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Strong Intra- and Interchain Orbital Coupling Leads to Multiband and High Thermoelectric Performance in Na$_2$Au$X$ ($X$ = P, As, Sb, and Bi)

Zhonghao Xia, Zhilong Yang, Yali Yang, Kaile Ren, Jiangang He

TL;DR

The study addresses the thermoelectric efficiency limit imposed by the intrinsic coupling among the Seebeck coefficient $S$, electrical conductivity $σ$, and lattice thermal conductivity $κ_L$. First-principles calculations reveal that Au-dz^2–X-pz intrachain hybridization together with interchain X-px/p_y coupling generates a highly dispersive multivalley valence band, enabling high PF while weakening interchain bonding suppresses $κ_L$. For p-type Na2AuBi, the predicted PF is 63.9 μW cm^-1 K^-2, $κ_L$ is 0.49 W m^-1 K^-1, and $ZT$ reaches 4.7 at 800 K along the zigzag chain direction. This work introduces a design paradigm that decouples charge and phonon transport by balancing strong orbital overlap with weak interchain bonding, offering a route to high-performance thermoelectrics in quasi-one-dimensional systems.

Abstract

The intrinsic coupling among electrical conductivity ($σ$), Seebeck coefficient ($S$), and lattice thermal conductivity ($κ_{\mathrm{L}}$) imposes a fundamental limit on the dimensionless figure of merit $ZT$ in thermoelectric (TE) materials. Increasing band degeneracy can effectively balance $σ$ and $S$, enabling a high power factor (PF, $S^{2}σ$). However, compounds with intrinsically large band degeneracy are scarce. Here, we present an unconventional strategy to realize elevated band degeneracy in zigzag-chain Na$_2$Au$X$ ($X$ = P, As, Sb, Bi) compounds by harnessing strong intra- and interchain orbital coupling. Pronounced hybridization between Au-$d_{z^{2}}$ and $X$-$p_{z}$ orbitals along the Au--$X$ zigzag chains, together with unexpectedly strong interchain $X$-$p_{x}/p_{y}$ coupling, produces a highly dispersive, multivalley valence band structure that supports an exceptional PF. Concurrently, the intrinsically weak interchain interactions arising from the quasi-one-dimensional framework, together with the weakened Au--$X$ and Au--Au bonds within the chains due to filling of $p$-$d^{*}$ antibonding states, result in an ultralow $κ_{\mathrm{L}}$. First-principles calculations combined with Boltzmann transport theory predict that $p$-type Na$_2$AuBi achieves a PF of $63.9\,μ\mathrm{W}\,\mathrm{cm}^{-1}\,\mathrm{K}^{-2}$, an ultralow $κ_{\mathrm{L}}$ of $0.49\,\mathrm{W}\,\mathrm{m}^{-1}\,\mathrm{K}^{-1}$, and a maximum $ZT$ of $4.7$ along the zigzag-chain direction at $800\,\mathrm{K}$. This work establishes a new design paradigm for high-efficiency TE materials by exploiting substantial orbital overlap in structurally weakly bonded, quasi-one-dimensional systems, opening promising avenues for the discovery and engineering of next-generation high-performance TE materials.

Strong Intra- and Interchain Orbital Coupling Leads to Multiband and High Thermoelectric Performance in Na$_2$Au$X$ ($X$ = P, As, Sb, and Bi)

TL;DR

The study addresses the thermoelectric efficiency limit imposed by the intrinsic coupling among the Seebeck coefficient , electrical conductivity , and lattice thermal conductivity . First-principles calculations reveal that Au-dz^2–X-pz intrachain hybridization together with interchain X-px/p_y coupling generates a highly dispersive multivalley valence band, enabling high PF while weakening interchain bonding suppresses . For p-type Na2AuBi, the predicted PF is 63.9 μW cm^-1 K^-2, is 0.49 W m^-1 K^-1, and reaches 4.7 at 800 K along the zigzag chain direction. This work introduces a design paradigm that decouples charge and phonon transport by balancing strong orbital overlap with weak interchain bonding, offering a route to high-performance thermoelectrics in quasi-one-dimensional systems.

Abstract

The intrinsic coupling among electrical conductivity (), Seebeck coefficient (), and lattice thermal conductivity () imposes a fundamental limit on the dimensionless figure of merit in thermoelectric (TE) materials. Increasing band degeneracy can effectively balance and , enabling a high power factor (PF, ). However, compounds with intrinsically large band degeneracy are scarce. Here, we present an unconventional strategy to realize elevated band degeneracy in zigzag-chain NaAu ( = P, As, Sb, Bi) compounds by harnessing strong intra- and interchain orbital coupling. Pronounced hybridization between Au- and - orbitals along the Au-- zigzag chains, together with unexpectedly strong interchain - coupling, produces a highly dispersive, multivalley valence band structure that supports an exceptional PF. Concurrently, the intrinsically weak interchain interactions arising from the quasi-one-dimensional framework, together with the weakened Au-- and Au--Au bonds within the chains due to filling of - antibonding states, result in an ultralow . First-principles calculations combined with Boltzmann transport theory predict that -type NaAuBi achieves a PF of , an ultralow of , and a maximum of along the zigzag-chain direction at . This work establishes a new design paradigm for high-efficiency TE materials by exploiting substantial orbital overlap in structurally weakly bonded, quasi-one-dimensional systems, opening promising avenues for the discovery and engineering of next-generation high-performance TE materials.

Paper Structure

This paper contains 3 sections, 4 equations, 7 figures.

Table of Contents

  1. Introduction
  2. COMPUTATIONAL DETAILS
  3. Acknowledgements

Figures (7)

  • Figure 1: (a) The crystal structure of Na$_2$Au$X$ ($X$ = P, As, Sb, and Bi). (b) Top view of the Au-X zigzag chain along the $x$ direction within $y$-$z$ plane. (c) Side view of the Au-X zigzag chain along $z$ axis. The yellow, blue, and cyan balls represent Au, $X$ and Na atoms, respectively. The red and pink lines indicate the shortest distances between two Bi atoms that are from two Au-$X$ zigzag chains within a plan containing Au-$X$ zigzag chain and across the plan, respectively. (d) Electron localization function (ELF) of Na$_2$AuBi. (e) The RDG isosurface corresponds to RDG = 0.2 a.u., which is colored on a BGR scale of -0.04 $<\mathrm{sign(\lambda_2)\rho}<$ 0.02 a.u.. (f) RDG as a function of $\mathrm{sign(\lambda_2)\rho}$ for the atomic interactions in Na$_2$AuBi.
  • Figure 2: (a) The Na-$X$, Au-Au, and Au-$X$ bond lengths of Na$_2$Au$X$ compounds. The red dashed line indicates the Au-Au bond length of Na$_2$Au havinga1972compounds. (b) -iCOHP and (c) the ratio of interatomic force constant ($\Phi_{ij}$) to average mass ($m_{ij}$) for Na$_2$Au$X$ ($X$ = P, As, Sb, and Bi).
  • Figure 3: The phonon dispersion, phonon density of states, lattice thermal conductivity spectrum $\kappa_\mathrm{L}$($\omega$), the ratio of cumulative $\kappa_\mathrm{L}$ to total lattice thermal conductivity $\kappa_\mathrm{L}^{\mathrm{t}}$ and the 3ph and 4ph scattering rates ($\tau^{-1}$) for (a) Na$_2$AuP (b) Na$_2$AuAs (c) Na$_2$AuSb (d) Na$_2$AuBi.
  • Figure 4: The calculated $\mathrm{\kappa_L}$ of Na$_2$AuX as a function of temperature in different directions, $\mathrm{\kappa^p}$, $\mathrm{\kappa^c}$ and $\mathrm{\kappa_L}$ are phonon population's contribution, additional coherence's contribution and total lattice thermal conductivity. (a), (b), (c), and (d) are Na$_2$AuP, Na$_2$AuAs, Na$_2$AuSb, and Na$_2$AuBi, respectively.
  • Figure 5: (a) The element projected band structure of Na$_2$AuBi. (b) The $d$-orbital projected band structure of Au atoms in Na$_2$AuBi. (c) The -COHP and schematic diagram of linear chain crystal field. (d) The maximally-localized Wannier functions of Au-$d_{z^2}$ with Bi-$p_z$ (interchain) and Bi-$p_x$ (intrachain). (e) The $p$-orbital projected band structure of Bi atoms in Na$_2$AuBi. (f) The Tight binding band model under different parameter fitting. (g) The valence band structure of Na$_2$AuBi under different stresses.
  • ...and 2 more figures