Collapse of the Normal-State Pseudogap at a Lifshitz Transition in the ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ Cuprate Superconductor

Collapse of the Normal-State Pseudogap at a Lifshitz Transition in the ${Bi}_{2} {Sr}_{2} {CaCu}_{2} O_{8 + δ}$ Cuprate Superconductor

S. Benhabib, A. Sacuto, M. Civelli, I. Paul, M. Cazayous, Y. Gallais, M.-A. Méasson, R. D. Zhong, J. Schneeloch, G. D. Gu, D. Colson, and A. Forget

Phys. Rev. Lett. 114, 147001 – Published 7 April 2015

Abstract

We report a fine tuned doping study of strongly overdoped ${Bi}_{2} {Sr}_{2} {CaCu}_{2} O_{8 + δ}$ single crystals using electronic Raman scattering. Combined with theoretical calculations, we show that the doping, at which the normal-state pseudogap closes, coincides with a Lifshitz quantum phase transition where the active holelike Fermi surface becomes electronlike. This conclusion suggests that the microscopic cause of the pseudogap is sensitive to the Fermi surface topology. Furthermore, we find that the superconducting transition temperature is unaffected by this transition, demonstrating that their origins are different on the overdoped side.

Received 21 October 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.147001

Authors & Affiliations

S. Benhabib¹, A. Sacuto^1,*, M. Civelli², I. Paul¹, M. Cazayous¹, Y. Gallais¹, M.-A. Méasson¹, R. D. Zhong³, J. Schneeloch³, G. D. Gu³, D. Colson⁴, and A. Forget⁴

¹Laboratoire Matériaux et Phénomènes Quantiques (UMR 7162 CNRS), Université Paris Diderot-Paris 7, Bâtiment Condorcet, 75205 Paris Cedex 13, France
²Laboratoire de Physique des Solides, UMR 8502 CNRS, Université Paris Sud, Bâtiment 510, 91405 Orsay Cedex, France
³Matter Physics and Materials Science, Brookhaven National Laboratory (BNL), Upton, New York 11973, USA
⁴Service de Physique de l’Etat Condensé, CEA-Saclay, 91191 Gif-sur-Yvette, France

^*alain.sacuto@univ-paris-diderot.fr

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Vol. 114, Iss. 14 — 10 April 2015

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Figure 1
(a)–(d) $T$ dependence of the Raman response $χ_{B_{1 g}}^{''}$ of overdoped Bi-2212. $2 Δ_{0}$ is defined as the position of the $B_{1 g}$ pair breaking peak. The location of the $300 {cm}^{- 1}$ phonon peak is marked by a dotted line. (e)–(h) Integrated Raman intensities are shown in (a)–(d), with cutoff $Λ = 850 {cm}^{- 1}$ . For each doping, $I_{B_{1 g}} (T)$ is normalized by $I_{B_{1 g}}$ (10 K). The red curve is a second order polynomial fit just above $T_{c}$ indicating the sign change of the slope. We found a remarkably linear dependence between $T_{c}$ and $2 Δ_{0}$ in the critical temperature range 90–50 K (cf. Ref. [22]). The doping level for each value of $T_{c}$ was fixed using the Tallon-Presland formula (cf. Ref. [22]).
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Figure 2
$B_{1 g}$ (red/grey) and $B_{2 g}$ (black) Raman responses of Bi-2212 at 10 K (superconducting state) and 110 K (normal state) in the overdoped range using a 532 nm laser. The [red (grey)] and black hatched areas indicate the magnitudes of the $B_{1 g}$ and the $B_{2 g}$ responses, respectively. The former increases compared to the latter as a function of doping up to $p_{c} = 0.22$ .
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Figure 3
Doping evolution of (i) the ratio $I_{B_{1 g}} / I_{B_{2 g}}$ of the integrated intensity [defined in Eq. (1)] in the superconducting and the normal states (filled and open circles respectively) with cutoff $Λ \approx 3 Δ_{0}$ , (ii) the loss of spectral weight related to the pseudogap (black stars). The peak in the ratio $I_{B_{1 g}} / I_{B_{2 g}}$ , both for the superconducting and the normal phases, coincides with the critical doping $p_{c} = 0.22$ where the pseudogap disappears. The peak is a consequence of a Lifshitz transition where the holelike Fermi surface of the dominant antibonding band becomes electronlike as the chemical potential crosses a van Hove singularity.
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Figure 4
(a)–(c) With doping, the holelike antibonding Fermi surface becomes electronlike at a Lifshitz transition. The dotted line is the antiferromagnetic Brillouin zone. HR denotes the hot region of the large scattering rate. (d) Doping dependence of the integrated intensity ratio $I_{B_{1 g}} / I_{B_{2 g}}$ in the normal (solid line) and superconducting (dashed line) states calculated from a theoretical model (see text), reproducing qualitatively the trend of Fig. 3. The curves are normalized (cf. Ref. [22]). (e)–(g) The associated van Hove singularity appears in $N_{B_{1 g}} (ω)$ (red/grey), the density of states weighted by the $B_{1 g}$ Raman vertex (defined in text). The van Hove singularity does not however appear in $N_{B_{2 g}} (ω)$ (black),which is multiplied by $(t / t^{'})^{2}$ for better visibility.
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Figure 5
Schematic phase diagram of temperature ( $T$ ) versus doping ( $p$ ) with with three material-dependent possible locations of the critical doping $p_{c}$ . This latter is defined where the normal state pseudogap closes, with respect to the superconducting (SC) dome [shaded blue (grey)]. (a) is realized in Bi-2212 (current study), (b) and (c) have been reported for LSCO [51] and Bi-2201 [52], respectively. The common feature in all three cases is the coincidence of $p_{c}$ with a Lifshitz transition where a Fermi surface changes from holelike to electronlike.
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Physical Review Letters

Collapse of the Normal-State Pseudogap at a Lifshitz Transition in the Bi2Sr2CaCu2O8+δ Cuprate Superconductor

S. Benhabib, A. Sacuto, M. Civelli, I. Paul, M. Cazayous, Y. Gallais, M.-A. Méasson, R. D. Zhong, J. Schneeloch, G. D. Gu, D. Colson, and A. Forget

Phys. Rev. Lett. 114, 147001 – Published 7 April 2015

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Collapse of the Normal-State Pseudogap at a Lifshitz Transition in the ${Bi}_{2} {Sr}_{2} {CaCu}_{2} O_{8 + δ}$ Cuprate Superconductor