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Doped SrTiO$_3$, one of the most dilute bulk systems to display superconductivity, is perhaps the first example of an unconventional superconductor, as it does not fit into the standard BCS paradigm. More than five decades of research has…
SrTiO$_3$ exhibits superconductivity for carrier densities $10^{19}-10^{21}$ cm$^{-3}$. Across this range, the Fermi level traverses a number of vibrational modes in the system, making it ideal for studying dilute superconductivity. We use…
Superconductivity has been observed in doped SrTiO$_3$ at charge-carrier densities below 10$^{18}$ cm$^{-3}$, where the density of states at the Fermi level of the itinerant electrons is several orders of magnitude lower than that of…
Bulk n-type SrTiO3 (STO) has long been known to possess a superconducting ground state at an exceptionally dilute carrier density. This has raised questions about the applicability of the BCS-Eliashberg paradigm with its underlying…
Superconductivity of doped SrTiO3 is proven to be a particular case of the broader concept of the non-adiabatic pairing mediated by phonons with frequency comparable or larger the Fermi energy. We argue that, for carrier concentrations…
Recent experiments on Nb-doped SrTiO$_3$ have shown that the superconducting energy gap to the transition temperature ratio maintains the Bardeen-Cooper-Schrieffer (BCS) value throughout its superconducting dome. Motivated by these and…
Recent experiments on electron- or hole-doped SrTiO$_{3}$ have revealed a hitherto unknown form of superconductivity, where the Fermi energy of the paired electrons is much lower than the energies of the bosonic excitations thought to be…
In our paper (W\"olfle and Balatsky, Phys. Rev. B 98, 104505 (2018)) we presented a microscopic theory of superconductivity for doped SrTiO$_{3}$ by proposing two pairing mechanisms acting simultaneously with relative strength depending on…
Surfaces and interfaces offer new possibilities for tailoring the many-body interactions that dominate the electrical and thermal properties of transition metal oxides. Here, we use the prototypical two-dimensional electron liquid (2DEL) at…
Doped SrTiO3 becomes a metal at extremely low doping concentrations n and is even superconducting with the superconducting transition temperature adopting a dome-like shape with the carrier concentration. It is shown here within the…
Several decades after the discovery of superconductivity in bismuthates, the strength of their electron-phonon coupling and its evolution with doping remain puzzling. To clarify these issues, polycrystalline hole-doped…
Electron-doped strontium titanate $\rm{SrTiO_3}$, known to be one of the most dilute superconductors, is investigated on the basis of the first-principles calculations. When the carrier density n decreases, the frequencies of the…
Superconductivity in low carrier density metals challenges the conventional electron-phonon theory due to the absence of retardation required to overcome Coulomb repulsion. In quantum critical polar metals, the Coulomb repulsion is heavily…
Motivated by the observation of superconductivity in SrTiO$_3$ and Bi, we analyze phonon-mediated superconductivity in three-dimensional systems at low carrier density, when the chemical potential $\mu$ (equal to Fermi energy at $T=0$) is…
W\"olfle and Balatsky Phys. Rev. B 98, 104505 (2018) have proposed a microscopic pairing mechanism for doped SrTiO$_3$ (STO) based on the ${\textit gradient}$ coupling of electronic density to the soft TO phonon mode. Since this coupling to…
The soft ferro-electric phonon in SrTiO3 observed with optical spectroscopy has an extraordinary strong spectral weight which is much stronger than expected in the limit of a perfectly ionic compound. The "charged phonon" in SrTiO3 is…
Superconductivity in doped SrTiO$_3$ was discovered in 1964, the first superconducting transition observed in a doped semiconductor. However, the mechanism of electron pairing in SrTiO$_3$ remains a subject of debate. By developing a…
Superconductivity in doped SrTiO$_3$ has remained an enduring mystery for over 50 years. The material's status as a ``quantum" ferroelectric metal, characterized by a soft polar mode, suggests that quantum criticality could play a pivotal…
Doped strontium titanate SrTiO$_3$ (STO) is one of the most dilute superconductors known today. The fact that superconductivity occurs at very low carrier concentrations is one of the two reasons that the pairing mechanism is not yet…
Superconductivity in novel bismuth-sulphur superconductors has attracted large research efforts, both experimental and theoretical, but a consensus on the nature of superconductivity in these materials has yet to be reached. Using density…