Critical Doping for the Onset of a Two-Band Superconducting Ground State in ${\mathrm{SrTiO}}_{3\ensuremath{-}\ensuremath{\delta}}$

Critical Doping for the Onset of a Two-Band Superconducting Ground State in ${SrTiO}_{3 - δ}$

Xiao Lin, German Bridoux, Adrien Gourgout, Gabriel Seyfarth, Steffen Krämer, Marc Nardone, Benoît Fauqué, and Kamran Behnia

Phys. Rev. Lett. 112, 207002 – Published 21 May 2014

Abstract

In doped ${SrTiO}_{3}$ superconductivity persists down to an exceptionally low concentration of mobile electrons. This restricts the relevant energy window and possible pairing scenarios. We present a study of quantum oscillations and superconducting transition temperature $T_{c}$ as the carrier density is tuned from $1 0^{17}$ to $1 0^{20} {cm}^{- 3}$ and identify two critical doping levels corresponding to the filling thresholds of the upper bands. At the first critical doping, which separates the single-band and the two-band superconducting regimes in oxygen-deficient samples, the steady increase of $T_{c}$ with carrier concentration suddenly stops. Near this doping level, the energy dispersion in the lowest band displays a downward deviation from parabolic behavior. The results impose new constraints for microscopic pairing scenarios.

Received 7 January 2014

DOI:https://doi.org/10.1103/PhysRevLett.112.207002

Authors & Affiliations

Xiao Lin¹, German Bridoux¹, Adrien Gourgout¹, Gabriel Seyfarth², Steffen Krämer², Marc Nardone³, Benoît Fauqué¹, and Kamran Behnia^1,*

¹Laboratoire de Physique et d’Étude des Matériaux-CNRS (ESPCI and UPMC), Paris 75005, France
²Laboratoire National des Champs Magnétiques Intenses-CNRS (UJF, UPS and INSA), Grenoble 38042, France
³Laboratoire National des Champs Magnétiques Intenses-CNRS (UJF, UPS and INSA), Toulouse 31400, France

^*kamran.behnia@espci.fr

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Vol. 112, Iss. 20 — 23 May 2014

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Figure 1
(a) Detected frequencies of quantum oscillations as a function of carrier concentration. At two critical doping levels, designated as $n_{c 1}$ and $n_{c 2}$ , a new frequency emerges. At each critical doping a new band starts to be occupied. (b) Superconducting resistive transition temperature (on a logarithmic axis) as a function of carrier concentration. Solid squares represent reduced samples ( ${SrTiO}_{3 - δ}$ ) and open squares Nb-doped samples ( ${SrTi}_{1 - x} {Nb}_{x} O_{3}$ with $x = 0.02$ , 0.01, 0.002, and 0.001). Error bars represent the width of transition. (c) $T_{c}$ (on a linear axis) as a function of carrier per formula unit. Our data are compared with those reported by Schooley and co-workers [2]. The red shaded region shows the rough contours of superconductivity in the ${SrTiO}_{3} / {LaAlO}_{3}$ interface [4, 17, 18].
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Figure 2
Low-temperature resistivity of reduced (a) and Nb-doped (b) single crystals. Note the continuous evolution of resistive transitions in reduced samples. As the doping increases, the transition first shifts to higher temperatures and then remains more or less constant.
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Figure 3
Left: a new frequency emerges in the Shubnikov–de Haas data in the vicinity of $n_{c 1}$ . When the carrier density is below $n_{c 1}$ , quantum oscillations display a single periodicity with split peaks and each peak is more prominent than its preceding neighbor (a). With increasing carrier density, a second frequency emerges on top of the first one (b)–(d). Data are plotted as a function of the inverse of magnetic field normalized by the principal frequency $F_{1}$ in order to simplify comparison. The Fermi surface of the lower band according to Ref. [13] is shown in panel (e) and its projection along the three high-symmetry axes in panels (f) and (g). In multidomain crystals, the two possible Fermi cross sections give rise to split peaks in quantum oscillations.
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Figure 4
(a) The effective mass in each band as a function of carrier concentration. The masses reported by an angle resolved photoemission spectroscopy study on a bulk sample at $n = 1.4 \times 1 0^{20} {cm}^{- 3}$ [19] is also shown for comparison. (b) Carrier concentration and its distribution among bands according to the detected frequency and assuming spherical Fermi surfaces. The total carrier density falls just below the Hall carrier density. Above $1.6 \times 1 0^{20} {cm}^{- 3}$ , the lower band becomes invisible because of its reduced mobility. (c) Lifshitz-Kosevitch analysis of the oscillations revealing two distinct masses for the lower and middle bands. Each color corresponds to a different oscillation. (d) The Fermi energy, defined as $ℏ^{2} k_{F}^{2} / 2 m_{c}$ in the two lower bands plotted as a function of corresponding $k_{F}$ . The middle band is shifted upward by the energy gap between the two bands. (e) Theoretical energy dispersion near the bottom of the bands according to Ref. [10].
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Physical Review Letters

Critical Doping for the Onset of a Two-Band Superconducting Ground State in SrTiO3−δ

Xiao Lin, German Bridoux, Adrien Gourgout, Gabriel Seyfarth, Steffen Krämer, Marc Nardone, Benoît Fauqué, and Kamran Behnia

Phys. Rev. Lett. 112, 207002 – Published 21 May 2014

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Critical Doping for the Onset of a Two-Band Superconducting Ground State in ${SrTiO}_{3 - δ}$