Quantum Critical Origin of the Superconducting Dome in ${\mathrm{SrTiO}}_{3}$

Quantum Critical Origin of the Superconducting Dome in ${SrTiO}_{3}$

Jonathan M. Edge, Yaron Kedem, Ulrich Aschauer, Nicola A. Spaldin, and Alexander V. Balatsky

Phys. Rev. Lett. 115, 247002 – Published 10 December 2015; Erratum Phys. Rev. Lett. 117, 219901 (2016)

Abstract

We expand the well-known notion that quantum criticality can induce superconductivity by proposing a concrete mechanism for superconductivity due to quantum ferroelectric fluctuations. To this end, we investigate the origin of superconductivity in doped ${SrTiO}_{3}$ using a combination of density functional and strong coupling theories within the framework of quantum criticality. Our density functional calculations of the ferroelectric soft mode frequency as a function of doping reveal a crossover related to quantum paraelectricity at a doping level coincident with the experimentally observed top of the superconducting dome. Thus, we suggest a model in which the soft mode fluctuations provide the pairing interaction for superconductivity carriers. Within our model, the low doping limit of the superconducting dome is explained by the emergence of the Fermi surface, and the high doping limit by departure from the quantum critical regime. We predict that the highest critical temperature will increase and shift to lower carrier doping with increasing ${}^{18}O$ isotope substitution, a scenario that is experimentally verifiable. Our model is applicable to other quantum paraelectrics, such as ${KTaO}_{3}$ .

Received 29 July 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.247002

Erratum

Erratum: Quantum Critical Origin of the Superconducting Dome in ${SrTiO}_{3}$ [Phys. Rev. Lett. 115, 247002 (2015)]

Jonathan M. Edge, Yaron Kedem, Ulrich Aschauer, Nicola A. Spaldin, and Alexander V. Balatsky

Phys. Rev. Lett. 117, 219901 (2016)

Authors & Affiliations

Jonathan M. Edge¹, Yaron Kedem^1,*, Ulrich Aschauer², Nicola A. Spaldin², and Alexander V. Balatsky^3,1,†

¹Nordita, Center for Quantum Materials, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden
²Materials Theory, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zürich, Switzerland
³Institute for Materials Science, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

^*Corresponding author. kedem@kth.se
^†avb@lanl.gov

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Vol. 115, Iss. 24 — 11 December 2015

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Figure 1
Literature values of the superconducting critical temperature [3] (circles) and calculated frequencies (this work) of the ferroelectric modes parallel ( $∥$ ) and perpendicular ( $⊥$ ) to the axis of the AFD rotations (red solid and dashed lines) as a function of the carrier concentration. The imaginary frequencies obtained at low doping indicate negative restoring forces corresponding to ferroelectric instabilities; as the carrier concentration is increased the ferroelectric mode hardens and its phonon frequency becomes real. The inset shows the calculated energy as a function of ferroelectric mode amplitude for various doping levels, illustrating the crossover from the classic ferroelectric double well potential energy to a single well, indicating a paraelectric ground state on increasing doping. As the charge carrier concentration is increased, $T_{c}$ first increases and then decreases, forming the characteristic superconducting dome. We see that the doping concentration at which $T_{c}$ drops to zero, $\sim 10^{20} e / {cm}^{3}$ , closely matches that at which the ferroelectric mode hardens.
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Figure 2
(a) Schematic phase diagram of STO as a function of carrier doping and isotope replacement. The orange circles mark the experimentally measured transition to superconductivity, as observed in Ref. [3]. The blue circles are the measured transition temperatures [14] from the paraelectric (PE) to the ferroelectric (FE) phase as a function of ${}^{18}O$ isotope substitution. Our DFT calculations suggest that the ferroelectric phase penetrates slightly into the nonzero doping regime, but then quickly disappears as doping suppresses ferroelectricity, although no experimental data for this transition line is available. The maximal value of doping at which the ferroelectric phase persists is labeled as $n^{*}$ . Although we have no precise calculation for $n^{*}$ , its value should lie in the range $10^{19} < n^{*} < 10^{20}$ . (b) Schematic illustration for the lowering of the lowest energy levels (dashed red lines) in the double well potential (black solid line) as $f_{18}$ is increased.
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Figure 3
Calculated $T_{c}$ as a function of doping level for several fractions of isotope replacement, $f_{18}$ . The blue diamonds are experimental results taken from Ref. [3]. Replacing ${}^{16}O$ with ${}^{18}O$ moves the QCP closer to the doping range relevant for superconductivity and causes a significant enhancement in $T_{c}$ . We use the parameters $A = 0.4$ , $B = 1 0^{- 6}$ $K^{- 2}$ , $C = 2.5 \times 10^{- 3} K^{- 1}$ , $D = 95 K^{1 / 2}$ , as defined in the main text.
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Physical Review Letters

Quantum Critical Origin of the Superconducting Dome in SrTiO3

Jonathan M. Edge, Yaron Kedem, Ulrich Aschauer, Nicola A. Spaldin, and Alexander V. Balatsky

Phys. Rev. Lett. 115, 247002 – Published 10 December 2015; Erratum Phys. Rev. Lett. 117, 219901 (2016)

Abstract

Erratum

Erratum: Quantum Critical Origin of the Superconducting Dome in SrTiO3 [Phys. Rev. Lett. 115, 247002 (2015)]

Jonathan M. Edge, Yaron Kedem, Ulrich Aschauer, Nicola A. Spaldin, and Alexander V. Balatsky

Phys. Rev. Lett. 117, 219901 (2016)

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Quantum Critical Origin of the Superconducting Dome in ${SrTiO}_{3}$

Erratum: Quantum Critical Origin of the Superconducting Dome in ${SrTiO}_{3}$ [Phys. Rev. Lett. 115, 247002 (2015)]