Much of the focus of modern condensed matter physics concerns control of quantum phases with examples that include flat band superconductivity in graphene bilayers (1), the interplay of magnetism and ferroelectricity (2), and induction of topological transitions by strain (3). Here we report the first observation of a reproducible and strong enhancement of the superconducting critical temperature, Tc, in strontium titanate (SrTiO3) obtained through careful strain engineering of interacting superconducting phase and the polar quantum phase (quantum paraelectric). Our results show a nearly 50% increase in Tc with indications that the increase could become several hundred percent. We have thus discovered a means to control the interaction of two quantum phases through application of strain, which may be important for quantum information science. Further, our work elucidates the enigmatic pseudogap-like and preformed electron pairs phenomena in low dimensional strontium titanate (4, 5) as potentially resulting from the local strain of jammed tetragonal domains. Main text:Among the main goals of this work is to address the open question of the nature of the superconducting pairing mechanism in strontium titanate (STO) (6, 7) and to inspire searches for enhanced superconducting temperatures in materials not just with suppressed to zero Kelvin structural transitions, as in (CaxSr1−x)3Rh4Sn13 (8), MoTe2 (9) and Lu(Pt1−xPdx)2In ( 10), but with incipient quantum phase transitions, for example, ScF3 which has a structural quantum phase transition (11), and may become superconducting when doped (12). It has been predicted that superconducting doped strontium titanate with its peculiar phonon dynamics (13-17) is an example of a superconductivity arising near an incipient quantum polar (quantum ferroelectric) phase transition (4,7,(18)(19)(20)(21)(22)(23)(24)(25)(26)(27), but this has not been fully demonstrated experimentally, in part, due to the fact that existing results on isotope effect and Ca substitution (25, 28) may be explained by non-uniformity in the chemical composition, and the absolute enhancement of the critical temperature values have not been found.It is also unusual to find a pseudogap-like behavior in superconductors that cannot be explained by compositional inhomogeneities, as is the case in cuprates (29). A pseudogap-like behaviors, such as a tunneling gap and a 2e charge transport, occur in STO at temperatures up to about 0.9 K, almost twice the bulk superconducting transition temperature (4, 5).

Magnetic Weyl semimetals are predicted to host emergent electromagnetic fields at heterogeneous strained phases or at the magnetic domain walls. Tunability and control of the topological and magnetic properties are crucial for revealing these phenomena, which are not well understood or fully realized yet. Here, a scanning superconducting quantum interference device microscope is used to image spontaneous magnetization and magnetic susceptibility of CeAlSi, a noncentrosymmetric ferromagnetic Weyl semimetal candidate. Large metastable domains are observed alongside stable ferromagnetic domains. The metastable domains most likely embody a type of frustrated or glassy magnetic phase, with excitations that may be of an emergent and exotic nature. Evidence is found that the heterogeneity of the two types of domains arises from magnetoelastic or magnetostriction effects. It is shown how these domains form, how they interact, and how they can be manipulated or stabilized with lattice strains estimated to be on picometer levels. This knowledge can be used in designing and fabricating devices made from CeAlSi and related materials for magnetic field sensing and magnetic memory applications.