Research ArticleCONDENSED MATTER PHYSICS

Vortex phase diagram and the normal state of cuprates with charge and spin orders

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Science Advances  14 Feb 2020:
Vol. 6, no. 7, eaay8946
DOI: 10.1126/sciadv.aay8946
  • Fig. 1 In-plane transport properties of striped cuprates.

    (A and B) T-x phase diagrams of LESCO and LNSCO, respectively, for H = 0; Tc0is the SC transition temperature, and Td2 is the transition temperature from the low-temperature orthorhombic (LTO) to a low-temperature tetragonal (LTT) structure. TCO and TSO are the onset temperatures for charge and spin orders, respectively. Dashed lines guide the eye. Vertical dashed lines show the doping of our single crystals. The data in (A) are reproduced from (59) and references therein, and those in (B) from (55, 59, 60) and references therein. (C and D) ρab(H) of La1.7Eu0.2Sr0.1CuO4 and La1.48Nd0.4Sr0.12CuO4, respectively, for several T. At low T, ρab(H) exhibits a strong peak at H = Hpeak(T). The right axes show the corresponding R□/layer in units of quantum resistance for Cooper pairs, RQ = h/(2e)2. (E and F) ρab(T) of La1.7Eu0.2Sr0.1CuO4 and La1.48Nd0.4Sr0.12CuO4, respectively, for several H ≤ 19 T. Solid lines guide the eye. The black dashed lines track the values of Tpeak(H).

  • Fig. 2 In-plane transport T-H phase diagram of striped cuprates with Hc axis.

    (A) La1.7Eu0.2Sr0.1CuO4. (B) La1.48Nd0.4Sr0.12CuO4. Tc(H) (black squares) mark the boundary of the pinned vortex lattice, which is a superconductor with ρab = 0 for all T < Tc(H) [region I; Tc(H) > 0]. H*(T) symbols mark the boundary of the viscous VL, in which dV/dI is non-ohmic [for H < H*(T)] and freezes into a VG at T = Tc = 0. Dashed red line guides the eye. Ohmic behavior is found at H > H*(T). H*(T = 0) thus corresponds to the upper critical field Hc2. Hpeak(T) (green dots) represent fields above, which the MR changes from positive to negative. The region H* < H < Hpeak, in which the MR is positive but transport is ohmic, is identified as the VL. Tpeak(H) (open blue diamonds) tracks the positions of the peak in ρab(T). Hc(T) is the field above which SC fluctuations are not observed. Gaussian fluctuations of the SC amplitude and phase are expected at the highest T and H<Hc(T). The highest field region (III) corresponds to the H-induced normal state. The dashed line in (A) is a fit with μ0Hc[T]=20.3[1(T[K]/35.4)2], and the error bars indicate the uncertainty in Hc that corresponds to 1 SD in the slopes of the linear fits in fig. S5. In (B), SC fluctuations vanish between 33 and 48 K for H = 0, and the dashed line is a guide to the eye. Zero-field values of TSO and TCO are also shown; both spin and charge stripes are known to be enhanced by H (see the main text). Except for Tc(H), lines do not represent phase boundaries but finite-temperature crossovers.

  • Fig. 3 Nonlinear in-plane transport in La1.7Eu0.2Sr0.1CuO4.

    (A) Differential resistance dV/dI as a function of dc current Idc for several H ≤ 18 T at T = 0.067 K. In the bottom trace, for which T < Tc(H = 4.8 T) ≈ 0.08 K, dV/dI is zero as expected in a superconductor. (B) dV/dI versus Idc for several T at H = 9 T. The linear resistance (dV/dI for Idc → 0) has a metallic-like temperature dependence, but at higher Idc > 20 μA, the temperature dependence of dV/dI is insulating-like. Dashed lines guide the eye.

  • Fig. 4 Temperature dependence of the in-plane resistivity ρab at the highest H, i.e., in the normal state.

    (A) La1.7Eu0.2Sr0.1CuO4. (B) La1.48Nd0.4Sr0.12CuO4. Solid lines are fits to ρab=ρab(H)ln(T0(H)/T), and dashed lines guide the eye. The arrow in (B) shows Tpeak(H = 19 T). Insets: Fitting parameters ρab(H) and T0(H).The decrease of the slopes ρab (black squares) with H indicates the weakening of the insulating-like ln(1/T) dependence with H. The linear extrapolation of ρab to zero (dashed line) provides a rough estimate of the field ∼55 T in La1.7Eu0.2Sr0.1CuO4, i.e., ∼71 T in La1.48Nd0.4Sr0.12CuO4, where insulating-like behavior vanishes.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/7/eaay8946/DC1

    Fig. S1. Determination of the zero-resistance Tc(H).

    Fig. S2. The dependence of the in-plane resistivity on T at intermediate fields.

    Fig. S3. Nonlinear in-plane transport in La1.7Eu0.2Sr0.1CuO4.

    Fig. S4. Nonlinear in-plane transport in La1.48Nd0.4Sr0.12CuO4.

    Fig. S5. In-plane MR of La1.7Eu0.2Sr0.1CuO4 versus H2 for several T>Tc0.

    Fig. S6. Comparison of studies of upper critical field in various underdoped cuprates at different hole concentrations (p).

    Fig. S7. Temperature dependence of the magnetic susceptibility and in-plane resistivity.

    Fig. S8. Comparison of the irreversibility fields Hirr(T) with the resistive Tc(H) in La1.7Eu0.2Sr0.1CuO4.

    References (61, 62)

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Determination of the zero-resistance Tc(H).
    • Fig. S2. The dependence of the in-plane resistivity on T at intermediate fields.
    • Fig. S3. Nonlinear in-plane transport in La1.7Eu0.2Sr0.1CuO4.
    • Fig. S4. Nonlinear in-plane transport in La1.48Nd0.4Sr0.12CuO4.
    • Fig. S5. In-plane MR of La1.7Eu0.2Sr0.1CuO4 versus H2 for several T>Tc0.
    • Fig. S6. Comparison of studies of upper critical field in various underdoped cuprates at different hole concentrations (p).
    • Fig. S7. Temperature dependence of the magnetic susceptibility and in-plane resistivity.
    • Fig. S8. Comparison of the irreversibility fields Hirr(T) with the resistive Tc(H) in La1.7Eu0.2Sr0.1CuO4.
    • References (61, 62)

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