Crossover in charge transport from one-dimensional copper-oxygen chains to two-dimensional ladders in ${\left(\text{La},\text{Y}\right)}_y{\left(\text{Sr},\text{Ca}\right)}_{14-y}{\text{Cu}}_{24}{\text{O}}_{41}$

The charge transport in the copper-oxygen chain/ladder layers of ${\left(\text{La},\text{Y}\right)}_y{\left(\text{Sr},\text{Ca}\right)}_{14-y}{\text{Cu}}_{24}{\text{O}}_{41}$ is investigated along two crystallographic directions in the temperature range from 50 to 700 K and for doping levels from $y\approx 6$ (number of holes $n_h<1$) to $y=0$ (number of holes $n_h=6$). A crossover from a one-dimensional hopping transport along the chains for $y\ge 3$ to a quasi-two-dimensional charge conduction in the ladder planes for $y\lesssim 2$ is observed. This is attributed to a partial hole transfer from chains to ladders when the hole doping exceeds $n_h\approx 4$ and approaches fully doped value $n_h=6$. For $y\lesssim 2$ a weak dielectric relaxation at radio frequencies and a microwave mode are detected, which might be recognized as signatures of a charge-density wave phase developed at short length scales in the ladder planes.

Figure 1

(Color online) dc resistivity and logarithmic derivatives of ${\left(\text{La},\text{Y}\right)}_y{\left(\text{Sr},\text{Ca}\right)}_{14-y}{\text{Cu}}_{24}{\text{O}}_{41}$ for various La/Y content $y$ along the $c$ [panels (a) and (b)] and the $a$ [panels (c) and (d)] crystallographic directions.

Figure 2

(Color online) Temperature dependence of the conductivity anisotropy of ${\left(\text{La},\text{Y}\right)}_y{\left(\text{Sr},\text{Ca}\right)}_{14-y}{\text{Cu}}_{24}{\text{O}}_{41}$ for various La/Y content $y$ normalized to the corresponding room temperature value.

Figure 3

Room temperature dc (circles) and ac conductivity at $10{\text{cm}}^{-1}$ (triangles) (Ref. 27) along the $c$ axis (left panel) and the $a$ axis (right panel) as a function of La/Y content $y$ and total hole count $n_h$. The full and dashed lines are guides to the eyes for dc and ac data, respectively.

Figure 4

Dielectric function and infrared conductivity in terahertz region of ${\text{Y}}_y{\text{Sr}}_{14-y}{\text{Cu}}_{24}{\text{O}}_{41}$ for various Y content $y=0.55$ (upper panel) and 1.6 (lower panel) along the $c$ and $a$ axes at several temperatures as indicated. Conductivity data for $y=0$ along the $a$ axis at 5 K (denoted as open triangles) are shown for comparison.

Figure 5

Conductivity spectra of $y=0$, 0.55, 1.6, and 3, $\mathbf{E}\parallel c$ in the radio-frequency range at representative temperatures (95, 125, 165, and 132.5 K, respectively) with comparable dc conductivities.

Figure 6

Real $\left({\epsilon }^{\prime }\right)$ and imaginary $\left({\epsilon }^{″}\right)$ parts of the dielectric function of ${\text{Y}}_y{\text{Sr}}_{14-y}{\text{Cu}}_{24}{\text{O}}_{41}$ for $y=0$ [panel (a)], $y=0.55$ [panel (b)], and $y=1.6$ [panel (c)] at representative temperatures of 125 K ($y=0$ and 0.55) and 145 K $\left(y=1.6\right)$ as a function of frequency, with the ac electric field applied along the $c$ axis. The full lines are fits to data using the generalized Debye expression $\epsilon \left(\omega \right)-{\epsilon }_{\text{HF}}=\Delta \epsilon /\left[1+{\left(i\omega {\tau }_0\right)}^{1-\alpha }\right]$.

Figure 7

Temperature dependence of mean relaxation times ${\tau }_0$ for $y=0.55$ and 1.6. Open and full circles are for $\mathbf{E}\parallel c$ and $\mathbf{E}\parallel a$, respectively.