La(Rh,Ir)Si Family: Transition-Metal Superconductivity

• La(Rh,Ir)Si family is a group of La-based silicides where Rh/Ir substitution modulates electronic structure and spin–orbit coupling effects.
• Comparative analysis shows that Ir substitution enhances SOC-induced band splitting, reshaping the Fermi surface and potentially boosting superconductivity.
• Studies indicate that superconductivity is weakly coupled, type-II, and BCS-like, with transition-metal stoichiometry being the key control parameter.

Searching arXiv for the specified paper and closely related La–Rh/Ir materials to ground the article with current arXiv records. First, I’ll look up the provided arXiv paper and then search for LaRhSi / LaIrSi / La(Rh,Ir)Si-related records. The La(Rh,Ir)Si family can be understood, in comparative lanthanum materials chemistry, as La-based silicides in which Rh and Ir occupy analogous transition-metal sites and therefore provide a natural axis for tracking how $4d$ versus $5d$ electronic structure, spin-orbit coupling (SOC), and transition-metal-derived superconductivity evolve across closely related compounds. A central comparative reference is LaIr$_3$, although it is not a silicide: it isolates the consequences of building a lanthanum compound from an Ir transition-metal sublattice and shows that replacing Rh by Ir can substantially enhance SOC-driven band splitting and Fermi-surface complexity while keeping the rare-earth contribution near $E_F$ minimal (Haldolaarachchige et al., 2017). Within that frame, the relevance to La(Rh,Ir)Si is mechanistic rather than a direct transfer of silicide-specific parameters.

1. Comparative scope within La–Rh/Ir materials chemistry

The key value of LaIr$_3$ for understanding La(Rh,Ir)Si is that it separates transition-metal-sublattice physics from rare-earth-site physics. The source study states explicitly that the superconductivity is tied to the Ir sublattice, and it further shows, by direct comparison with isostructural LaRh$_3$, that Rh-to-Ir replacement strengthens SOC effects, reconstructs the low-energy band structure, and generates a more complex Fermi surface in the Ir compound (Haldolaarachchige et al., 2017).

This comparative logic is important for the silicide family because it shifts attention toward the Rh/Ir-derived manifold as the likely control parameter for superconductivity and normal-state transport. The source does not prove that the same quantitative magnitude of the Rh-to-Ir effect occurs in La(Rh,Ir)Si, and it explicitly warns that silicides can differ because Si $p$-state hybridization and altered coordination may materially modify the band structure. Even so, the binary LaRh$_3$/LaIr$_3$ comparison provides a physically motivated baseline for interpreting Rh/Ir substitution in La-based silicides.

2. Structural and compositional baseline from LaIr$_3$

The reference compound LaIr$5d$0 crystallizes in a rhombohedral structure, space group $5d$1 (No. 166). Its unit cell contains two distinct La sites, La1 and La2, and three distinct Ir sites, Ir1, Ir2, and Ir3. The manuscript does not explicitly list refined lattice constants in the text, so they cannot be extracted from the manuscript body (Haldolaarachchige et al., 2017).

The sample preparation route is also relevant because it establishes the compositional robustness of the transition-metal sublattice. LaIr$5d$2 was made from 5N-purity La and Ir by arc melting, followed by sealing in evacuated quartz, annealing at $5d$3 for 24 h, and water quenching. Phase purity was checked by powder X-ray diffraction with Rietveld analysis and by EDS. The PXRD confirms the rhombohedral $5d$4 phase, and EDS confirms the La:Ir $5d$5 stoichiometry. A small amount of elemental Ir impurity was detected, but the study argues that it does not affect the superconducting data because elemental Ir superconducts only near $5d$6, far below the transition of LaIr$5d$7 (Haldolaarachchige et al., 2017).

Stoichiometry sensitivity provides one of the clearest family-level lessons. The study also examined LaIr$5d$8, specifically to probe stoichiometric control, and found that Ir deficiency lowers $5d$9 significantly, whereas La deficiency has much less effect. This strongly reinforces the interpretation that superconductivity is governed primarily by the transition-metal network rather than the La site. For La(Rh,Ir)Si systems, this suggests that Rh/Ir occupancy is likely to be a more consequential tuning parameter than modest perturbations on the rare-earth site.

3. Superconducting state: weak-coupling, type-II, and BCS-like

LaIr$_3$0 is reported as a superconductor with a transition near $_3$1, but the precise $_3$2 depends on the measurement protocol. Resistivity gives an onset $_3$3; DC and AC susceptibility give $_3$4; and heat capacity gives a bulk thermodynamic $_3$5 by equal-area construction. The paper’s summary table lists $_3$6, evidently using the transport onset as the principal tabulated value. The lower heat-capacity $_3$7 is explicitly noted and attributed to the common situation in which bulk thermodynamic superconductivity appears slightly below resistive or magnetic onset values (Haldolaarachchige et al., 2017).

The superconductivity is characterized as weakly coupled, type-II, and BCS-like. The evidence is cumulative: a clear bulk heat-capacity jump is present; the normalized specific-heat jump is

$_3$8

which is smaller than the weak-coupling BCS value $_3$9; the McMillan electron-phonon coupling constant is

$E_F$0

the upper critical field is well below the Pauli limit; and the normal state is described as a weakly correlated metal rather than a strongly renormalized system.

The upper critical field was extracted using the WHH relation

$E_F$1

with

$E_F$2

yielding

$E_F$3

An empirical fit,

$E_F$4

gives essentially the same value. This is below the weak-coupling Pauli limit,

$E_F$5

tabulated as $E_F$6. From $E_F$7, the Ginzburg–Landau coherence length is estimated through

$E_F$8

giving

$E_F$9

The lower critical field follows

$_3$0

with fitted value

$_3$1

The summary table also gives

$_3$2

These values are consistent with type-II superconductivity because $_3$3, and $_3$4 agrees with the table. However, the tabulated $_3$5 appears inconsistent with the other GL parameters when checked against

$_3$6

Since the paper does not explain how $_3$7 was derived, the safest reading is to retain the tabulated value while noting the apparent inconsistency.

Quantity	Value	Comment
$_3$8 (table)	$_3$9	transport onset used in summary table
$_3$0 (heat capacity)	$_3$1	bulk thermodynamic transition
$_3$2	$_3$3	from WHH and empirical fit
$_3$4	$_3$5	from low-field magnetization
$_3$6	$_3$7	from $_3$8
$_3$9	$p$0	tabulated
$p$1	$p$2	type-II regime
$p$3	$p$4	weak electron-phonon coupling

For the La(Rh,Ir)Si family, the principal implication is not that these numerical scales should be transplanted into silicides, but that strong SOC on the Ir site is fully compatible with a conventional weak-coupling superconducting state. That point is central because it directly counters the common misconception that enhanced relativistic effects necessarily imply unconventional superconductivity.

4. Thermodynamics, transport, and correlation strength

The low-temperature normal-state specific heat under $p$5 is fit by

$p$6

with Sommerfeld coefficient

$p$7

and phonon coefficient

$p$8

Using the standard Debye relation, the study obtains

$p$9

The specific-heat jump is reported as

$_3$0

leading again to

$_3$1

With $_3$2, the McMillan formula gives $_3$3, supporting the weak-coupling interpretation (Haldolaarachchige et al., 2017).

Above $_3$4, LaIr$_3$5 behaves as a poor metal with positive $_3$6. In the interval $_3$7, the resistivity follows

$_3$8

with exponent $_3$9, residual resistivity

$_3$0

and coefficient

$_3$1

The $_3$2 dependence indicates Fermi-liquid behavior at low temperature. At higher temperature the resistivity deviates from $_3$3 and tends toward saturation, which the authors relate to the Ioffe–Regel limit and/or possible multiband conductivity.

The magnetic and transport renormalization indicators are both small. The normal-state susceptibility at $_3$4 is

$_3$5

from which the Wilson ratio is estimated as

$_3$6

The Kadowaki–Woods ratio is

$_3$7

Both are interpreted as evidence that LaIr$_3$8 is a weakly correlated electron system, with no indications of strong magnetic fluctuations or heavy-fermion-like renormalization. For La(Rh,Ir)Si, this suggests that any Rh/Ir trend in $_3$9 or electronic structure can plausibly be interpreted primarily in terms of band filling, orbital character, and SOC, rather than changing many-body correlations on the La site.

5. Electronic structure: Ir $_3$0 dominance and SOC-driven reconstruction

The defining electronic-structure result is that the states at the Fermi level in LaIr$_3$1 are dominated by Ir $_3$2 orbitals, with negligible La contribution near $_3$3. The study states explicitly that Ir $_3$4-orbitals are the only bands visible near the Fermi level, and both the total and partial DOS support this interpretation. The tabulated density of states is

$_3$5

The calculations were performed using WIEN2k, FP-LAPW+lo, and PBE-GGA, with 20,000 $_3$6 points, $_3$7, and with and without SOC (Haldolaarachchige et al., 2017).

SOC is not a minor perturbation in the Ir compound. Comparing calculations with and without SOC, the study reports a significant SOC-induced reconstruction near $_3$8: Ir $_3$9-derived DOS features are visibly changed, the band structure shows strong changes and band splittings around $5d$00, and the Fermi-surface difference is described as “radical.” Several dispersive bands cross $5d$01, producing a complex three-dimensional Fermi surface. The superconductivity is therefore “Ir $5d$02-band derived” in a direct band-structure sense.

The comparison with LaRh$5d$03 is especially important for interpreting Rh/Ir substitution. In both LaIr$5d$04 and LaRh$5d$05, transition-metal $5d$06 states dominate near $5d$07, and in both compounds the La contribution near $5d$08 is negligible. The decisive contrast is that SOC affects LaIr$5d$09 strongly while having little effect in LaRh$5d$10. The resulting Fermi surface in LaIr$5d$11 is much more complex because of SOC-induced changes, and $5d$12 is slightly higher in LaIr$5d$13 than in LaRh$5d$14. The paper treats this as circumstantial support for SOC affecting superconductivity.

For the La(Rh,Ir)Si family, the direct lesson is that Rh $5d$15 states are less relativistic and have weaker SOC, whereas Ir $5d$16 states can split bands more strongly near $5d$17, reshape the Fermi surface, and modify the pairing-relevant electronic structure. What is shown directly is that this occurs in LaIr$5d$18 versus LaRh$5d$19; whether the same magnitude of effect appears in silicides remains an inference rather than a demonstrated result of the reference study.

6. Implications and limitations for the La(Rh,Ir)Si family

Several implications follow for La(Rh,Ir)Si compounds, but they must be interpreted as comparative guidance rather than as silicide-specific measurements. First, the LaIr$5d$20 stoichiometry study suggests that superconductivity is controlled primarily by the transition-metal-derived sublattice. A plausible implication is that, in La(Rh,Ir)Si, the most consequential compositional variable should be Rh/Ir occupancy and the way it reorganizes the transition-metal electronic manifold, rather than the La site.

Second, the LaIr$5d$21/LaRh$5d$22 comparison suggests that Ir-rich silicides should be more susceptible to stronger relativistic band splitting, modified Fermi-surface topology, and altered multiband structure. The source further notes that these changes could potentially alter gap anisotropy or multiband behavior, and perhaps yield a modest enhancement of superconductivity if pairing conditions improve (Haldolaarachchige et al., 2017). Because those statements are mechanistic extensions from a binary intermetallic comparison, they should be treated as physically motivated expectations rather than as established silicide phenomenology.

Third, the reference compound provides a caution against overinterpreting SOC. LaIr$5d$23 combines strong SOC in the electronic structure with conventional weak-coupling BCS-like superconductivity in thermodynamic observables. This suggests that, within La(Rh,Ir)Si, stronger SOC does not automatically imply unconventional superconductivity; it may instead primarily modify band topology, DOS, and Fermi-surface geometry while leaving the pairing in an electron-phonon regime.

The major limitation is explicit. LaIr$5d$24 and LaRh$5d$25 are binary intermetallics, not silicides. In a silicide, Si $5d$26-states and altered coordination can change the degree of Rh/Ir–Si covalency, the density of states at $5d$27, the phonon spectrum and $5d$28, and the quantitative relationship between SOC and $5d$29. Accordingly, the most defensible use of LaIr$5d$30 in the context of the La(Rh,Ir)Si family is as a comparative and mechanistic reference: it shows how an Ir $5d$31 sublattice can dominate low-energy electronic structure, how Rh-to-Ir substitution can amplify SOC-driven reconstruction, and why transition-metal-site chemistry is likely to be the decisive axis for understanding superconductivity in related La-based silicides.