Soft modes in semiconducting SrTiO3: II. The ferroelectric mode

Quantum Critical Origin of the Superconducting Dome inSrTiO3

“…1 we show how, on electron doping, the modulus of the mode frequency decreases, corresponding to a weakening of the ferroelectric instability, and the frequency eventually becomes real -signaling a single high-symmetry energy minimum (inset to Fig. 1) -at a doping concentration of ∼ 10 20 cm −3 , which is in agreement with experimental data [7]. Since there is now only one minimum of the potential well, there are clearly no quantum fluctuations between equivalent states.…”

“…The dielectric constant is strongly temperature dependent, and diverges at low temperature in a manner characteristic of a ferroelectric phase transition [6].In fully oxidised samples the square of the polar TO mode frequency decreases linearly with decreasing temperature and when extrapolated should become imaginary at finite temperature, indicative of a ferroelectric instability [7] at low temperature. Rather than manifesting ferroelectric behavior, however, STO is a so-called quantum paraelectric, in which quantum fluctuations at zero temperature suppress the transition to the ferroelectric state [6] as is also manifested by a leveling off of the TO mode at a real frequency at low temperature [7]. The quantum paraelectric state is characterized by low energy excitations and large ferroelectric fluctuations [8], and it has been speculated that these might be relevant for the superconductivity [9,10].…”

Superconductivity mediated by polar modes in ferroelectric metals

“…2b ) or decreasing gap of the soft transverse-optical polar phonon frequency 6,S1-S3,S32,S33 , Ω( q ), connected with the ferroelectric QCP. Ω( q ) is relatively weakly dependent on n up to of the order of 10 19 cm −3 S34,S35 30 and its n dependence is accounted for in the model calculations that follow. This behaviour is reminiscent of the increase of T c observed on approaching magnetic QCPs in nearly magnetic metals 31 .…”

Doping and temperature-dependent optical properties of oxygen-reducedBaTiO3−δ

“…The origin of the soft mode hardening in SrTiO 3−δ has been discussed by Bäuerle et al 29 Based on the formalism proposed by Trunov et al 48 it was demonstrated that the role of the free carrier concentration in the soft mode hardening is negligible. The authors, therefore, have attributed the soft mode dependence in SrTiO 3−δ to the change in the long-range dipole-dipole interaction and local potential due to oxygen vacancies.…”

“…This effect is opposite to the case of the SrTiO 3−δ and Nb-doped SrTiO 3 crystals where the soft mode frequency increases with carrier density in a wide concentration range. 25,29 In the rhombohedral phase, T < 195 K, metallic B4 sample shows splitting of the soft mode into the low-and high-frequency components. The high-frequency component detected as a shoulder in the σ 1 (ω) plot at ω ≈ 242 cm −1 recovers to that of the undoped BaTiO 3 at ω T O1 ≈ 241 cm −1 .…”