Critical Doping for the Onset of a Two-Band Superconducting Ground State inSrTiO3−δ

Abstract

In doped SrTiO3 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, Tc as the carrier density is tuned from 10 17 to 10 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 Tc 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.Superconductiviy is induced in insulating SrTiO 3 by introducing n-type charge carriers through chemical doping[1] and survives over three orders of magnitude of carrier concentration. The transition temperature, T c , peaks to 0.45 K around a carrier density of n H ∼ 10 20 cm −3 [2]. A superconducting dome has also been detected in the metallic interfaces of SrTiO 3 [3] when the carrier density is modulated by a gate voltage bias [4]. In unconventional superconductors, such as high-T c cuprates, superconducting domes are often attributed to the proximity of a magnetic order or a Mott insulator. The recent discovery of superconducting dome in gate-tuned MoS 2 [5] in absence of a competing order, however, highlights the limits of our current understanding of the interplay between carrier concentration and superconductivity and motivates a fresh reexamination of superconducting domes. In the specific case of SrTiO 3 , superconductivity occurs in the vicinity of an aborted ferroelectric order[6] and survives deep inside the dilute metallic regime when the Fermi temperature becomes more than one order of magnitude lower than the Debye temperature [7]. This is a second puzzle in addition to the one raised by the drop in T c on the overdoped side. These two questions, raised at the opposite limits of the superconducting dome, remain unsettled.According to band calculations[9-11], doping SrTiO 3 with n-type carriers can fill three bands one after the other. Once the critical threshold for the occupation of a band is attained, a new Fermi surface concentric with the previous one emerges. Previous studies of quantum oscillations in bulk doped SrTiO 3 [7, 12-14] have detected both multiple-frequency [7,13,14] and singlefrequency [7,14] oscillations at different doping levels, but did not determine these critical doping levels. Moreover, according to tunneling experiments, doped SrTiO 3 beyond a carrier density of 10 19 cm −3 is a multi-gap superconductor [8]. The interplay between multi-band occupation in the normal state and multi-gap superconductivity has been a subject of recent theoretical attention [20].We present a systematic study of quantum oscillations and superconducting transition as a function of carrier con...

Interface superconductivity

“…The shape of the T c versus doping curves obtained by Lin et al are possibly linked to the filling of different bands [55]. Interfacial superconductivity develops only around a density of about 1 10 19 cm −3 .…”

“…While the maximum T c is about the same for both LAO/STO and bulk STO, the doping range over which superconductivity is found in crystals is broad. Figure 7 shows the bulk T c versus the 3D carrier density reported in various studies [54,55] along with our own data on Nb-doped STO crystals. Also shown is the 3D carrier density at which superconductivity develops for the LAO/STO interface.…”

A ferroelectric quantum phase transition inside the superconducting dome of Sr1−xCaxTiO3−δ

“…According to our data, at least in a finite window between the two local maxima close to two critical doping levels, n c1 and n c2 , of Ca-free SrTiO 3−δ (ref. 6), superconductivity is strengthened by Ca substitution. As sketched in Fig.…”

“…We find that T c is enhanced in the vicinity of the critical doping at which the ferroelectric-like order is destroyed (n * Ca = 1.7 × 10 19 cm −3 in Sr 0.991 Ca 0.009 TiO 3−δ ). For this level of Ca content, n * Ca lies between the two critical doping levels, n c1 and n c2 , of Ca-free SrTiO 3−δ where the T c is almost flat 6 . A definite confirmation of the quantum critical scenario requires an extensive study employing bulk probes 29 and confirming that the enhancement in critical temperature occurs always near n * Ca , which shifts with Ca content, and is not pinned to n c1 and n c2 .…”

“…1d), with frequencies 5,6,21 matching the carrier density expected from the magnitude of the Hall coefficient. This dilute metal is subject to a superconducting instability 2,5,6 . The aim of this study is to find what happens to metallicity and ferroelectricity when one removes oxygen and substitutes Sr with Ca.…”