2Spatial phase inhomogeneity at the nano-to microscale is widely observed in stronglycorrelated electron materials. The underlying mechanism and possibility of artificially controlling the phase inhomogeneity are still open questions of critical importance for both the phase transition physics and device applications. Lattice strain has been shown to cause the coexistence of metallic and insulating phases in the Mott insulator VO 2 . By continuously tuning strain over a wide range in single-crystal VO 2 micro-and nanobeams, here we demonstrate the nucleation and manipulation of one-dimensionally ordered metal-insulator domain arrays along the beams. Mott transition is achieved in these beams at room temperature by active control of strain. The ability to engineer phase inhomogeneity with strain lends insight into correlated electron materials in general, and opens opportunities for designing and controlling the phase inhomogeneity of correlated electron materials for micro-and nanoscale device applications. 3Correlated Electron Materials (CEMs) offer a wide spectrum of properties featuring various types of phase transitions, such as superconductivity, metal-insulator transition, and colossal magnetoresistance 1 . A spatial phase inhomogeneity or micro-domain structure is frequently observed in these materials 2 , where multiple physical phases co-exist at the nano-to microscale at temperatures where a pure phase is expected. Despite decades of investigation, the question of whether the phase inhomogeneity is intrinsic or caused by external stimuli (extrinsic) still remains largely unanswered. This question not only plays a critical role in our understanding of the CEM physics, but also directly determines the spatial scale of CEM device applications.Lattice strain, if tuned continuously, would be a sensitive means to shed light on the origin of the phase inhomogeneity. In contrast to conventional materials, where elastic deformation causes continuous, minor variations in material properties, lattice strain has profound influence on the electrical, optical, and magnetic properties of CEMs through coupling between the charge, spin, and orbital degrees of freedom of electrons 3 . If phase inhomogeneity is absent in strain-free, single-crystal specimens, but can be introduced and modulated by external strain, it would then be possible to eliminate or strain engineer the inhomogeneity and domains in CEMs for nanoscale device applications. Previous strain studies of CEMs have been limited to epitaxial thin films. Biaxial strain imposed from lattice mismatch with the substrate has been shown to remarkably enhance the order parameters in ferroelectric 4-6 and high-Tc superconducting epilayers 7 . In these films the lattice-mismatch strain distribution is complicated by misfit dislocations. In contrast, free-standing, single-crystal CEM nanostructures are dislocation-free, and can be subjected to coherent and continuously tunable external stress. CEM phase transitions and domain dynamics can then be explored through in s...

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Superheating and supercooling effects are characteristic kinetic processes in firstorder phase transitions, and asymmetry between them is widely observed. In materials where electronic and structural degrees of freedom are coupled, a wide, asymmetric hysteresis may occur in the transition between electronic phases. Structural defects are known to seed heterogeneous nucleation of the phase transition, hence reduce the degree of superheating and supercooling. Here we show that in the metal-insulator transition of single-crystal VO 2 , a large kinetic asymmetry arises from the distinct spatial extension and distribution of two basic types of crystal defects: point defects and twin walls.Nanometer-thick twin walls are constantly consumed but re-generated during the transition to the metal phase, serving as dynamical heterogeneous nucleation seeds and eliminating superheating; On the other hand, the transition back to the insulator phase relies on nucleation at point defects because twinning is structurally forbidden in the metal phase, leading to a large supercooling. By controlling the formation, location and extinction of these defects, the kinetics of the phase transition might be externally modulated, offering possible routes toward new memory and logic device technologies.3