Narrow Results

STM/STS is used to examine the charge order in the pseudogap state on underdoped Bi2212 crystals with different hole-doping levels (p). We report that although the data for the period of charge order are slightly scattered, it is nearly 4a × 4a (a: the lattice constant) and exhibits no obvious dependence on p in the p-range examined.

STM/STS experiments have been performed in ${\mathrm{\text{Bi}}}_2{\mathrm{\text{Sr}}}_{1.7}{\mathrm{\text{R}}}_{0.3}{\mathrm{\text{CuO}}}_{6+\delta }$ (R-Bi2201) systems with $\mathrm{\text{R}}=\mathrm{\text{La}}$ and Eu, which are of a nearly optimal doping level $p_o$ but have different $T_c$ values, 35 K and 20 K, respectively, to examine interplane disorder effects on the superconducting (SC) gap and the pseudogap (PG) that is accompanied by a checkerboard-type charge order (CCO). We report that as interplane disorders are strengthened by replacing La with Eu in optimal Bi2201, the antinodal PG size ${\Delta }^{\ast }$ increases from $\sim 30\mathrm{\text{meV}}$ to $\sim 60\mathrm{\text{meV}}$, which is comparable to the value for an underdoping level $p∕p_o\sim 0.5$ in La-Bi2201. On the other hand, the period of CCO in optimal Eu-Bi2201 is the same as in optimal La-Bi2201, about five times lattice constant $\sim 5a$ along the Cu–O bond directions; it remains unchanged even if the PG develops markedly to the same degree as for $p∕p_o\sim 0.5$ in La-Bi2201, whose period is $\sim 4a$.

The recently discovered charge order is an intrinsic and universal property of cuprate superconductors, however, its microscopic origin remains debated. Here we review briefly the theoretical work about the nature of charge order in cuprate superconductors. In particular, we show that the electron self-energy obliterates the electron Fermi surface around the antinodal region, leaving behind disconnected Fermi arcs located around the nodal region. The charge-order state on the other hand is driven by the Fermi-arc instability, with a characteristic wavevector corresponding to the hot spots of the Fermi arcs rather than the antinodal nesting vector. Since the pseudogap emanates from the electron self-energy, the Fermi arc, charge order, and pseudogap in cuprate superconductors are intimately related each other.

Within the framework of the t-t${}^{\prime }-$J model, the evolution of the charge-order state with the next nearest-neighbor (NN) hopping in the electron-doped cuprate superconductors is studied. It is shown that although the magnitude of the charge-order wave vector increases with the increase of the next NN hopping in the hole-doped case, the charge-order wave vector in the electron-doped side decreases with the increase of the next NN hopping, reflecting an asymmetric next NN hopping dependence of the charge-order state between the hole- and electron-doped cuprate superconductors.

The multi-step transition by the field inducement is reported in pristine Pr_2/3Ca_1/3-MnO₃ manganites. This step effect shows a strong dependence on the temperature and field sweep rate, which is sensitive to thermal perturbation. The results prove that they are related with the internal magnetic structure of phase-separated Pr_2/3Ca_1/3MnO₃ manganites in low temperatures, while the influence of sweep rate can be accounted for within a martensitic-like scenario.