# The Impact of Short-Range (Gaussian) Disorder Correlations on Superconducting Characteristics

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## Abstract

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## 1. Introduction

## 2. Model

#### Disorder Model

## 3. Results

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Feigel’man, M.V.; Ioffe, L.B.; Kravtsov, V.E.; Yuzbashyan, E.A. Eigenfunction Fractality and Pseudogap State near the Superconductor-Insulator Transition. Phys. Rev. Lett.
**2007**, 98, 27001. [Google Scholar] [CrossRef] - Burmistrov, I.S.; Gornyi, I.V.; Mirlin, A.D. Enhancement of the Critical Temperature of Superconductors by Anderson Localization. Phys. Rev. Lett.
**2012**, 108, 17002. [Google Scholar] [CrossRef] [PubMed] - Stosiek, M.; Lang, B.; Evers, F. Self-consistent-field ensembles of disordered Hamiltonians: Efficient solver and application to superconducting films. Phys. Rev. B
**2020**, 101, 144503. [Google Scholar] [CrossRef] - Goldman, A.M.; Marković, N. Superconductor-Insulator Transitions in the Two-Dimensional Limit. Phys. Today
**1998**, 51, 39–44. [Google Scholar] [CrossRef] - Ma, M.; Lee, P.A. Localized superconductors. Phys. Rev. B
**1985**, 32, 5658–5667. [Google Scholar] [CrossRef] [PubMed] - Gantmakher, V.F.; Dolgopolov, V.T. Superconductor-insulator quantum phase transition. Uspekhi Fizicheskih Nauk
**2010**, 180, 3. [Google Scholar] [CrossRef] - Sadovskii, M.V. Superconductivity and localization. Phys. Rep.
**1997**, 282, 225–348. [Google Scholar] [CrossRef] - Trivedi, N.; Scalettar, R.T.; Randeria, M. Superconductor-insulator transition in a disordered electronic system. Phys. Rev. B
**1996**, 54, R3756–R3759. [Google Scholar] [CrossRef] - Trivedi, N.; Loh, Y.L.; Bouadim, K.; Randeria, M. Emergent granularity and pseudogap near the superconductor-insulator transition. J. Phys. Conf. Ser.
**2012**, 376, 12001. [Google Scholar] [CrossRef] - Gastiasoro, M.N.; Andersen, B.M. Enhancing superconductivity by disorder. Phys. Rev. B
**2018**, 98, 184510. [Google Scholar] [CrossRef] - Neverov, V.D.; Lukyanov, A.E.; Krasavin, A.V.; Vagov, A.; Croitoru, M.D. Correlated disorder as a way towards robust superconductivity. Commun. Phys.
**2022**, 5, 177. [Google Scholar] [CrossRef] - Sacépé, B.; Feigel’man, M.; Klapwijk, T.M. Quantum breakdown of superconductivity in low-dimensional materials. Nat. Phys.
**2020**, 16, 734–746. [Google Scholar] [CrossRef] - Croitoru, M.D.; Shanenko, A.A.; Peeters, F.M.; Axt, V.M. Parity-fluctuation induced enlargement of the ratio Δ
_{E}/k_{B}T_{c}in metallic grains. Phys. Rev. B**2011**, 84, 214518. [Google Scholar] [CrossRef] - Saini, N.L.; Rossetti, T.; Lanzara, A.; Missori, M.; Perali, A.; Oyanagi, H.; Bianconi, A. Tuning of the Fermi level at the second subband of a superlattice of quantum wires in the CuO2 plane: A possible mechanism to raise the critical temperature. J. Supercond.
**1996**, 9, 343–348. [Google Scholar] [CrossRef] - Castro, D.D.; Agrestini, S.; Campi, G.; Cassetta, A.; Colapietro, M.; Congeduti, A.; Continenza, A.; Negri, S.D.; Giovannini, M.; Massidda, S.; et al. European Physical Society Italian Physical Society EDP Sciences The Institute of Physics The amplification of the superconducting T
_{c}by combined effect of tuning of the Fermi level and the tensile micro-strain in Al_{1-x}Mg_{x}B_{2}. Europhys. Lett. (EPL)**2002**, 58, 278–284. [Google Scholar] [CrossRef] - Silveira, R.d.L.; Croitoru, M.D.; Pugach, N.G.; Romaguera, A.R.d.C.; Albino Aguiar, J. Engineering low-temperature proximity effect in clean metals by spectral singularities. New J. Phys.
**2023**, 25, 93009. [Google Scholar] [CrossRef] - Fang, L.; Jia, Y.; Mishra, V.; Chaparro, C.; Vlasko-Vlasov, V.K.; Koshelev, A.E.; Welp, U.; Crabtree, G.W.; Zhu, S.; Zhigadlo, N.D.; et al. Huge critical current density and tailored superconducting anisotropy in SmFeAsO
_{0.8}F_{0.15}by low-density columnar-defect incorporation. Nat. Commun.**2013**, 4, 3655. [Google Scholar] [CrossRef] - Ghigo, G.; Torsello, D.; Ummarino, G.; Gozzelino, L.; Tanatar, M.; Prozorov, R.; Canfield, P. Disorder-Driven Transition Superconducting Order Parameter in Proton Irradiated Single Crystals. Phys. Rev. Lett.
**2018**, 121, 107001. [Google Scholar] [CrossRef] - Zhao, K.; Lin, H.; Xiao, X.; Huang, W.; Yao, W.; Yan, M.; Xing, Y.; Zhang, Q.; Li, Z.X.; Hoshino, S.; et al. Disorder-induced multifractal superconductivity in monolayer niobium dichalcogenides. Nat. Phys.
**2019**, 15, 904–910. [Google Scholar] [CrossRef] - Tsai, W.F.; Yao, H.; Läuchli, A.; Kivelson, S.A. Optimal inhomogeneity for superconductivity: Finite-size studies. Phys. Rev. B
**2008**, 77, 214502. [Google Scholar] [CrossRef] - Ghosal, A.; Randeria, M.; Trivedi, N. Role of Spatial Amplitude Fluctuations in Highly Disordereds-Wave Superconductors. Phys. Rev. Lett.
**1998**, 81, 3940–3943. [Google Scholar] [CrossRef] - Ghosal, A.; Randeria, M.; Trivedi, N. Inhomogeneous pairing in highly disordereds-wave superconductors. Phys. Rev. B
**2001**, 65, 14501. [Google Scholar] [CrossRef] - Dubi, Y.; Meir, Y.; Avishai, Y. Nature of the superconductor–insulator transition in disordered superconductors. Nature
**2007**, 449, 876–880. [Google Scholar] [CrossRef] - Brun, C.; Cren, T.; Cherkez, V.; Debontridder, F.; Pons, S.; Fokin, D.; Tringides, M.C.; Bozhko, S.; Ioffe, L.B.; Altshuler, B.L.; et al. Remarkable effects of disorder on superconductivity of single atomic layers of lead on silicon. Nat. Phys.
**2014**, 10, 444–450. [Google Scholar] [CrossRef] - Lemarié, G.; Kamlapure, A.; Bucheli, D.; Benfatto, L.; Lorenzana, J.; Seibold, G.; Ganguli, S.C.; Raychaudhuri, P.; Castellani, C. Universal scaling of the order-parameter distribution in strongly disordered superconductors. Phys. Rev. B
**2013**, 87, 184509. [Google Scholar] [CrossRef] - Noat, Y.; Cherkez, V.; Brun, C.; Cren, T.; Carbillet, C.; Debontridder, F.; Ilin, K.; Siegel, M.; Semenov, A.; Hubers, H.W.; et al. Unconventional superconductivity in ultrathin superconducting NbN films studied by scanning tunneling spectroscopy. Phys. Rev. B
**2013**, 88, 14503. [Google Scholar] [CrossRef] - Mondal, M.; Kamlapure, A.; Chand, M.; Saraswat, G.; Kumar, S.; Jesudasan, J.; Benfatto, L.; Tripathi, V.; Raychaudhuri, P. Phase Fluctuations in a Strongly Disordereds-Wave NbN Superconductor Close to the Metal-Insulator Transition. Phys. Rev. Lett.
**2011**, 106, 47001. [Google Scholar] [CrossRef] - Mondal, M.; Kamlapure, A.; Ganguli, S.C.; Jesudasan, J.; Bagwe, V.; Benfatto, L.; Raychaudhuri, P. Enhancement of the finite-frequency superfluid response in the pseudogap regime of strongly disordered superconducting films. Sci. Rep.
**2013**, 3, 1357. [Google Scholar] [CrossRef] - Saito, Y.; Nojima, T.; Iwasa, Y. Highly crystalline 2D superconductors. Nat. Rev. Mater.
**2016**, 2, 16094. [Google Scholar] [CrossRef] - Petrović, A.P.; Ansermet, D.; Chernyshov, D.; Hoesch, M.; Salloum, D.; Gougeon, P.; Potel, M.; Boeri, L.; Panagopoulos, C. A disorder-enhanced quasi-one-dimensional superconductor. Nat. Commun.
**2016**, 7, 12262. [Google Scholar] [CrossRef] - Peng, J.; Yu, Z.; Wu, J.; Zhou, Y.; Guo, Y.; Li, Z.; Zhao, J.; Wu, C.; Xie, Y. Disorder Enhanced Superconductivity toward TaS
_{2}Monolayer. ACS Nano**2018**, 12, 9461–9466. [Google Scholar] [CrossRef] - Feigel’man, M.; Ioffe, L.; Kravtsov, V.; Cuevas, E. Fractal superconductivity near localization threshold. Ann. Phys.
**2010**, 325, 1390–1478. [Google Scholar] [CrossRef] - Weinrib, A.; Halperin, B.I. Critical phenomena in systems with long-range-correlated quenched disorder. Phys. Rev. B
**1983**, 27, 413–427. [Google Scholar] [CrossRef] - de Moura, F.A.B.F.; Lyra, M.L. Delocalization in the 1D Anderson Model with Long-Range Correlated Disorder. Phys. Rev. Lett.
**1998**, 81, 3735. [Google Scholar] [CrossRef] - Carpena, P.; Bernaola-Galván, P.; Ivanov, P.C.; Stanley, H.E. Metal–insulator transition in chains with correlated disorder. Nature
**2002**, 418, 955–959. [Google Scholar] [CrossRef] [PubMed] - Kawarabayashi, T.; Ono, Y.; Ohtsuki, T.; Kettemann, S.; Struck, A.; Kramer, B. Unconventional conductance plateau transitions in quantum Hall wires with spatially correlated disorder. Phys. Rev. B
**2007**, 75, 235317. [Google Scholar] [CrossRef] - Pilati, S.; Giorgini, S.; Prokof’ev, N. Superfluid Transition in a Bose Gas with Correlated Disorder. Phys. Rev. Lett.
**2009**, 102, 150402. [Google Scholar] [CrossRef] [PubMed] - Liew, S.F.; Cao, H. Optical properties of 1D photonic crystals with correlated and uncorrelated disorder. J. Opt.
**2010**, 12, 24011. [Google Scholar] [CrossRef] - Keen, D.A.; Goodwin, A.L. The crystallography of correlated disorder. Nature
**2015**, 521, 303–309. [Google Scholar] [CrossRef] - Simonov, A.; Goodwin, A.L. Designing disorder into crystalline materials. Nat. Rev. Chem.
**2020**, 4, 657–673. [Google Scholar] [CrossRef] - Damasceno, P.F.; Engel, M.; Glotzer, S.C. Predictive Self-Assembly of Polyhedra into Complex Structures. Science
**2012**, 337, 453–457. [Google Scholar] [CrossRef] [PubMed] - Dzero, M.; Huang, X. Correlated disorder in a Kondo lattice. J. Phys. Condens. Matter
**2012**, 24, 75603. [Google Scholar] [CrossRef] [PubMed] - Bonzom, V.; Gurau, R.; Smerlak, M. Universality in p-spin glasses with correlated disorder. J. Stat. Mech. Theory Exp.
**2013**, 2013, L02003. [Google Scholar] [CrossRef] - Girschik, A.; Libisch, F.; Rotter, S. Topological insulator in the presence of spatially correlated disorder. Phys. Rev. B
**2013**, 88, 14201. [Google Scholar] [CrossRef] - Alamir, A.; Capuzzi, P.; Kashanian, S.V.; Vignolo, P. Probing quantum transport by engineering correlations in a speckle potential. Phys. Rev. A
**2014**, 89, 23613. [Google Scholar] [CrossRef] - Pilati, S.; Fratini, E. Ferromagnetism in a repulsive atomic Fermi gas with correlated disorder. Phys. Rev. A
**2016**, 93, 51604. [Google Scholar] [CrossRef] - Zierenberg, J.; Fricke, N.; Marenz, M.; Spitzner, F.P.; Blavatska, V.; Janke, W. Percolation thresholds and fractal dimensions for square and cubic lattices with long-range correlated defects. Phys. Rev. E
**2017**, 96, 62125. [Google Scholar] [CrossRef] - Campi, G.; Gioacchino, M.D.; Poccia, N.; Ricci, A.; Burghammer, M.; Ciasca, G.; Bianconi, A. Nanoscale Correlated Disorder in Out-of-Equilibrium Myelin Ultrastructure. ACS Nano
**2017**, 12, 729–739. [Google Scholar] [CrossRef] [PubMed] - Dikopoltsev, A.; Herzig Sheinfux, H.; Segev, M. Localization by virtual transitions in correlated disorder. Phys. Rev. B
**2019**, 100, 140202. [Google Scholar] [CrossRef] - Mangelis, P.; Koch, R.J.; Lei, H.; Neder, R.B.; McDonnell, M.T.; Feygenson, M.; Petrovic, C.; Lappas, A.; Bozin, E.S. Correlated disorder-to-order crossover in the local structure of K
_{x}Fe_{2-y}Se_{2-z}S_{z}. Phys. Rev. B**2019**, 100, 94108. [Google Scholar] [CrossRef] - Derlet, P.M. Correlated disorder in a model binary glass through a local SU(2) bonding topology. Phys. Rev. Mater.
**2020**, 4, 125601. [Google Scholar] [CrossRef] - Gavrichkov, V.A.; Shan’ko, Y.; Zamkova, N.G.; Bianconi, A. Is There Any Hidden Symmetry in the Stripe Structure of Perovskite High-Temperature Superconductors? J. Phys. Chem. Lett.
**2019**, 10, 1840–1844. [Google Scholar] [CrossRef] - Fomin, I.A. Effect of correlated disorder on the temperature of unconventional cooper pairing: 3He in aerogel. JETP Lett.
**2008**, 88, 59–63. [Google Scholar] [CrossRef] - Fomin, I.A. Anomalous temperature dependence of the order parameter of a superconductor with weakly correlated impurities. JETP Lett.
**2011**, 93, 144–146. [Google Scholar] [CrossRef] - Shi, R.; Fang, W.H.; Vasenko, A.S.; Long, R.; Prezhdo, O.V. Efficient passivation of DY center in CH3NH3PbBr3 by chlorine: Quantum molecular dynamics. Nano Res.
**2021**, 15, 2112–2122. [Google Scholar] [CrossRef] - Zhao, X.; Vasenko, A.S.; Prezhdo, O.V.; Long, R. Anion Doping Delays Nonradiative Electron–Hole Recombination in Cs-Based All-Inorganic Perovskites: Time Domain ab Initio Analysis. J. Phys. Chem. Lett.
**2022**, 13, 11375–11382. [Google Scholar] [CrossRef] - Wu, Y.; Liu, D.; Chu, W.; Wang, B.; Vasenko, A.S.; Prezhdo, O.V. Fluctuations at Metal Halide Perovskite Grain Boundaries Create Transient Trap States: Machine Learning Assisted Ab Initio Analysis. ACS Appl. Mater. Interfaces
**2022**, 14, 55753–55761. [Google Scholar] [CrossRef] [PubMed] - Wu, Y.; Chu, W.; Vasenko, A.S.; Prezhdo, O.V. Common Defects Accelerate Charge Carrier Recombination in CsSnI3 without Creating Mid-Gap States. J. Phys. Chem. Lett.
**2021**, 12, 1948–7185. [Google Scholar] [CrossRef] - Liu, D.; Wu, Y.; Vasenko, A.S.; Prezhdo, O.V. Grain boundary sliding and distortion on a nanosecond timescale induce trap states in CsPbBr3: ab initio investigation with machine learning force field. Nanoscale
**2023**, 15, 285–293. [Google Scholar] [CrossRef] - Clément, D.; Varón, A.F.; Retter, J.A.; Sanchez-Palencia, L.; Aspect, A.; Bouyer, P. Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle. New J. Phys.
**2006**, 8, 165. [Google Scholar] [CrossRef] - Billy, J.; Josse, V.; Zuo, Z.; Bernard, A.; Hambrecht, B.; Lugan, P.; Clément, D.; Sanchez-Palencia, L.; Bouyer, P.; Aspect, A. Direct observation of Anderson localization of matter waves in a controlled disorder. Nature
**2008**, 453, 891–894. [Google Scholar] [CrossRef] [PubMed] - Aspect, A.; Inguscio, M. Anderson localization of ultracold atoms. Phys. Today
**2009**, 62, 30–35. [Google Scholar] [CrossRef] - Delande, D.; Orso, G. Mobility Edge for Cold Atoms in Laser Speckle Potentials. Phys. Rev. Lett.
**2014**, 113, 60601. [Google Scholar] [CrossRef] [PubMed] - Astrakharchik, G.E.; Krutitsky, K.V.; Navez, P. Phase diagram of quasi-two-dimensional bosons in a laser-speckle potential. Phys. Rev. A
**2013**, 87, 61601. [Google Scholar] [CrossRef] - Fratini, M.; Poccia, N.; Ricci, A.; Campi, G.; Burghammer, M.; Aeppli, G.; Bianconi, A. Scale-free structural organization of oxygen interstitials in La
_{2}CuO_{4+y}. Nature**2010**, 466, 841–844. [Google Scholar] [CrossRef] - Gurevich, E.; Iomin, A. Generalized Lyapunov exponent and transmission statistics in one-dimensional Gaussian correlated potentials. Phys. Rev. E
**2011**, 83, 11128. [Google Scholar] [CrossRef] - Jing-Hui, L. System Driven by Correlated Gaussian Noises Related with Disorder. Chin. Phys. Lett.
**2007**, 24, 2505–2508. [Google Scholar] [CrossRef] - Wang, Y.; Nandkishore, R.M. Interplay between short-range correlated disorder and Coulomb interaction in nodal-line semimetals. Phys. Rev. B
**2017**, 96, 115130. [Google Scholar] [CrossRef] - Horner, H. Drift, creep and pinning of a particle in a correlated random potential. Zeitschrift für Phys. B Condens. Matter
**1996**, 100, 243–257. [Google Scholar] [CrossRef] - Izrailev, F.M.; Krokhin, A.A. Localization and the Mobility Edge in One-Dimensional Potentials with Correlated Disorder. Phys. Rev. Lett.
**1999**, 82, 4062–4065. [Google Scholar] [CrossRef] - Lugan, P.; Aspect, A.; Sanchez-Palencia, L.; Delande, D.; Grémaud, B.; Müller, C.A.; Miniatura, C. One-dimensional Anderson localization in certain correlated random potentials. Phys. Rev. A
**2009**, 80, 23605. [Google Scholar] [CrossRef] - Das, S.K.; Singh, V.N.; Majumdar, P. Magnon spectrum in the domain ferromagnetic state of antisite-disordered double perovskites. Phys. Rev. B
**2013**, 88, 214428. [Google Scholar] [CrossRef] - Marcuzzi, M.; Minář, J.; Barredo, D.; de Léséleuc, S.; Labuhn, H.; Lahaye, T.; Browaeys, A.; Levi, E.; Lesanovsky, I. Facilitation Dynamics and Localization Phenomena in Rydberg Lattice Gases with Position Disorder. Phys. Rev. Lett.
**2017**, 118, 63606. [Google Scholar] [CrossRef] [PubMed] - Ro, S.; Kafri, Y.; Kardar, M.; Tailleur, J. Disorder-Induced Long-Ranged Correlations in Scalar Active Matter. Phys. Rev. Lett.
**2021**, 126, 48003. [Google Scholar] [CrossRef] [PubMed] - Micnas, R.; Ranninger, J.; Robaszkiewicz, S. Superconductivity in narrow-band systems with local nonretarded attractive interactions. Rev. Mod. Phys.
**1990**, 62, 113–171. [Google Scholar] [CrossRef] - Zhu, J.X. Bogoliubov-de Gennes Method and Its Applications; Springer: Berlin/Heidelberg, Germany, 2016; Volume 924. [Google Scholar]
- de Braganca, R.H.; Croitoru, M.D.; Shanenko, A.A.; Aguiar, J.A. Effect of Material-Dependent Boundaries on the Interference Induced Enhancement of the Surface Superconductivity Temperature. J. Phys. Chem. Lett.
**2023**, 14, 5657–5664. [Google Scholar] [CrossRef] - Hannibal, S.; Kettmann, P.; Croitoru, M.D.; Axt, V.M.; Kuhn, T. Persistent oscillations of the order parameter and interaction quench phase diagram for a confined Bardeen-Cooper-Schrieffer Fermi gas. Phys. Rev. A
**2018**, 98, 53605. [Google Scholar] [CrossRef] - Hannibal, S.; Kettmann, P.; Croitoru, M.D.; Axt, V.M.; Kuhn, T. Dynamical vanishing of the order parameter in a confined Bardeen-Cooper-Schrieffer Fermi gas after an interaction quench. Phys. Rev. A
**2018**, 97, 13619. [Google Scholar] [CrossRef] - Tarat, S.; Majumdar, P. Charge dynamics across the disorder-driven superconductor-insulator transition. EPL (Europhys. Lett.)
**2014**, 105, 67002. [Google Scholar] [CrossRef] - Croitoru, M.D.; Shanenko, A.A.; Vagov, A.; Milošević, M.V.; Axt, V.M.; Peeters, F.M. Phonon limited superconducting correlations in metallic nanograins. Sci. Rep.
**2015**, 5, 16515. [Google Scholar] [CrossRef] - Croitoru, M.D.; Shanenko, A.A.; Vagov, A.; Vasenko, A.S.; Milošević, M.V.; Axt, V.M.; Peeters, F.M. Influence of Disorder on Superconducting Correlations in Nanoparticles. J. Supercond. Nov. Magn.
**2016**, 29, 605–609. [Google Scholar] [CrossRef] - Makse, H.A.; Havlin, S.; Schwartz, M.; Stanley, H.E. Method for generating long-range correlations for large systems. Phys. Rev. E
**1996**, 53, 5445–5449. [Google Scholar] [CrossRef] - Hu, K.; Ivanov, P.C.; Chen, Z.; Carpena, P.; Eugene Stanley, H. Effect of trends on detrended fluctuation analysis. Phys. Rev. E
**2001**, 64, 11114. [Google Scholar] [CrossRef] [PubMed] - Chen, Z.; Hu, K.; Carpena, P.; Bernaola-Galvan, P.; Stanley, H.E.; Ivanov, P.C. Effect of nonlinear filters on detrended fluctuation analysis. Phys. Rev. E
**2005**, 71, 11104. [Google Scholar] [CrossRef] - Coronado, A.V.; Carpena, P. Size Effects on Correlation Measures. J. Biol. Phys.
**2005**, 31, 121–133. [Google Scholar] [CrossRef] [PubMed] - Croitoru, M.D.; Gladilin, V.N.; Fomin, V.M.; Devreese, J.T.; Kemerink, M.; Koenraad, P.M.; Sauthoff, K.; Wolter, J.H. Electroluminescence spectra of an STM-tip-induced quantum dot. Phys. Rev. B
**2003**, 68, 195307. [Google Scholar] [CrossRef] - Croitoru, M.D.; Gladilin, V.N.; Fomin, V.M.; Devreese, J.T.; Magnus, W.; Schoenmaker, W.; Sorée, B. Quantum transport in a nanosize double-gate metal-oxide-semiconductor field-effect transistor. J. of Appl. Phys.
**2003**, 96, 2305–2310. [Google Scholar] [CrossRef] - Kettmann, P.; Hannibal, S.; Croitoru, M.D.; Axt, V.M.; Kuhn, T. Pure Goldstone mode in the quench dynamics of a confined ultracold Fermi gas in the BCS-BEC crossover regime. Phys. Rev. A
**2017**, 96, 33618. [Google Scholar] [CrossRef] - Yang, C.N. Concept of Off-Diagonal Long-Range Order and the Quantum Phases of Liquid He and of Superconductors. Rev. Mod. Phys.
**1962**, 34, 694–704. [Google Scholar] [CrossRef] - Scalapino, D.J.; White, S.R.; Zhang, S.C. Superfluid density and the Drude weight of the Hubbard model. Phys. Rev. Lett.
**1992**, 68, 2830–2833. [Google Scholar] [CrossRef] - Scalapino, D.J.; White, S.R.; Zhang, S. Insulator, metal, or superconductor: The criteria. Phys. Rev. B
**1993**, 47, 7995–8007. [Google Scholar] [CrossRef] [PubMed] - Croitoru, M.D.; Buzdin, A.I. The Fulde–Ferrell–Larkin–Ovchinnikov state in layered d-wave superconductors: In-plane anisotropy and resonance effects in the angular dependence of the upper critical field. J. Phys. Condens. Matter
**2013**, 25, 125702. [Google Scholar] [CrossRef] [PubMed] - Croitoru, M.; Buzdin, A. In Search of Unambiguous Evidence of the Fulde–Ferrell–Larkin–Ovchinnikov State in Quasi-Low Dimensional Superconductors. Condens. Matter
**2017**, 2, 30. [Google Scholar] [CrossRef]

**Figure 1.**Statistical distribution of the absolute value of the order parameter ${\mathsf{\Delta}}_{i}$, calculated for various values of the disorder strength (from top to bottom: $V=0.8;2.0;3.2;4.8$) and various disorder correlation degree (colors).

**Figure 2.**Statistical distribution of the absolute value of the order parameter ${\mathsf{\Delta}}_{i}$ in two models calculated for the same effective correlation length. The notations $\alpha $ and ${\alpha}_{0}$ correspond to the degree of disorder correlation for Gaussian and power law decay, respectively.

**Figure 3.**The Fourier transform of the spatial correlation function of the order parameter for several values of $\alpha $.

**Figure 5.**Diamagnetic and paramagnetic contributions to ${D}_{s}^{0}$ as functions of V for several values of $\alpha $.

**Figure 6.**The superfluid stiffness ${D}_{s}^{0}$ as a function of V, calculated for several values of $\alpha $.

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**MDPI and ACS Style**

Neverov, V.D.; Lukyanov, A.E.; Krasavin, A.V.; Vagov, A.; Croitoru, M.D.
The Impact of Short-Range (Gaussian) Disorder Correlations on Superconducting Characteristics. *Condens. Matter* **2024**, *9*, 6.
https://doi.org/10.3390/condmat9010006

**AMA Style**

Neverov VD, Lukyanov AE, Krasavin AV, Vagov A, Croitoru MD.
The Impact of Short-Range (Gaussian) Disorder Correlations on Superconducting Characteristics. *Condensed Matter*. 2024; 9(1):6.
https://doi.org/10.3390/condmat9010006

**Chicago/Turabian Style**

Neverov, Vyacheslav D., Alexander E. Lukyanov, Andrey V. Krasavin, Alexei Vagov, and Mihail D. Croitoru.
2024. "The Impact of Short-Range (Gaussian) Disorder Correlations on Superconducting Characteristics" *Condensed Matter* 9, no. 1: 6.
https://doi.org/10.3390/condmat9010006