Small bipolarons and extended states of guest Na and Rb atoms in quasi-two-dimensional disordered $M_{7.8-\delta }{\mathrm{Al}}_{7.8}{\mathrm{Si}}_{8.2}{\mathrm{O}}_{32.0}$ ($M$=Na, Rb)

The evolution of the electronic properties of guest Na and Rb atoms in a disordered deformable lattice is investigated for a series of guest-atom densities $n$. The quasi-two-dimensional host $M_{7.8-\delta }{\mathrm{Al}}_{7.8}{\mathrm{Si}}_{8.2}{\mathrm{O}}_{32.0}$ ($M$=Na, Rb), known as zeolite P, is used. The Na system is a stubborn bipolaronic insulator to the maximum $n$ of 1.03. In contrast, the Rb system exhibits a crossover from a bipolaronic insulator to a conducting phase analogous to a disordered metal at $n$ = 0.89. A critical region undergoing polaronic melting appears in the vicinity of the crossover on the insulating side, evidenced by a reduction in the small bipolaron absorption band and a drop in the activation energy. Transition to the conducting phase coincides with the appearance of a midinfrared band and an increase in the charge-carrier decay length, suggesting the polaronic and extended nature of the carriers. These findings constitute rare examples of electron-lattice coupling opening (or closing) a mobility gap and scaling the continuity (or discontinuity) of a conducting transition in the face of disorder.

Figure 1

The structure of the host material. (a) Aluminosilicate framework of zeolite P. The constructing element, the GIS cage with Si/Al = 1, is illustrated on the right-hand side. The purple spheres represent the cations (Na or Rb) that form the deformable lattice. The blue dotted lines represent the connections between cage voids of adjacent channels forming a diamond lattice. (b) Channel view along the $b$ (or $a$) axis. SEM images of (c) Na-form and (d) Rb-form zeolite P.

Figure 2

Room-temperature optical absorption spectra of (a) ${\mathrm{Na}}_n$/${\mathrm{Na}}_2$-P and (b) ${\mathrm{Rb}}_n$/${\mathrm{Rb}}_2$-P. The dotted lines in (b) starting at $n$ = 0.81 indicate reduction in the band at approximately 8500 ${\mathrm{cm}}^{-1}$. Best fits of small-polaron absorption [Eq. (1)] on ${\mathrm{Na}}_n$/${\mathrm{Na}}_2$-P (c) at $n$ = 0.05 and (d) at $n$ = 0.41 and on ${\mathrm{Rb}}_n$/${\mathrm{Rb}}_2$-P (e) at $n$ = 0.12. (f) Absorption bands of ${\mathrm{Na}}_n$/${\mathrm{Na}}_2$-P and ${\mathrm{Rb}}_n$/${\mathrm{Rb}}_2$-P at the lowest values of $n$.

Figure 3

Transport properties of ${\mathrm{Na}}_n$/${\mathrm{Na}}_2$-P, ${\mathrm{K}}_n$/${\mathrm{K}}_2$-P, and ${\mathrm{Rb}}_n$/${\mathrm{Rb}}_2$-P. (a) The $T$ dependence of $\rho$ pertaining to ${\mathrm{Rb}}_n$/${\mathrm{Rb}}_2$-P. (b) The $n$ dependence of $\rho$ at 300 K for ${\mathrm{Na}}_n$/${\mathrm{Na}}_2$-P, ${\mathrm{K}}_n$/${\mathrm{K}}_2$-P [15], and ${\mathrm{Rb}}_n$/${\mathrm{Rb}}_2$-P. The dashed lines are guides for the eye. The vertical green and blue dotted lines indicate the $n$ at which a conducting phase is observed in ${\mathrm{Rb}}_n$/${\mathrm{Rb}}_2$-P and ${\mathrm{K}}_n$/${\mathrm{K}}_2$-P [15], respectively. (c) Fits of the model given in Eq. (2) for ${\mathrm{Rb}}_n$/${\mathrm{Rb}}_2$-P. (d) The $n$ dependence of estimated $\mathrm{\Delta }E$ for ${\mathrm{Rb}}_n$/${\mathrm{Rb}}_2$-P. The shaded area marks a critical region, as explained in the text. The vertical dotted line indicates the conducting phase at $n=0.89$.

Figure 4

Magnetic properties of ${\mathrm{Na}}_n$/${\mathrm{Na}}_2$-P and ${\mathrm{Rb}}_n$/${\mathrm{Rb}}_2$-P. The $T$ dependence of $\chi$ pertaining to (a) ${\mathrm{Na}}_n$/${\mathrm{Na}}_2$-P, at $n=0.29$, 0.41, 0.71, 0.83, and 1.03, and (b) ${\mathrm{Rb}}_n$/${\mathrm{Rb}}_2$-P, at $n=0.29$, 0.52, 0.70, 0.81, and 0.89. Curie-Weiss fit for (c) ${\mathrm{Na}}_n$/${\mathrm{Na}}_2$-P, at $n=0.71$, and (d) ${\mathrm{Rb}}_n$/${\mathrm{Rb}}_2$-P, at $n=0.70$. (e) The $n$ dependence of estimated $C$ for ${\mathrm{Na}}_n$/${\mathrm{Na}}_2$-P and ${\mathrm{Rb}}_n$/${\mathrm{Rb}}_2$-P. The right axis gives the percentage of guest electrons carrying a magnetic moment of spin $S$ = $\frac{1}{2}$. The vertical dotted line indicates the conducting phase of ${\mathrm{Rb}}_n$/${\mathrm{Rb}}_2$-P at $n=0.89$.

Figure 5

Phase diagram of ${\mathrm{Rb}}_n$/${\mathrm{Rb}}_2$-P depicting a continuous transition from localized to critical to extended states.