Evolution from a Nodeless Gap to ${d}_{{x}^{2}\mathbf{\ensuremath{-}}{y}^{2}}$-Wave in Underdoped ${\mathrm{La}}_{2\mathbf{\ensuremath{-}}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$

Evolution from a Nodeless Gap to $d_{x^{2} - y^{2}}$ -Wave in Underdoped ${La}_{2 - x} {Sr}_{x} {CuO}_{4}$

E. Razzoli, G. Drachuck, A. Keren, M. Radovic, N. C. Plumb, J. Chang, Y.-B. Huang, H. Ding, J. Mesot, and M. Shi

Phys. Rev. Lett. 110, 047004 – Published 25 January 2013

Abstract

Using angle-resolved photoemission spectroscopy (ARPES), it is revealed that the low-energy electronic excitation spectra of highly underdoped superconducting and nonsuperconducting ${La}_{2 - x} {Sr}_{x} {CuO}_{4}$ cuprates are gapped along the entire underlying Fermi surface at low temperatures. We show how the gap function evolves to a $d_{x^{2} - y^{2}}$ form with increasing temperature or doping, consistent with the vast majority of ARPES studies of cuprates. Our results provide essential information for uncovering the symmetry of the order parameter(s) in strongly underdoped cuprates, which is a prerequisite for understanding the pairing mechanism and how superconductivity emerges from a Mott insulator.

Received 9 June 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.047004

Authors & Affiliations

E. Razzoli¹, G. Drachuck², A. Keren², M. Radovic^1,3, N. C. Plumb¹, J. Chang^1,3, Y.-B. Huang⁴, H. Ding⁴, J. Mesot^1,3, and M. Shi¹

¹Swiss Light Source, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
²Department of Physics, Technion, Haifa 32000, Israel
³Institut de la Matiere Complexe, EPF Lausanne, CH-1015 Lausanne, Switzerland
⁴Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

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Vol. 110, Iss. 4 — 25 January 2013

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Figure 1
ARPES spectra for LSCO with $x = 0.08$ ( $T_{c} = 20 K$ ) and $x = 0.145$ ( $T_{c} = 33 K$ ). (a)–(d) Intensities along the zone diagonal [the arrow in (k)] at $T = 10$ , 54, 88, and 137 K for $x = 0.08$ . The spectra were obtained by the DFD method [4]. (e)–(h) EDCs from (a)–(d) in the vicinity of $k_{F}$ . (i), (j) Images in the vicinity of $k_{F}$ at 10 and 137 K. Each EDC is normalized to the intensity at the peak position (circles). (k) The FS of LSCO $x = 0.08$ obtained from tight-binding fits to the experimental data. The arrow indicates the cut along which the ARPES data were taken. (l),(m) The same as (a)–(d) but for LSCO ( $x = 0.145$ ) at $T = 12$ and 40 K. (n),(o) EDCs from (l), (m) close to $k_{F}$ .Reuse & Permissions
Figure 2
EDCs at $k_{F}$ on the zone diagonal for LSCO. The EDCs were obtained by deconvoluting the raw ARPES data to remove the broadening due to the finite instrumental resolution [4]. (a) EDCs as a function of temperature for $x = 0.08$ . Curves are offset vertically for clarity. (b) EDCs for $x = 0.03$ at 10 K, and for $x = 0.08$ at 10 and 54 K. Curves are offset horizontally to align the peak position to that of the EDC for $x = 0.08$ at 10 K. (c),(d) EDCs at 10 K as a function of doping ( $x$ ). Curves in (c) are offset vertically for clarity and in (d) are offset horizontally to align the peak position to that of the EDC for $x = 0.08$ at 10 K.Reuse & Permissions
Figure 3
ARPES spectra for LSCO ( $x = 0.08$ ). (a)–(c) Symmetrized EDCs as a function of temperature at $k_{F}$ [points $a$ , $b$ , and $c$ shown in (d)]. (d) The $k_{F}$ (closed circles) at which the symmetrized EDCs are shown in (a)–(c). (e) Energy gap as a function of FS angle $ϕ$ . The symbols are the experimentally determined energy gaps at various temperatures. The solid lines are $| Δ_{d_{x^{2} - y^{2}}} + i Δ_{d_{x y}} |$ with $Δ_{d_{x^{2} - y^{2}}}^{0} = 38.52 meV$ and from top to bottom $Δ_{d_{x y}}^{0} = 20$ , 16.6, 13.5, and 0 meV (pure $d_{x^{2} - y^{2}}$ -form), respectively.Reuse & Permissions
Figure 4
ARPES spectra of LSCO ( $x = 0.08$ , $T_{c} = 20 K$ ) measured at 54 K. (a)–(f) Intensities along 6 cuts indicated in (h). The spectra were obtained by the DFD method. (g) Dispersions obtained by tracing the EDC peaks of (a)–(f) in the vicinity of $k_{F}$ . For clarity the dispersions along cuts 2–6 were offset horizontally. (h) The upper half of BZ and cuts along which the data in (a)–(f) were taken. (i) Energy gap as a function of FS angle $ϕ$ . The closed circles are the gap extracted from the difference between $E_{F}$ and the maximal energy that the backbending dispersions reach. The triangles are the gap obtained from symmetrized EDCs [Fig. 3e]. The dashed and solid lines are the $| Δ_{d_{x^{2} - y^{2}}} |$ and $| Δ_{d_{x^{2} - y^{2}}} + i Δ_{d_{x y}} |$ , respectively.Reuse & Permissions

Physical Review Letters

Evolution from a Nodeless Gap to dx2−y2-Wave in Underdoped La2−xSrxCuO4

E. Razzoli, G. Drachuck, A. Keren, M. Radovic, N. C. Plumb, J. Chang, Y.-B. Huang, H. Ding, J. Mesot, and M. Shi

Phys. Rev. Lett. 110, 047004 – Published 25 January 2013

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Evolution from a Nodeless Gap to $d_{x^{2} - y^{2}}$ -Wave in Underdoped ${La}_{2 - x} {Sr}_{x} {CuO}_{4}$