Microscopic Theory of Superionic Phase Transitions: Nonadiabatic Dynamics and Many-Body Effects

Abstract

Superionic phase transitions have attracted extensive interest for decades due to their promising applications and rich underlying physics. In particular, complicated many-body effects and nonadiabatic dynamics are believed to play essential roles, limiting the explanatory power of phenomenological approaches and obscuring the microscopic mechanisms at play. In this work, we develop a unified theoretical framework for describing solid-state ionic conduction. After reviewing the conventional approximations, we construct a general lattice model that applies to both normal ionic and superionic conductors. By incorporating the nonadiabatic concerted-hopping mechanism and the many-body Coulomb interaction within a self-consistent mean-field scheme, we identify these two effects as the fundamental driving forces behind type-I and type-II superionic phase transitions, respectively. Our model directly reproduces key experimental observations. Within this unified framework, we further provide a comprehensive comparison between the two types of transitions. Overall, our work offers microscopic insight into superionic phase transitions and provides guidance for the design and optimization of advanced solid-state ionic conductors.

Figures (5)

• Figure 1: Schematic of physical pictures for normal ionic conduction. (a) Thermally excited crystal lattice as an incoherent superposition of thermal phonons. (b) Mobile ions that are confined within the adiabatic potential given by the host lattice do stochastic motion driven by the thermal excitation (schematicized as a heat bath). Tight-binding approximation further simplifies the potential landscape into lattice of sites and inter-site transitions.
• Figure 2: Schematic of ensemble-averaged evolution along different phonon modes. For each time step $t\rightarrow t+\tau$, the ionic density can evolve through thermal energy exchange with different phonon modes $(s_l,\bm{q}_l), l=1,2,\ldots$. The statistically observable evolution is then averaged over all possible channels. Note that the initial-phase configuration of Eq. \ref{['eq:trajectory_mode_initial_phase']} is not explicitly schematized.
• Figure 3: Results of 1D model. Schematic (a) without and (b) with the external electric field. (c) Eigenvalues of '$+$' branch with parameters $P_0=0.60, \gamma=0.88,f=0.5$. The absolute stable mode is at $k=0$ with $\kappa_{k,+}=0$.
• Figure 4: Self-consistent mean-field calculation of one-dimensional model. (a) Schematic of many-body effect: the hopping ion will receive Coulomb repulsion from neighboring mobile ions. (b) Ionic polarization $\gamma$ and (c) ionic conductivity with weak nonadiabatic strength $M_0=0.25$ eV, which yield type-II superionic phase transition. (d) Schematic of nonadiabatic hopping: when one ion hops, it compresses the host lattice so that reduces the hopping barrier of the neighboring ions. (e) Average hopping possibility $P_0$, and (f) ionic conductivity with strong nonadiabatic effect $M_0=2.0$ eV, which yield type-I superionic phase transition. Data in type-I superionic phase is not plotted since they are not valid due to the breakdown of tight-binding approximation. Inter-site Coulomb repulsion strength $K_0=0.5$ eV; single-particle adiabatic hopping barrier $\Lambda_0=0.25$ eV; filling number $n_0=1$. Note that the type-II transition temperature $T_{\rm p}$ is used as a reference temperature for the plot.
• Figure 5: Schematic of 2D honeycomb model. (a) Structure of MCrX$_2$ (M=Cu,Ag; X=S,Se). (b,c) Schematic of nearest-neighboring ionic hopping.