Can a truly free-standing monolayer (say, of silicon or a complex oxide) exist without tearing? The challenge is and thermal fluctuations . A 2D crystal is an entropy-defying object; at any finite temperature, long-wavelength fluctuations can crumple it. The theory (Mermin-Wagner) says true long-range crystalline order is impossible in 2D—but real materials are finite and have bending rigidity.
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Historically, studying 2D materials meant growing them on a foreign substrate (like silicon or sapphire). However, the substrate interferes. It dopes the material, screens electron interactions, and stifles thermal vibrations.