Enhancement of the superconducting transition temperature in cuprate heterostructures

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Enhancement of the superconducting transition temperature in cuprate heterostructures

Lilach Goren and Ehud Altman

Phys. Rev. B 79, 174509 – Published 7 May 2009

Abstract

Is it possible to increase $T_{c}$ by constructing cuprate heterostructures, which combine the high pairing energy of underdoped layers with the large carrier density of proximate overdoped layers? We investigate this question within a model bilayer system using an effective theory of the doped Mott insulator. Interestingly, the question hinges on the fundamental nature of the superconducting state in the underdoped regime. Within a plain slave boson mean-field theory, there is absolutely no enhancement of $T_{c}$ . However, we do get a substantial enhancement for moderate interlayer tunneling when we use an effective low energy theory of the bilayer in which the effective quasiparticle charge in the underdoped regime is taken as an independent phenomenological parameter. We study the $T_{c}$ enhancement as a function of the doping level and the interlayer tunneling, and discuss possible connections to recent experiments by Yuli et al. [Phys. Rev. Lett. 101, 057005 (2008)]. Finally, we predict a unique paramagnetic reduction in the zero-temperature phase stiffness of coupled layers, which depends on the difference in the current carried by quasiparticles on the two types of layers as ${(J_{1} - J_{2})}^{2}$ .

Received 16 October 2008

DOI:https://doi.org/10.1103/PhysRevB.79.174509

Authors & Affiliations

Lilach Goren and Ehud Altman

Department of Condensed Matter Physics, The Weizmann Institute of Science, 76100 Rehovot, Israel

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Vol. 79, Iss. 17 — 1 May 2009

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Figure 1
(Color online) Illustration of the two-dimensional low energy dispersion of a bilayer consisting of a $d$ -wave superconducting layer and a nominally metallic layer. The four outer (red) surfaces mark the original Dirac cones of the superconducting layer. The inner (blue) surfaces are the Dirac cones induced by the proximity effect on the metallic layer. The closed (blue) curve denotes the original Fermi surface of that layer.Reuse & Permissions
Figure 2
(Color online) Phase diagram of the bilayer system from microscopic theory. The critical temperature $T_{c}$ (normalized by its maximal value for two identical underdoped layers, $T_{c, 0}^{max}$ ) vs doping of the underdoped layer. The doping level of the metallic layer is $y = 0.35$ . The dashed line is the result of two identical underdoped layers. (a) "Bare" SBMFT calculation. No enhancement of $T_{c}$ . (b) SBMFT with renormalized quasiparticle charge of $α_{1} = 0.5$ in the underdoped layer. Maximal $T_{c}$ enhanced by $\sim 40 %$ in the heterostructure. Optimal doping shifted down, consistent with experiment of Yuli et al. (Ref. 10).Reuse & Permissions
Figure 3
(Color online) Optimal interlayer tunneling. The critical temperature $T_{c}$ is plotted vs the interlayer coupling $t_{⊥} / t$ $(t = t_{1} = t_{2})$ . Different curves correspond to different doping levels of the underdoped layer and all curves are normalized by the critical temperature of two underdoped layers of the same doping level, $T_{c, 0} (x)$ . The doping of the metallic layer is $y = 0.35$ . Inset: the self-consistent gap $Δ$ and the proximity gap $Δ_{prox}$ as calculated from the bilayer energy spectrum, plotted vs the interlayer tunneling $t_{⊥} / t$ for doping $x = 0.11$ . This suggests that the optimal value of $t_{⊥}$ is determined by the point where the antiproximity effect on the gap of the underdoped layer overtakes the proximity gap in the normal layer.Reuse & Permissions
Figure 4
(Color online) Paramagnetic reduction in the zero-temperature stiffness. $ρ_{s} (T = 0)$ of the bilayer system (doping levels $x = 0.11$ and $y = 0.35$ ) is plotted against ${(J_{1} - J_{2})}^{2} / t^{2}$ , where $t = t_{1} = t_{2}$ is the bare in layer tunneling and $J_{l} = α_{l} v_{F l}$ are the quasiparticle currents of the two layers. Here $v_{F l}$ are the Fermi velocities at the nodes in the respective layers. We used the quasiparticle charge $α_{2} = 1$ for the normal layer and varied $α_{1}$ of the underdoped layer.Reuse & Permissions
Figure 5
(Color online) Phase diagram of bilayer LSCO from the phenomenological theory. Plots of the critical temperature for a bilayer with different interlayer tunneling $t_{⊥} / t$ computed using the phenomenological approach of Sec. 4C (solid red curves). This is compared to the measured critical temperature in bulk LSCO (black circles) taken from Ref. 23. The dashed line is a linear interpolation of data for $Δ (x) / 2$ (antinodal gap) (Ref. 24), taken as an estimate for the mean-field critical temperature.Reuse & Permissions

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