Kondo-Peierls transition with nonsymmorphic zone boundary gap formation

TL;DR

Nonsymmorphic degeneracies at the Brillouin zone boundary enable uniform $Q=0$ order to open a Brillouin-zone gap through symmetry breaking. The authors develop a Kondo lattice model with intersite exchange $J_{ij}$ and apply Abrikosov-fermion mean-field theory to reveal anisotropic Kondo-singlet orders that lift zone-boundary degeneracies. They identify $\varepsilon_g$ and $\varepsilon'_g$ uniform orders that produce $k$-space gap openings consistent with CeCoSi's intermediate phase, and provide phase diagrams and band reconstructions illustrating the gap formation along zone boundaries. The work offers a microscopic, symmetry-based mechanism for Peierls-like gap formation in nonsymmorphic Kondo lattices and supports the interpretation of CeCoSi's pressure-dependent order without quadrupole moments; supplemental results confirm the robustness of these conclusions against variations in interlayer couplings $J'$.

Abstract

We study nonsymmorphic space group symmetry breakings in correlated electron systems. Under nonsymmorphic symmetry, it is well known that there are degeneracies in the electronic Bloch states at the Brillouin zone boundaries. When the system undergoes a phase transition into an ordered phase with breaking the nonsymmorphic symmetry, the degeneracy is lifted. This happens even when the order parameter is uniform. We point out that this general feature leads to various {\it uniform} Peierls transition in nonsymmorphic systems. In particular, we show that such mechanism of the Peierls gap formation can be realized accompanying with uniform anisotropic Kondo singlet formations. This explains the hidden electric order observed in CeCoSi.

Figures (7)

• Figure 1: (Color online) Schematic electronic configurations and energy dispersion $\epsilon_{k_x}$ along $k_x$. (a) isotropic and (b) parity mixed local configuration, which retain nSSs in the zigzag chain. (c) Sublattice-symmetry-breaking configuration, where there are no nSSs. Horizontal lines represent the chemical potential.
• Figure 2: (Color online) (a) Crystal structure of CeCoSi. (b) Top view of the single layer on the $xy$ plane. The unit cell is enclosed by a black line, and the hopping parameters $t$ and $t'$, and the Kondo coupling $J$ are schematically indicated. (c) Local order parameters around the $f_1$ site, $\phi_\alpha=\tfrac{1}{4}\sum_{i-j}C_{\alpha,i-j}\langle\phi_{i-j}\rangle$: $\alpha=$A, B, X, or Y. Numbers besides the bonds indicate the coefficient $C_{\alpha,i-j}$. Similar definitions are applied to $\{\phi'\}$'s for the $f_2$ site.
• Figure 3: (Color online) (a) Phase diagram as functions of $T$ and the conduction electron filling $\nu$ for $t=-0.5$, $t'=0.3$, $t_z=0.1$, and $J=0.3$. The schematic configuration of $\phi$'s is also shown. (b)--(g) Schematic configuration of $\phi$'s. The color and the thickness of the bonds represent the sign and the magnitude of $\phi$'s, respectively. The spheres are Ce, Co, and Si atoms as in Fig. \ref{['fig:2']}. Primary symmetry-breaking fields are depicted for simplicity. In (c), only "$x$ part" is shown for the E phase with $\bm{\phi}' = \bm{\phi}$. In (g), the arrows indicate the pure imaginary order parameters in which the direction toward Ce (large orange sphere) is positive.
• Figure 4: (Color online) Band dispersion along a high-symmetry path for (a) $\mu=1.2$ and (b) $\mu=1.4$, where $J$ and $t$'s are the same as in Fig. \ref{['fig:3']}. The position labels are indicated in (a) on the $k_z=0$ and $\pi$ planes. The bare dispersion (thin black) and the dispersion for the A phase (thick red) have degeneracy at the BZ boundary. In (a), the $yz$ type $\varepsilon_g$ phase appears below $T\sim 0.12$ and the BZ-boundary degeneracy for $k_y=\pi$ is lifted, while that for $k_x=\pi$ is retained. In (b), the $yz+zx$ type $\varepsilon^\prime_g$ phase appears below $T\sim 0.07$ and there is no BZ-boundary degeneracy.
• Figure 5: (a) Kondo coupling $J$ and $J'$. (b) Local order parameters associated with $J'$ around the $f_1$ site, $\varphi_\alpha=\tfrac{1}{4}\sum_{i-j}C_{\alpha,i-j}\varphi_{i-j}$: $\alpha=$A, B, X, or Y. Numbers besides the bonds indicate the coefficient $C_{\alpha,i-j}$ in the linear combination. Similar definitions are applied to $\{\varphi'\}$'s for the $f_2$ site.