields of 10 kOe, 20 kOe, 30 kOe and 40 kOe and temperatures of 0.45 K, 1.2 K, and 2.5 K. For each field and temperature, 10 consecutive STM images were summed and the 2DFT was calculated from the summed image. The image … view at source ↗
Figure 11
Figure 11. Figure 11: (a) and (c) Current–voltage (I–V) characteristics measured at 300 mK for the 50 nm and 5 nm a-ReZr samples, respectively, at different applied magnetic fields. (b) and (d) Representative I–V curve (blue line) for the 50 nm and 5 nm sample at 300 mK and 30 kOe. The dashed red line represents a tangent drawn to the region where the slope corresponds to the Bardeen–Stephen flux-flow resistance Rff. The criti… view at source ↗
Figure 12
Figure 12. Figure 12: (a) Temperature dependence of the elementary pinning contribution F MNX ∝ 1 − X6  6 (black), ZX = 1 − iexp [−X − X5 6/2p6 ] (blue), where A = 0.3, t0 = 0.5 and p = 0.2, and FX = F MNXZX (red); here t = T/Yá . Calculated values of (b)  ∝ 1/F and (c) − ∝ B/F6 , with and without collective pinning correction; B ∝ 1 − X6 /1 + X6  is the viscous drag coefficient. While inverse melting produces on… view at source ↗
read the original abstract

In Type II superconductors, the vortex lattice can exhibit "inverse melting," transitioning from a liquid to a crystalline solid as temperature increases. While recently observed via scanning tunneling microscopy in a 20 nm thick amorphous Re6Zr thin film, this work investigates the corresponding d.c. transport and low-frequency magnetic screening responses. By identifying distinct signatures of these transitions and integrating scanning tunneling spectroscopy imaging, we construct a comprehensive vortex-state phase diagram in the magnetic field-temperature parameter space. Furthermore, we demonstrate that inverse melting is thickness-dependent: a 5 nm film retains an inhomogeneous liquid state, while a 50 nm film maintains a crystalline solid structure except near the upper critical field.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports d.c. transport and low-frequency AC magnetic screening measurements on amorphous Re6Zr thin films of 5 nm, 20 nm, and 50 nm thicknesses. Building on prior STM work, it identifies signatures of inverse melting (liquid-to-solid transition with increasing temperature) and constructs a vortex-state phase diagram in the H-T plane. The central claim is that inverse melting is thickness-dependent: the 5 nm film remains in an inhomogeneous liquid state while the 50 nm film maintains a crystalline solid structure except near the upper critical field.

Significance. If the transport signatures reliably track the same inverse-melting line across thicknesses, the work would provide a practical method to map vortex phases without STM and demonstrate that film thickness can be used to tune the vortex solid-liquid boundary, which is relevant for understanding dimensionality effects in vortex matter.

major comments (2)
  1. [Results (phase diagram construction) and Discussion] The phase assignments for the 5 nm and 50 nm films rest on the untested assumption that the same d.c. resistivity drops and AC screening features mark the liquid-solid inverse melting transition calibrated only against 20 nm STM data (prior work). No independent structural probe (STM or neutron scattering) is reported on the 5 nm or 50 nm samples to confirm that thickness-induced changes in pinning or inhomogeneity do not alter or mask the signatures. This directly undermines the thickness-dependence claim.
  2. [Methods and Figure captions] No explicit criteria, thresholds, or error bars are provided for identifying the phase boundaries from transport and screening data, nor are raw data or fitting procedures shown for the claimed transitions. This makes it impossible to judge whether the observed features support the stated liquid-to-solid assignments.
minor comments (2)
  1. [Abstract] The abstract states that STS imaging is integrated, but it is unclear whether new STS data were acquired on the 5 nm and 50 nm films or whether only the prior 20 nm data are used.
  2. [Experimental methods] Notation for the AC screening response (e.g., real/imaginary parts of susceptibility) should be defined consistently with standard conventions in the vortex literature.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments. We address each of the major comments below.

read point-by-point responses

  1. Referee: The phase assignments for the 5 nm and 50 nm films rest on the untested assumption that the same d.c. resistivity drops and AC screening features mark the liquid-solid inverse melting transition calibrated only against 20 nm STM data (prior work). No independent structural probe (STM or neutron scattering) is reported on the 5 nm or 50 nm samples to confirm that thickness-induced changes in pinning or inhomogeneity do not alter or mask the signatures. This directly undermines the thickness-dependence claim.

    Authors: We agree that the phase assignments for the 5 nm and 50 nm films are extrapolated from the transport signatures calibrated on the 20 nm film with STM data. While this is an assumption, the d.c. resistivity and AC screening features are standard indicators used in vortex matter studies, and their consistency across thicknesses supports our interpretation of thickness-dependent behavior. However, to address the concern, we will revise the discussion section to explicitly note this assumption and discuss potential influences of thickness on the signatures. We do not have additional structural data on these samples. revision: partial

  2. Referee: No explicit criteria, thresholds, or error bars are provided for identifying the phase boundaries from transport and screening data, nor are raw data or fitting procedures shown for the claimed transitions. This makes it impossible to judge whether the observed features support the stated liquid-to-solid assignments.

    Authors: We will include explicit criteria and thresholds for the phase boundaries in the revised manuscript, along with error bars where applicable. Raw data and details of the analysis procedures will be provided in the supplementary material to allow for independent assessment of the transitions. revision: yes

standing simulated objections not resolved
  • Lack of independent structural probes on the 5 nm and 50 nm films to directly confirm the phase assignments.

Circularity Check

0 steps flagged

No circularity: purely experimental phase diagram from transport, screening, and STM data

full rationale

The manuscript is an experimental study that identifies d.c. transport and AC screening signatures of vortex transitions, integrates them with scanning tunneling spectroscopy imaging, and maps a thickness-dependent phase diagram. No derivations, equations, fitted parameters renamed as predictions, or self-referential constructions appear. Prior STM observation on the 20 nm film is cited as calibration for signature identification; this is external experimental input rather than a self-citation chain that forces the result. The thickness dependence for 5 nm and 50 nm films rests on the assumption that the same signatures apply, but this is an empirical extrapolation, not a definitional or fitted reduction. The paper is self-contained against its own data sets and external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Experimental observation paper; relies on standard superconductivity phenomenology but introduces no new free parameters, axioms, or invented entities.

pith-pipeline@v0.9.0 · 5681 in / 1001 out tokens · 30855 ms · 2026-05-25T02:53:19.361392+00:00 · methodology

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Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

  1. [1]

    PD performed the transport measurements and analyze d the data

    Acknowledgements: This work was supported by the Department of Atomic Energy, Government of India. PD performed the transport measurements and analyze d the data. PD, SS and SD performed the two-coil mutual inductance measurement and analyzed the data . RD, AJ, SD and PD performed the STS measurements and PD and RD analyzed the data. AD, JJ and VB provide...

    work page 1957

  2. [2]

    Phys. Rev. B 62 , 11838 (2000). 15 7 J. Aragón Sánchez, R. Cortés Maldonado, N. R. Cejas Bolecek et al. Unveiling the vortex glass phase in the surface and volume of a type-II superconductor. Commun Phys 2, 143 (2019) 8 A. Yazdani, W. R. White, M. R. Hahn, M. Gabay, M. R. Beasley, and A. Kapitulnik, Observation of Kosterlitz- Thouless-type melting of the ...

    work page 2000