Metal-Insulator Transition in a Deformable Lattice

Metal-insulator transition (MIT) in disorder systems with critical effects of electron-lattice coupling near the mobility edge remains under debate. A discontinuous transition between small (bi)polarons and extended states was proposed within the adiabatic approximation [1]. On the other hand, theoretical treatment of the MIT in a deformable lattice proposed a continuous transition [2]. Despite many zealous theoretical efforts, this remains unresolved. In addressing this, we experimentally investigate the MIT in a deformable lattice, controlling the random potential through electron-density modulation and electron-lattice coupling strength (λ) by varying the guest element (Na, K, Rb, or Cs) encapsulated within a quasi-two-dimensional host. Physical properties were investigated using optical, magnetic, transport, and electron spin resonance measurements. We bring to light the importance of the magnitude of λ on the conducting transition (or freezing) and its continuity (or discontinuity). We conjecture that both theories [1,2] apply, perhaps in distinct coupling regimes, and propose a phase diagram for the disorder- and polaron-driven MIT in a deformable lattice.
[1] M. H. Cohen et al., Phys. Rev. Lett. 51, 1202 (1983)
[2] D. Di Sante et al., Phys. Rev. Lett. 118, 036602 (2017)