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A central problem in modern condensed matter physics is the understanding of materials with strong electron correlations. Despite extensive work, the essential physics of many of these systems is not understood and there is very little ability to make predictions in this class of materials. In this manuscript we share our personal views on the major open problems in the field of correlated electron systems. We discuss some possible routes to make progress in this rich and fascinating field. This manuscript is the result of the vigorous discussions and deliberations that took place at Johns Hopkins University during a three-day workshop January 27, 28, and 29, 2020 that brought together six senior scientists and 46 more junior scientists. Our hope, is that the topics we have presented will provide inspiration for others working in this field and motivation for the idea that significant progress can be made on very hard problems if we focus our collective energies. 

Motivated by recent experiments on pump-induced polar ordering in the quantum paraelectric Sr⁢Ti⁢O3, we study a driven phonon system close to a second-order phase transition. Analyzing its classical dynamics, we find that sufficiently strong driving leads to transitions into polar phases whose structures, determined by the light polarization, are not all accessible in equilibrium. In addition, for certain intensity profiles, we demonstrate the possibility of two-step transitions as a function of fluence. For even stronger field intensities, the possibility of period-doubling and chaotic behavior is demonstrated. Finally we develop a generalized formalism that allows us to consider quantum corrections to the classical dynamics in a systematic fashion. We predict a shift in the critical pump fluence due to quantum fluctuations with a characteristic dependence on the fluence increase rate that should be observable in experiment. 

Twisted interfaces between stacked van der Waals (vdW) cuprate crystals present a platform for engineering superconducting order parameters by adjusting stacking angles. Using a cryogenic assembly technique, we construct twisted vdW Josephson junctions (JJs) at atomically sharp interfaces between Bi₂Sr₂CaCu₂O_8+xcrystals, with quality approaching the limit set by intrinsic JJs. Near 45° twist angle, we observe fractional Shapiro steps and Fraunhofer patterns, consistent with the existence of two degenerate Josephson ground states related by time-reversal symmetry (TRS). By programming the JJ current bias sequence, we controllably break TRS to place the JJ into either of the two ground states, realizing reversible Josephson diodes without external magnetic fields. Our results open a path to engineering topological devices at higher temperatures.