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Self-optimized superconductivity attainable by interlayer phase separation at cuprate interfaces

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Science Advances  29 Jul 2016:
Vol. 2, no. 7, e1600664
DOI: 10.1126/sciadv.1600664
  • Fig. 1 Experimental setup and present theoretical model of the cuprate interface.

    (A) Schematic experimental setup of the cuprate interface (2). (B) Top: Illustration of the interface model for cuprates. The dotted line denotes the interface between the metallic and the insulating layer. The color schematically illustrates the change in the carrier concentration obtained in the present work. Bottom: Two hypothetical bulk or single-layer phases with charge inhomogeneity within a layer. (C) Layer dependence of onsite energy level chosen to model the interface (red line). In the metallic phase, the onsite energy level is assumed to change linearly. This is an approximation that takes into account the effect of interlayer atomic diffusion [blue curve; taken from the study of Logvenov et al. (20)] combined with effects from the Madelung potential and the spatial extension of the Wannier orbital at the interface. (D) Onsite level of a sharp interface modeled by means of an ab initio calculation for x = 0.4.

  • Fig. 2 Layer dependence of doping concentration around the interface.

    (A) Layer and level-slope dependence of carrier density (filled circles and blue surface). At the fourth layer, the green curve is taken from the μbulkbulk relation, and the two horizontal gray sheets show the phase separation boundaries determined in (B). Note that μbulk = μ4 ~ ε4 − 2.4 is satisfied, indicating that the grand canonical ensemble is realized for ν = 4. The phase separation region in the bulk is also evaded around the interface in any layer ν. In contrast, the noninteracting case with the same δ4 plotted for Δε = 0.1 (red line) enters the present phase separation region. (B) Relation between the hole density δbulk = δ and the chemical potential μbulk = μ in the uniform bulk system calculated within the canonical ensemble for a single layer representative of the bulk (10). The Maxwell construction (dashed line) determines the phase separation as the gray region between δbulk ~ 0.2 and 0. (C) Hole density at interfaces δ1 shows pinning against bulk hole density δbulk.

  • Fig. 3 Superconducting correlations and amplitudes.

    (A) Spatial dependence of d-wave superconducting correlations at the interface (ν = 1) for Δε = 0.2 and δbulk ~ 0.32 (blue squares) compared with that of the uniform bulk for a hole density similar to that at the interface (~0.20). The red circles are obtained for the bulk (stacked layers) with uniform chemical potential. The saturation at long distances r indicates long-range order. The data sets are for the linear size in the plane direction, L = 14, for which we confirmed convergence to the thermodynamic limit. (B) Bulk hole density dependence of squared superconducting amplitude at the interface (ν = 1) defined by Embedded Image. Embedded Image hardly depends on the bulk hole densities. (C) Layer dependence of Embedded Image. This function is strongly peaked at the interface ν = 1.

  • Fig. 4 Relation between chemical potential and hole concentration.

    (A) Chemical potentials μ4 (determined from Eq. 6) as a function of the hole density δ4 at the fourth layer for several choices of Δε are plotted as curves with symbols. Here, δν is defined as Embedded Image. For a choice of Δε, μ4 curves are drawn by changing the total electron number in the whole slab. We assume that μ4 converges to the bulk chemical potential μbulk (green curve), which was calculated in the study of Misawa and Imada (10). Therefore, the realistic bulk hole density δbulk is determined from the crossing point between the bulk chemical potential μbulk given by the green curve and μ4 for each choice of Δε. Cases with different δbulk are obtained from different Δε. The nonmonotonic behavior of the green curve signals the existence of a phase separation region. A Maxwell construction (horizontal dashed line) allows us to determine the coexistence region as 0 < δ < δPS ~ 0.2 (gray area). (B) Chemical potentials μν (determined from Eq. 6) as a function of the hole density δν for ν = 1 to 4 for several choices of Δε are plotted as symbols. It follows the bulk behavior shown by the green curve, indicating that each layer behaves as a single layer (or uniform bulk) in the μ-δ relation with negligible effects from tz. (C) Chemical potential difference μν − μPS plotted as a function of the onsite-level difference εν − εPS. The straight bold line shows that the chemical potential at each layer shifts in accordance with the shift of the onsite level, again indicating that the effects of tz is negligible and each layer behaves as the grand canonical ensemble with the hole onsite level εν.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/7/e1600664/DC1

    Text (sections A and B)

    fig. S1. First-principles estimate of electronic structure around a sharp interface.

    fig. S2. Chemical potential in bulk metal and saturated superconducting correlation at the interface as functions of bulk hole concentration in the case of a sharp interface.

    References (4651)

  • Supplementary Materials

    This PDF file includes:

    • Text (sections A and B)
    • fig. S1. First-principles estimate of electronic structure around a sharp interface.
    • fig. S2. Chemical potential in bulk metal and saturated superconducting correlation at the interface as functions of bulk hole concentration in the case of a sharp interface.
    • References (4651)

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