LaIrSi: Chiral Topology & Superconductivity

• LaIrSi is a noncentrosymmetric chiral cubic intermetallic that combines crystalline chirality, multifold band topology, and unconventional superconductivity.
• Its normal state features a twofold quadruple Weyl node at Γ, which evolves under spin–orbit coupling into spin‑split multifold fermions with significant Chern charges.
• Experimental studies reveal nodal-line superconductivity below Tc = 2.1 K, attributed to SOC-driven singlet-triplet mixing and anisotropic Fermi-surface warping.

Searching arXiv for recent and foundational papers on LaIrSi to ground the article in the literature. {"query":"LaIrSi chiral crystal Weyl superconductivity arXiv", "max_results": 10} Searching arXiv for the specific topological and superconducting works associated with LaIrSi and related chiral crystals. {"query":"(Zhang et al., 2020) LaIrSi (Shang et al., 30 Aug 2025) chiral crystals", "max_results": 10} LaIrSi is a noncentrosymmetric chiral-cubic intermetallic in space group $P2_13$ (No. 198) that has emerged as a platform for intertwined crystalline chirality, multifold band topology, and unconventional superconductivity. In the topological-band literature, LaIrSi and related LaIrSi-type compounds were proposed to host a twofold unconventional Weyl node at $\Gamma$ with monopole charge $|C|=4$ in the spinless setting, together with a phononic analogue in the same crystal symmetry (Zhang et al., 2020). In later work on the superconducting La(Rh,Ir)Si family, LaIrSi was identified as a double-helix chiral crystal with strong spin-orbit coupling (SOC), multifold fermions, helicoid Fermi arcs, and nodal-line superconductivity below $T_c=2.1$ K (Shang et al., 30 Aug 2025).

1. Crystal structure, chirality, and symmetry

LaIrSi crystallizes in the noncentrosymmetric, chiral-cubic space group $P2_13$ (No. 198), with La, Ir, and Si each occupying $4a$ Wyckoff sites. One structural summary gives a primitive cubic lattice parameter $a\approx 6.7$ Å, with La at $(u,u,u)$, $u\approx 0.14$, Ir at $(v,v,v)$, $\Gamma$0, and Si at $\Gamma$1, $\Gamma$2; another refinement gives $\Gamma$3 Å with La at $\Gamma$4, Ir at $\Gamma$5, and Si at $\Gamma$6. Both descriptions place the compound in the same chiral cubic structure and agree that inversion and mirror symmetries are absent (Zhang et al., 2020).

The symmetry content emphasized in the topological analysis consists of only proper rotations, notably three twofold axes and a $\Gamma$7 axis along $\Gamma$8. In the superconductivity study, the crystal is further described as a double-helix chiral crystal: viewed down the $\Gamma$9 axis, the Ir-Si sublattice forms a right-handed helix, while the La sublattice winds in the opposite sense (Shang et al., 30 Aug 2025).

These symmetry properties are central because $|C|=4$0 has neither inversion nor mirror but does retain $|C|=4$1 and the three $|C|=4$2 axes combined with fractional translations. In the spinless case, the little group at $|C|=4$3 admits a two-dimensional $|C|=4$4 irreducible representation, and time-reversal symmetry with $|C|=4$5 guarantees that this $|C|=4$6 representation is twofold degenerate. The same lack of inversion also permits singlet-triplet mixing in the superconducting state.

2. Normal-state electronic topology

In LaIrSi-type compounds, the spinless topological analysis identifies a twofold quadruple Weyl node exactly at the $|C|=4$7 point, described as the only TRIM carrying the $|C|=4$8 representation for space group 198. Numerically, via Wilson-loop or Berry-flux integration, the corresponding twofold crossing at $|C|=4$9 carries $T_c=2.1$0 for the valence band in the absence of SOC (Zhang et al., 2020).

The later DFT+SOC study of superconducting LaIrSi reports a more detailed normal-state structure near $T_c=2.1$1. It finds 10 bands crossing $T_c=2.1$2, dominated by La $T_c=2.1$3, Ir $T_c=2.1$4, and Si $T_c=2.1$5 states. Without SOC, there is a twofold and a threefold crossing just below $T_c=2.1$6 at $T_c=2.1$7, plus a double Weyl at $T_c=2.1$8; including SOC lifts most degeneracies except along $T_c=2.1$9-$P2_13$0. At $P2_13$1, the SOC-induced splitting is $P2_13$2 meV in LaIrSi, compared with only $P2_13$3 meV in LaRhSi. With SOC, $P2_13$4 hosts a fourfold degeneracy with Chern charge $P2_13$5 approximately $P2_13$6 meV below $P2_13$7, and a threefold node with $P2_13$8 further down; at $P2_13$9, the spinless double Weyl of $4a$0 splits into a spin-1 triplet and a single Weyl (Shang et al., 30 Aug 2025).

The same work states that the bulk compensation $4a$1 enforces helicoid Fermi arcs spanning $4a$2-$4a$3 on the $4a$4 surface. This places LaIrSi in the broader class of chiral topological metals whose surface electronic structure is tied to multifold bulk nodes rather than only conventional twofold Weyl points.

3. Effective Hamiltonians and topological charge

For the spinless twofold crossing at $4a$5, the low-energy $4a$6 Hamiltonian in the $4a$7-doublet basis is given, to third order in $4a$8, by

$4a$9

with real constants $a\approx 6.7$0 and $a\approx 6.7$1. Along the $a\approx 6.7$2 line, where $a\approx 6.7$3, the diagonal term proportional to $a\approx 6.7$4 dominates and there is no linear splitting; in generic directions the off-diagonal quadratic terms open the gap. This symmetry-enforced mixture of cubic dispersion along $a\approx 6.7$5 and quadratic dispersion in generic directions is the stated origin of the quadruple Weyl character with $a\approx 6.7$6 (Zhang et al., 2020).

Including SOC converts the spinless twofold $a\approx 6.7$7 representation at $a\approx 6.7$8 into a fourfold $a\approx 6.7$9 representation. In the symmetry analysis of LaIrSi-type materials, this produces a spin-$(u,u,u)$0 Weyl node at $(u,u,u)$1, and the corresponding $(u,u,u)$2 linearized Hamiltonian is written in the $(u,u,u)$3 basis as

$(u,u,u)$4

with $(u,u,u)$5. In that description, the highest doublet carries $(u,u,u)$6, and the spinless twofold $(u,u,u)$7 node evolves into a spinful fourfold $(u,u,u)$8 node together with twelve ordinary spin-$(u,u,u)$9 Weyl nodes of $u\approx 0.14$0 that are “emitted” and later annihilated as SOC is ramped up (Zhang et al., 2020).

A complementary $u\approx 0.14$1 model is given around $u\approx 0.14$2 in the superconductivity study: $u\approx 0.14$3 with $u\approx 0.14$4, $u\approx 0.14$5 eV, $u\approx 0.14$6 eV$u\approx 0.14$7Å$u\approx 0.14$8, $u\approx 0.14$9 eV$(v,v,v)$0Å, $(v,v,v)$1 eV$(v,v,v)$2Å$(v,v,v)$3, and $(v,v,v)$4 eV for LaIrSi. The corresponding eigenvalues are

$(v,v,v)$5

Here the $(v,v,v)$6 term is explicitly identified as the $(v,v,v)$7-wrapping term (Shang et al., 30 Aug 2025).

4. Superconductivity and nodal-line gap structure

Muon-spin spectroscopy and band-structure analysis place LaIrSi in a distinct superconducting regime within the La(Rh,Ir)Si family. Zero-field $(v,v,v)$8SR finds no additional relaxation below $(v,v,v)$9 K, implying that time-reversal symmetry is preserved. In transverse field, $\Gamma$00 mT produces Gaussian relaxation from the flux-line lattice, from which the effective penetration depth $\Gamma$01 is extracted. The resulting superfluid density $\Gamma$02 is flat at low $\Gamma$03 in LaRhSi but follows a sub-quadratic $\Gamma$04 with $\Gamma$05-1.5 in LaIrSi, which is taken as evidence for line nodes (Shang et al., 30 Aug 2025).

The pairing Hamiltonian is written as

$\Gamma$06

with

$\Gamma$07

Because inversion is broken, $\Gamma$08 and $\Gamma$09 mix. The corresponding BdG spectrum is

$\Gamma$10

Line nodes occur when

$\Gamma$11

are simultaneously satisfied (Shang et al., 30 Aug 2025).

To fit the $\Gamma$12SR data, the anisotropic Fermi surfaces are mapped onto equivalent spherical radii $\Gamma$13, giving

$\Gamma$14

The fitted ratio is $\Gamma$15 in LaRhSi, corresponding to no nodes, and $\Gamma$16 in LaIrSi, corresponding to nodal lines. The same study presents a tuning picture in which $\Gamma$17, with LaRhSi at $\Gamma$18 eV outside the nodal regime and LaIrSi at $\Gamma$19 eV inside it; a critical $\Gamma$20 eV is predicted for the appearance of nodal lines in the lower-energy band (Shang et al., 30 Aug 2025).

This establishes LaIrSi, within that study, as the first demonstration of topological nodal-line superconductivity in a chiral crystal. The proposed mechanism is notable because the nodal-line state is attributed to isotropic SOC of a specific strength, rather than to a strongly anisotropic SOC.

5. Phonons, pseudospin texture, and experimental access

The topological analysis extends beyond electrons to phonons. Because phonons are integer-spin bosons with $\Gamma$21 in the same space group, the fourth and fifth phonon branches in LaIrSi form an analogous twofold $\Gamma$22-crossing at $\Gamma$23. First-principles DFPT identifies a twofold phonon Weyl node at $\Gamma$24 between modes 4 and 5 carrying $\Gamma$25, eight single phonon Weyl nodes with $\Gamma$26 on the eight $\Gamma$27 lines close to $\Gamma$28, and twelve single Weyl nodes with $\Gamma$29 on the $\Gamma$30, $\Gamma$31, or $\Gamma$32 planes (Zhang et al., 2020).

For a generic twofold Weyl Hamiltonian $\Gamma$33, the pseudospin is

$\Gamma$34

and its wrapping number on a small sphere $\Gamma$35 is

$\Gamma$36

For $\Gamma$37, the pseudospin wraps the sphere four times; in the chiral cubic case, the texture may be decomposed into eight half-skyrmions along the $\Gamma$38 directions, each contributing $\Gamma$39 (Zhang et al., 2020).

Several experimental consequences are explicitly proposed. For electronic structure, ARPES surface-state mapping on the $\Gamma$40 face is expected to show four Fermi arcs from $\Gamma$41 in the spinless case or eight from the spinful $\Gamma$42 node, with connections to projected ordinary Weyl nodes on $\Gamma$43 planes. Negative magnetoresistance in a chiral magnetic field is predicted to exhibit a fourfold amplified chiral-anomaly signal, and the circular photogalvanic effect tuned between spin-$\Gamma$44 bands may display a quantized photocurrent $\Gamma$45 with $\Gamma$46, provided the chemical potential lies in the required window (Zhang et al., 2020).

For phonons, inelastic neutron scattering or IXS is proposed to detect an “X-shaped” crossing at $\Gamma$47 THz along $\Gamma$48-$\Gamma$49-$\Gamma$50, with unequal intensities on either side of $\Gamma$51 because of differing eigenvector character. Raman-active phonons near $\Gamma$52 are expected to show a twofold degenerate $\Gamma$53 mode whose frequency follows cubic dispersion in the $\Gamma$54 direction, yielding an unusual $\Gamma$55 linewidth in high-resolution phonon-dispersion measurements (Zhang et al., 2020).

The superconductivity work adds further probes: low-temperature STM or ARPES are suggested as ways to search for surface-flat-band Andreev states or drumhead modes associated with the coexistence of Berry-charged multifold fermions and line nodes, while power-law low-temperature behavior such as $\Gamma$56 and $\Gamma$57 is proposed as an independent verification of line nodes (Shang et al., 30 Aug 2025).

6. Family context, tuning principles, and nomenclature

LaIrSi is treated not as an isolated compound but as part of the La(Rh,Ir)Si family and, more broadly, as a representative of LaIrSi-type chiral cubic materials. In the topological study, a series of LaIrSi-type materials is proposed to host twofold quadruple Weyl nodes in both electronic systems and phonon spectra (Zhang et al., 2020). In the superconductivity study, the comparison to LaRhSi is central: replacing $\Gamma$58-Rh with $\Gamma$59-Ir significantly enhances SOC and correlates with the change from a fully gapped superconducting state in LaRhSi to nodal-line superconductivity in LaIrSi (Shang et al., 30 Aug 2025).

The design principles stated for further materials discovery are specific. The superconductivity study identifies three ingredients: a chiral space group $\Gamma$60, moderately large isotropic SOC $\Gamma$61 to mix singlet and triplet pairing, and anisotropic Fermi-surface warping encoded in the $\Gamma$62-wrapping term $\Gamma$63. It suggests screening other $\Gamma$64 binaries and ternaries such as PdBiSe, SbPtS, ReSi, and RhGe for $\Gamma$65 meV and favorable $\Gamma$66, and it states that chemical substitution or uniaxial strain can tune $\Gamma$67 and drive fully gapped to nodal-line crossovers (Shang et al., 30 Aug 2025).

A separate point of terminology is that “LaIrSi” also appears, in unrelated networking literature, as an alternative name for the Link-identified Routing (LiR) architecture for LEO satellite networks. There it denotes a source-route-style forwarding architecture based on in-packet Bloom filters and link identifiers rather than a crystalline material (Zhang et al., 2024). This unrelated usage is purely nominal. In condensed-matter and superconductivity contexts, LaIrSi refers to the chiral intermetallic compound in space group $\Gamma$68.

Taken together, the literature presents LaIrSi as a chiral crystal in which structural handedness, noncentrosymmetric symmetry, multifold topology, and mixed-parity superconductivity are all active on experimentally relevant energy scales. A plausible implication is that apparently different descriptions of its nodal content—spinless twofold quadruple Weyl physics, SOC-split multifold fermions near $\Gamma$69 and $\Gamma$70, and nodal-line superconductivity—should be read as sector-specific views of the same chiral electronic environment rather than as mutually exclusive classifications.