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Memristor is a promising building block for the next generation nonvolatilerandom access memory and bio-inspired computing systems. Organizing memristorsinto high density crossbar arrays, although challenging, is critical to meetthe ever-growing high capacity and low energy demands of these applicationsespecially in the big data era. Here, we construct memristor crossbars with asingle-layer density up to 4.5 terabits per inch square, an order of magnitudedenser than the state- of-the-art 64-layer triple level cell NAND flashtechnology. The memristors in the crossbars are 2 $\times$ 2 nm$^2$ in size,capable of switching with tens of nano ampere electric current. The denselypacked memristor crossbars of extremely small working devices provides apower-efficient solution for high density information storage and processing.

Memristor Crossbars with 4.5 Terabits-per-Inch-Square Density and Two Nanometer Dimension