Driven-dissipative systems in two dimensions can differ substantially from their equilibrium counterparts. In particular, a dramatic loss of off-diagonal algebraic order and superfluidity has been predicted to occur because of the interplay between coherent dynamics and external drive and dissipation in the thermodynamic limit. We show here that the order adopted by the system can be substantially altered by a simple, experimentally viable tuning of the driving process. More precisely, by considering the longwavelength phase dynamics of a polariton quantum fluid in the optical parametric oscillator regime, we demonstrate that simply changing the strength of the pumping mechanism in an appropriate parameter range can substantially alter the level of effective spatial anisotropy induced by the driving laser and move the system into distinct scaling regimes. These include (i) the classic algebraically ordered superfluid below the Berezinskii-Kosterlitz-Thouless (BKT) transition, as in equilibrium; (ii) the nonequilibrium, longwavelength-fluctuation-dominated Kardar-Parisi-Zhang (KPZ) phase; and the two associated topologicaldefect-dominated disordered phases caused by proliferation of (iii) entropic BKT vortex-antivortex pairs or (iv) repelling vortices in the KPZ phase. Furthermore, by analyzing the renormalization group flow in a finite system, we examine the length scales associated with these phases and assess their observability in current experimental conditions.

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).

We investigate the effects of strain on superconductivity with particular reference to SrTiO3. Assuming that a ferroelectric mode that softens under tensile strain is responsible for the coupling, an increase in the critical temperature and range of carrier densities for superconductivity is predicted, while the peak of the superconducting dome shifts towards lower carrier densities. Using a Ginzburg-Landau approach in 2D, we find a linear dependence of the critical temperature on strain: if the couplings between the order parameter and strains in different directions differ while their sum is fixed, different behaviours under uniaxial and biaxial (uniform) strain can be understood.