Introduction to Charge Order in the Cuprates

The 1986 discovery of high-temperature superconductivity in La\(_{2-x}\)Ba\(_x\)CuO\(_4\) [1] quickly led to the synthesis of a wide variety of multinary copper-oxide compounds with even higher superconducting transition temperatures (\(T_{\text {c}}\)) [2]. Among others, these include other ‘214’ compounds, derived from La\(_2\)CuO\(_4\) (LCO), such as La\(_{2}\)CuO\(_{4+\delta }\), La\(_{2-x}\)Sr\(_x\)CuO\(_4\) (LSCO), La\(_{1.6-x}\)Nd\(_{0.4}\)Sr\(_x\)CuO\(_4\) (LNSCO), as well as the electron-doped Nd\(_{2-x}\)Ce\(_{x}\)CuO\(_4\) (NCCO); compounds having the ‘123’ structure as in YBa\(_2\)Cu\(_3\)O\(_{6+x}\) (YBCO), PrBa\(_2\)Cu\(_3\)O\(_{6+x}\) (PBCO), DyBa\(_2\)Cu\(_3\)O\(_{6+x}\) (DBCO) or (Ca\(_x\)La\(_{1-x}\))(Ba\(_{1.75-x}\)La\(_{0.25+x}\))Cu\(_3\)O\(_y\) (CLBLCO); and compounds with even more complicated structures such as Bi\(_2\)Sr\(_{2}\)CuO\(_{6+\delta }\) (Bi2201), HgBa\(_2\)CuO\(_{4+\delta }\) (Hg1201) and their double and trilayer derivatives Bi\(_2\)Sr\(_{2}\)CaCu\(_2\)O\(_{8+\delta }\) (Bi2212), Bi\(_2\)Sr\(_{2}\)Ca\(_2\)Cu\(_3\)O\(_{10+\delta }\) (Bi22-23) and HgBa\(_2\)CaCu\(_2\)O\(_{6+\delta }\) (Hg1212), HgBa\(_2\)Ca\(_2\)Cu\(_3\)O\(_{8+\delta }\) (Hg1223) respectively. The distinct crystal structures of each of these compounds leads to a wide variety of ordering tendencies, which often depend dramatically on slight changes in structural degrees of freedom. However, in all cases underlying similarities, including the presence of one or more CuO\(_2\) planes, lead to a generic phase diagram hosting antiferromagnetism, charge order, superconductivity and an enigmatic pseudogap phase.