Chiral Weyl-Kondo semimetals and hexagonal heavy fermion systems

Abstract

Strong correlation, in concert with symmetry and topology, engenders novel gapless phases of matter, though only a tip of the iceberg has been seen. An exemplary framework is provided by Weyl-Kondo semimetals, in which Weyl fermions develop through crystalline symmetry constraints on the emergent low-energy heavy-fermion excitations. This paradigm has opened up new opportunities to explore correlated topologies without a noninteracting counterpart, but fully realizing this potential requires a large base of candidate materials. Here we confront the challenge on both fronts by studying heavy fermion systems with hexagonal space groups. This family contains a large number of chiral nonsymmorphic crystal structures that promote Weyl degeneracies and, in addition, feature geometric frustration in the $f$-electron magnetism. Our calculations for the heavy fermion states identify Weyl-Kondo semimetals with chiral or achiral Weyl nodes in the respective structural classes. We also develop a new search strategy for the difficult case of strongly correlated materials, using a combination of materials database, symmetry classification and experiments, and propose as candidate topological heavy fermion systems the chiral CePt$_2$B and achiral Ce$_2$NiGe$_3$ and Ce$_6$Co$_{2-δ}$Si$_3$. Our findings raise the prospect for strongly correlated metallic topology in the unusual setting of exotic quantum magnetism.

Figures (34)

• Figure 1: (a) Hexagonal Bravais lattice in three dimensions in which the primitive unit cell is denoted by thick black lines. The three Bravais lattice vectors $\mathbf{a}_i$ ($i=1,2,3$) are also shown. (b) Brillouin zone (BZ) and the high-symmetry points of hexagonal crystal systems. The three reciprocal lattice vectors $\mathbf{G}_i$ ($i=1,2,3$) are also shown. Throughout this work, we refer to the top (or bottom) BZ boundary as $\mathbf{k} = k_1 \mathbf{G}_1 + k_2 \mathbf{G}_2 + k_3 \mathbf{G}_3$ with $k_3 = 1/2$ (or $k_3 = - 1/2$). (c) Schematic representation of the chiral WKSM phase, where the Kondo-driven Weyl point and anti-Weyl point that carry opposite chiral charges are located at different energies. The heavy-fermion energy scale is set by the Kondo scale $k_{\rm B} T_{\rm K}$. The Fermi energy is denoted as $E_F$. (d) The crystal structure of a periodic Anderson model on a hexagonal crystal system with two sub-lattices per unit cell. The sub-lattice at $(0,0,0)$ is denoted by black filled circles, and the sub-lattice at $(0,0,1/2)$ is denoted by blue filled circles. The itinerant $c$ electrons are denoted by wave packets with their electron spins represented by arrows. The $f$ electrons are localized on the sub-lattices $(0,0,0)$ and $(0,0,1/2)$, and we also use arrows to indicate their fluctuating magnetic moments. The Kondo singlet emerges through the antiferromagnetic Kondo interaction between the localized $f$ electron and the itinerant $c$ electron. This leads to the paramagnetic phase of the periodic Anderson model with heavy-fermion excitations.
• Figure 2: (a) Unit cell of a chiral crystal in space group no. 173. (b) Unit cell of a chiral crystal in space group no. 180. (c) The excitation spectrum of the hexagonal periodic Anderson model with chiral space group no. 173 ($P 6_3$) and (d) with chiral space group no. 180 ($P 6_2 22$). The color map indicates the portion of the $f$ electron for a given excitation. The energies are in unit of nearest hopping amplitude $t$. In (e) and (f), we show the enlarged view of the band crossings demonstrating the low-energy heavy Weyl fermions in (c) and (d), respectively. In (e) and (f) we also label the chiral charge of each Weyl point. The Kondo energy scale is denoted as $k_{\rm B} T_{\rm K}$.
• Figure 3: (a) Schematic illustration of the materials searching procedure for hexagonal crystal systems. Starting from compounds crystallizing in hexagonal structures, we identify space groups hosting nonsymmorphic band crossings. We further focus on Ce-, Yb-, and U-based compounds that have been previously or newly synthesized and experimentally characterized. This screening process leads to the identification of new candidate materials for chiral and achiral WKSMs. (b) DFT band structures (with spin-orbit couplings) of CePt$_2$B with chiral space group no. 180 ($P 6_2 22$). (c) The corresponding zoomed-in band structure along $\Gamma-A$ and $K-H$. The symmetry enforced Weyl points are marked with their topological charges.
• Figure S1: (a) Unit cell in chiral space group no. 173. Solid dots are the atoms and transparent dots are their inversion symmetric positions. If inversion is restored by placing atoms at these inversion-related positions, the space group symmetry rise to no. 176. (b) Unit cell in chiral space group no. 173 with mirrored atomic configuration of (a). (c) Top view of the unit cell in (a) showing broken mirror symmetries. Dashed lines indicate the potential mirror symmetries in hexagonal lattice. Solid dots are the atoms and transparent dots are their mirror symmetric positions. (d) Top view of (b). The mirror symmetry that maps between left panels with right panels is illustrated as the vertical gray bars in (c) and (d).
• Figure S2: (a) The excitation spectrum of the hexagonal periodic Anderson model with space group no. 173 ($P 6_3$). The Kondo scale $k_{\rm B} T_{\rm K}$ is also denoted. The color map indicates the portion of the $f$ electron for a given excitation. Due to the presence of $\{ C_{2z} \mathcal{T} | 0,0,1/2 \}$ symmetry, where $\mathcal{T}$ is the spin-1/2 time-reversal operation, all the energy bands on the top or bottom BZ boundary [Fig. 1(b) in main text], e.g. along $A-L$ and $H-A$ high-symmetry lines, are twofold-degenerate. We also provide a derivation of such twofold degeneracy in \ref{['sec:implication_C2zT_0_0_one_half_SG_173']}. (b) The distribution of hourglass-type Weyl points together with their topological charges (the color map) in the three-dimensional BZ. Due to the presence of spin-1/2 time-reversal symmetry, given a Weyl point at momentum $\mathbf{k}_*$ with a topological charge $C$, there will be another Weyl point at momentum $-\mathbf{k}_*$ with the same topological charge $C$.