Interplay between Ferrolectricity And Superconductivity

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Among doped semiconductors with a superconducting ground state, SrTiO3 is distinguished by the precocity of its superconductivity. With only 10-5 electrons per formula unit(f.u.), the system becomes superconducting. When carrier density exceeds 0.02/f.u., it ceases to be so. This superconducting dome raises two distinct and still unanswered questions: how does superconductivity persist in the dilute limit despite the hierarchy inversion between Fermi and Debye temperatures? Why does it disappear on the overdoped side in spite of the steady increase in the electronic density of states? The insulating parent of this remarkable superconductor is a quantum paraelectric, which becomes a true ferroelectric by replacing strontium with calcium. The two partners have recently discovered that the two orders coexist in Ca-substituted-oxygen-deficient strontium titanate. At first sight, such a coexistence appears surprising. Ferroelectricity is a state of matter in which the solid hosts a macroscopic reversible static electric dipole. Since mobile electrons of a metal are expected to screen such a dipole, only ionic insulators which lack inversion symmetry are expected to qualify as true ferroelectrics. Superconductivity is an electron instability in a metal triggered by an attractive interaction overcoming the Coulomb repulsion among electrons and creating Cooper pairs which condensate macroscopically. These two states of matter have little in common. Their mutual exclusiveness was considered even stronger than the documented animosity between superconductivity and magnetism. However, we have found that when mobile electrons and electric dipoles are both dilute, they can coexist and the superconducting instability of electrons and ferroelectric alignment of dipoles do not impede each other. This experimental observation raises a host of new questions: How many mobile electrons does it take to screen a dipole and how do the dynamical aspects of the screening process have to be considered in the dilute limit? How do dipoles inside a Fermi sea communicate with each other? How do Cooper pairs and aligned dipoles interact? How to compare ferroelectric quantum criticality with its magnetic counterpart?This proposal aims to document the consequences of the proximity between ferroelectric, superconducting and antiferrodistortive orders in SrTiO3 subject to various dopants (niobium, lanthanum, calcium, barium, oxygen vacancies…) as well as in its sister compound EuTiO3. The two partners possess complementary expertise. The German partner has been active in exploring the complex conductance in a broad range of frequency and has strong expertise in single-crystal growth of rare-earth titanates and thermodynamic studies of quantum phase transitions. The French partner has been studying electric, thermoelectric and thermal transport at zero frequency in extreme conditions of temperature and magnetic field.