Theory of Quantum Oscillations in Cuprate Superconductors

Cuprate supercoductors show pseudogap state below its transition temperature T*. The pseudogap state is distinct from superconducting state (critical temperature Tc < T*). Two states may coexist and superconductivity developes from the pseudogap state which can be explained by commensurate and incommensurate d-density wave (dDW) orders. Quantum oscillations help us to understand the pseudogap state. Hall coefficient, magnetization, conductance and specific heat oscillate as a function of external field in YBa2Cu 3O6+delta (YBCO), Nd2-xCexCuO 4 (NCCO) and other cuprates. The oscillation frequency F is proportional to the area of closed-orbits in reconstructed Fermi surface. High magnetic field for quantum oscillation experiment suppresses superconductivity. Therefore, quantum oscillations measure reconstructed Fermi surface of pseudogap state.;Electron-doped cuprate superconductor NCCO shows only hole pocket frequency peak. Experimental results can be explained by period-2 dDW order and white-noise disorder. Disorder in the system removes electron pocket frequency and adjusts the amount of magnetic breakdown effect corresponding to very high frequency. Period-8 density wave order can explain quantum oscillations in the pseudogap state of hole-doped YBCO. Only electron pocket frequency is observed. Period-8 dDW order generates small but many hole pockets in the reconstructed Fermi surface. Small hole pocket frequency is too slow to be observed.