Layered XZnBi (X = Rb, Cs) with Pudding-Mold Bands, Complex Fermi Surfaces and Low Thermal Conductivity: A First-Principles Study of Thermoelectric Properties

TL;DR

This work addresses the challenge of achieving high thermoelectric performance by exploiting stacking order and complex Fermi-surface topology in layered Zintl compounds XZnBi (X=Rb, Cs). Using first-principles electronic structure calculations with SOC, Boltzmann transport, and explicit electron–phonon coupling (EPW), the authors reveal pudding-mold conduction bands and sixfold valence-pocket degeneracy that favor Seebeck coefficient and conductivity, while lattice dynamics yield ultra-low $k_l$ and strong anisotropy. A key finding is that relaxing time modeling matters: CRTA overestimates transport and ZT, whereas EPW-based results produce more realistic values (e.g., $Z T$ around 0.5–1.0 at high temperatures) and highlight stacking as a critical design parameter, with AB CsZnBi showing particularly favorable phonon scattering. These insights provide practical design principles for engineering high-efficiency Zintl thermoelectrics through stacking control and accurate scattering treatments. $k_l$ values are below 2 W m$^{-1}$ K$^{-1}$, and the pudding-mold band structure enables a favorable balance of carrier mobility and DOS; together, these features offer a route to improved TE performance in layered Zintl systems.

Abstract

Layered Zintl compounds exhibit significant tunability of thermoelectric (TE) parameters facilitated by their multiple elemental combinations and flexibility in stacking order within the layers. In this work, the effect of stacking order on TE properties of theoretically predicted layered Zintl compounds XZnBi (X = Rb, Cs) is studied using 1st-principles calculations and Boltzmann equations. The materials are semiconductors having moderate band gaps ranging from 0.44 to 0.52 eV. There exist six identical hole pockets for valence band maxima due to the crystal symmetry. This leads to high band degeneracy but simultaneously promotes intervalley scatterings. While as for conduction bands, the Fermi surface consists of a single but highly anisotropic, quasi-two dimensional electron pockets with cylindrical shape along z-axis. This kind of Fermi surface is a characteristic of a pudding mold band shape. It facilitates a unique combination of heavy and light electron masses, simultaneously optimizing Seebeck coefficient and electrical conductivity. At first, electronic transport coefficients are calculated using constant relaxation time approximation (CRTA) or electron-phonon coupling matrix elements (el-ph). The calculated relaxation times are then integrated with transport results to get the realistic values of TE parameters. The analysis of three-phonon scattering reveals low thermal conductivity ($k_{l}$) below 2 W/m/K in these compounds. The $k_{l}$ also depends on stacking order with the values of nearly half in AB stacking as compared to that of AA stacking. These combined factors lead to a high ZT at 900 K, reaching to a maximum of 2.42 using CRTA and 0.52 when el-ph are included. The study highlights the potential of XZnBi systems as promising TE materials as well as the critical roles of stacking and el-ph in accurately evaluating TE properties.

Figures (10)

• Figure 1: Crystal structure of XZnBi in AA stacking (left) and AB stacking (right) as seen along (a, c) x-y direction and (b, d) z-direction.
• Figure 2: Electronic band structure of RbZnBi (a, c) and CsZnBi (b, d) in AA and AB stacking, respectively, along high-symmetry paths. The $\Gamma$-K and $\Gamma$-M paths are in x-y plane while $\Gamma$-Z is along z-axis.
• Figure 3: Electron and hole pockets near conduction band minimum (CBM) and valence band maximum (VBM) for RbZnBi (a, c) and CsZnBi (b, d) in AB stacking. Isoenergy values of 0.35 eV (CBM) and 0.22 eV (VBM) are used above and below the Fermi level, respectively
• Figure 4: Temperature and direction dependent electron and hole relaxation times ($\tau$) for XZnBi in (a) AA and (b) AB stacking configurations.
• Figure 5: (a) Anisotropic lattice thermal conductivity ($k_{l}$) as a function of temperature along x (z) direction in AA and AB stacked XZnBi. (b) Cumulative lattice thermal conductivity as a function of mean free path along different directions and staking orders.