PtBi Alloys: Structure and Function

• PtBi alloys are materials that include substitutional Pt₁₋ₓBiₓ thin films and ordered PtBi₂ intermetallics, where crystal symmetry and dimensionality dictate their electronic properties.
• Cubic PtBi₂ exhibits compensated semimetallicity with sixfold fermions and extreme magnetoresistance, while trigonal PtBi₂ features noncentrosymmetric Weyl semimetallicity with tunable surface superconductivity on Fermi arcs.
• These compounds also enhance spintronic functionalities such as spin–orbit torque and terahertz emission, and promise innovative applications like two-dimensional ferroelectric metallicity with a robust Edelstein effect.

PtBi alloys comprise both substitutional Pt$_{1-x}$Bi$_x$ metallic films and ordered Pt–Bi intermetallics, most prominently the polymorphs of stoichiometric PtBi$_2$. Across these material classes, the decisive variables are crystal symmetry, dimensionality, and surface termination rather than Pt:Bi ratio alone. The literature represented by cubic $Pa\bar 3$ PtBi$_2$, trigonal noncentrosymmetric PtBi$_2$, layered stoichiometric PtBi$_2$, dilute PtBi thin-film alloys, and monolayer PtBi$_2$ shows a coherent set of themes: compensated semimetallic transport, symmetry-protected topological fermions, surface-selective superconductivity on Fermi arcs, and strong spin–charge interconversion in Pt-based spintronic heterostructures (Thirupathaiah et al., 2020).

1. Chemical scope and structural polymorphism

In the Pt–Bi system, “PtBi alloys” refers in practice to two distinct materials categories. The first is substitutional Pt$_{1-x}$Bi$_x$ thin films, exemplified by Pt$_x$0Bi$_x$1, Pt$_x$2Bi$_x$3, Pt$_x$4Bi$_x$5, and Pt$_x$6Bi$_x$7, which are used as functional nonmagnetic layers in spintronic and terahertz devices (Winkel et al., 2023). The second is ordered intermetallic PtBi$_x$8, whose polymorphs are electronically non-equivalent.

The cubic polymorph is described as cubic PtBi$_x$9, pyrite-type PtBi$_2$0, or $_2$1-PtBi$_2$2, and crystallizes in space group $_2$3, $_2$4, with lattice parameter $_2$5 in the ARPES/DFT study and $_2$6 in the thermodynamic study; the latter also quotes $_2$7 (Thirupathaiah et al., 2020). A separate layered stoichiometric PtBi$_2$8 phase was reported in space group $_2$9 with $Pa\bar 3$0 and $Pa\bar 3$1, built from alternate stacking of Pt layers and Bi bilayers along $Pa\bar 3$2 (Xu et al., 2016). The noncentrosymmetric Weyl-semimetal phase central to the surface-superconductivity literature is trigonal PtBi$Pa\bar 3$3, usually denoted $Pa\bar 3$4-PtBi$Pa\bar 3$5 and in some papers $Pa\bar 3$6-PtBi$Pa\bar 3$7, with space group $Pa\bar 3$8 and two inequivalent Bi-terminated cleavage surfaces, decorated honeycomb and kagome-type (Vocaturo et al., 2024).

This polymorphism is not a nominal crystallographic detail. It controls whether PtBi$Pa\bar 3$9 realizes a cubic compensated semimetal with multifold fermions, a layered anisotropic metal, or a noncentrosymmetric Weyl semimetal whose surface Fermi arcs can superconduct. The same point appears in broader Pt–Bi chemistry: the first ternary SrPtBi$_2$0 in the Sr–Pt–Bi system crystallizes in $_2$1, was predicted by an adaptive genetic algorithm, and exhibits Pt–Bi interactions accounting for $_2$2 of the total ICOHP-weighted bonding contribution, yet shows no superconductivity down to $_2$3 K (Gui et al., 2017). This suggests that Pt–Bi bonding is structurally decisive but not by itself sufficient to determine the low-energy quantum state.

2. Cubic PtBi$_2$4: compensated semimetallicity, sixfold fermions, and conventional lattice thermodynamics

Cubic $_2$5 PtBi$_2$6 is the best-characterized ordered Pt–Bi intermetallic in the normal state. High-quality crystals grown from Bi-rich self-flux with Pt:Bi $_2$7, homogenized at $_2$8 and slowly cooled to $_2$9, are metallic down to $_2$0 K, display almost temperature-independent diamagnetic susceptibility at $_2$1 Oe, and show $_2$2 with $_2$3 (Correa et al., 2022). In transport, the magnetoresistance is parabolic up to $_2$4 T, reaches $_2$5, and exhibits Shubnikov–de Haas oscillations above about $_2$6 T at $_2$7 K (Correa et al., 2022).

Quantum-oscillation work reconstructs a multiband compensated Fermi surface containing three ellipsoid-like hole pockets $_2$8 at $_2$9, one intricate electron pocket $_2$0 at $_2$1, and electron and hole octahedral pockets $_2$2 and $_2$3 at $_2$4. The summed densities are $_2$5 and $_2$6, establishing compensation within about $_2$7 (Zhao et al., 2018). The same study reports $_2$8, $_2$9, $_2$0 magnetoresistance at $_2$1 T, and identifies the light, anisotropic $_2$2 hole pockets as likely major contributors to the mobility (Zhao et al., 2018). In this sense, the extreme magnetoresistance of cubic PtBi$_2$3 is explained primarily by compensation rather than by topology alone.

Band-topologically, cubic PtBi$_2$4 hosts a symmetry-protected sixfold fermion on the $_2$5-R line. DFT places the near-$_2$6 sixfold crossing about $_2$7 meV above $_2$8, whereas ARPES places it about $_2$9 meV below $_{1-x}$0, making it unusually accessible to low-energy transport (Thirupathaiah et al., 2020). The protection is attributed to the crystal symmetries of space group $_{1-x}$1, especially the threefold screw $_{1-x}$2 along $_{1-x}$3, the twofold screw $_{1-x}$4 along $_{1-x}$5, together with inversion $_{1-x}$6 and time-reversal symmetry $_{1-x}$7 (Thirupathaiah et al., 2020). Under a Zeeman field along $_{1-x}$8, the sixfold point splits into $_{1-x}$9 type-II Weyl cones, with $_x$0 Weyl nodes on the $_x$1 axis and $_x$2 on each of the $_x$3, $_x$4, and $_x$5 directions (Thirupathaiah et al., 2020). This makes cubic PtBi$_x$6 a rare Pt–Bi platform for transport beyond ordinary Dirac and Weyl semimetals.

Its lattice thermodynamics are comparatively simple. For cubic symmetry, the measured linear expansivity along $_x$7 obeys

$_x$8

The low-temperature data yield $_x$9, and $_x$00 nearly coincides with the specific heat $_x$01, which the authors interpret through

$_x$02

Fitting

$_x$03

gives $_x$04, $_x$05, and $_x$06 K. With $_x$07 GPa, the inferred $_x$08, close to the canonical expectation $_x$09, and no magnetostriction is detected up to $_x$10 T, with $_x$11 (Correa et al., 2022). The cubic Pt–Bi alloy therefore combines nontrivial band topology with largely conventional low-temperature lattice dynamics.

3. Trigonal PtBi$_x$12 in the normal state: Weyl topology, inversion breaking, and Fermi-surface tunability

The trigonal noncentrosymmetric PtBi$_x$13 phase is the normal-state basis for the surface-superconductivity literature. In this phase, PtBi$_x$14 is a type-I Weyl semimetal with $_x$15 Weyl points near the Fermi energy and topological surface Fermi arcs on both decorated-honeycomb and kagome-type terminations (Vocaturo et al., 2024). A representative low-energy Weyl point lies at $_x$16 meV above $_x$17, while another set occurs near $_x$18 meV (Vocaturo et al., 2024). The near-$_x$19 bands are dominated by Bi $_x$20 states with smaller Pt $_x$21 contribution, and the Fermi arcs are localized mainly within the first $_x$22 layers, corresponding to roughly $_x$23 (Vocaturo et al., 2024).

The microscopic origin of this Weyl semimetallicity is not assigned primarily to spin–orbit coupling. DFT work that interpolates between the experimentally realized $_x$24 structure and a centrosymmetric $_x$25 parent argues that trigonal PtBi$_x$26 should be understood as a noncentrosymmetric $_x$27 distortion that both breaks inversion symmetry and reduces translational symmetry (Palumbo et al., 28 Mar 2025). In that treatment, inversion breaking generates short-range hopping asymmetries of order $_x$28 eV, exceeding the quoted Bi $_x$29 local SOC matrix elements of $_x$30 and $_x$31 eV, while the low-energy Set I Weyl nodes closest to the Fermi level survive even without SOC (Palumbo et al., 28 Mar 2025). This suggests that in trigonal PtBi$_x$32 the dominant energy scale shaping the semimetallic normal state is the distortion-induced orbital physics associated with reduced translational symmetry, with SOC mainly refining the nodal structure.

Surface-resolved ARPES further shows that the two terminations are electronically inequivalent in ways directly relevant to superconductivity. On the decorated-honeycomb termination, a type-I van Hove singularity sits about $_x$33 meV below $_x$34; on the kagome-type termination, the Fermi arc develops a strongly renormalized, nearly flat segment about $_x$35 meV below $_x$36, with bare and renormalized Fermi velocities of $_x$37 and $_x$38, respectively (Kuibarov et al., 2 Sep 2025). The same work reports substantial spatial variation of Fermi-arc width across a $_x$39m beam spot, implying that the energy alignment of these low-energy features is locally tunable (Kuibarov et al., 2 Sep 2025). This suggests a mechanism by which nominally stoichiometric PtBi$_x$40 can show strongly location-dependent superconducting energy scales.

Bulk transport in the trigonal phase is likewise multiband and electronically fragile. Hall and Nernst measurements reveal a crossover compatible with temperature- and magnetic-field-dependent evolution of hole-like pockets, while DFT shows a Lifshitz transition between $_x$41 and $_x$42 meV Fermi-level shifts, associated with connected or disconnected finger-like hole structures (Caglieris et al., 18 Apr 2025). In-plane angular transport shows further complexity: $_x$43, $_x$44, and high-order planar Hall and AMR features emerge near $_x$45 and $_x$46 only below a field-dependent temperature $_x$47, with $_x$48, $_x$49, $_x$50, and $_x$51 T (Cai et al., 19 Jul 2025). These results place trigonal PtBi$_x$52 among the Pt–Bi materials where topology, multiband transport, and Fermi-surface anisotropy are inseparable.

4. Surface superconductivity in trigonal PtBi$_x$53

The defining recent development in PtBi research is the observation that superconductivity can be confined to the topological surface states of trigonal PtBi$_x$54, while the bulk remains metallic or superconducts only at far lower temperature. ARPES established that below about $_x$55 K the Fermi arcs gap out while the bulk states remain normal, directly motivating the view of PtBi$_x$56 as an intrinsic topological surface-superconductivity candidate (Changdar et al., 2 Jul 2025). In high-resolution laser ARPES, the superconducting gap closes at the center of each arc on the $_x$57-M line, grows away from that point, and reaches a maximum near $_x$58; the coherence-peak shift between arc center and arc edge is about $_x$59 meV, the maximum leading-edge gap is about $_x$60 meV in one cleave, and the gap disappears between $_x$61 and $_x$62 K (Changdar et al., 2 Jul 2025). Repetition on four crystals from different batches places the node at the same momentum, implying a reproducible nodal structure (Changdar et al., 2 Jul 2025).

A separate STM/STS literature reports much larger and much more variable local energy scales. One study found superconducting spectra on both Bi terminations already at $_x$63 K, with local $_x$64 spanning $_x$65 to $_x$66 meV, representative fits of $_x$67 and $_x$68 meV, and survival of the surface state to about $_x$69 T (Schimmel et al., 2023). A later temperature-dependent STS study reported a zero-bias conductance reduction of $_x$70 at $_x$71 K, a gap estimate from the half width at half minimum of $_x$72 meV, and gap closure around $_x$73 K; the same work modeled the spectra with a Dynes form using $_x$74 meV and $_x$75 (Besproswanny et al., 14 Jul 2025). Another STM/STS study on the decorated honeycomb termination reported spatially uniform gaps of $_x$76 meV over hundreds of nanometers, together with extended low-energy in-gap Andreev bound states that intensify as the tip approaches the sample and are interpreted through an anisotropic chiral order parameter

$_x$77

(Huang et al., 18 Jul 2025).

At the opposite end of the reported scale, very-low-temperature STM on $_x$78-PtBi$_x$79 finds a small, BCS-like surface gap centered at $_x$80 meV with width $_x$81 meV, $_x$82 K, and $_x$83 T, together with a hexagonal vortex lattice and $_x$84 nm (Moreno et al., 6 Aug 2025). That work emphasizes reproducible surface superconductivity on both terminations, direct vortex imaging, Josephson tunneling, and quasiparticle-interference weight enhanced at scattering vectors associated with the Fermi arcs (Moreno et al., 6 Aug 2025). It explicitly does not support the most extreme earlier gap and field scales.

The literature therefore contains a genuine unresolved spread in spectroscopic scales. Reported surface-superconducting values range from ARPES gaps of order $_x$85 meV and nodal superconductivity below $_x$86 K, through STS gaps of about $_x$87 meV with $_x$88 K, to a reproducible small-gap surface state with $_x$89 meV and $_x$90 K (Kuibarov et al., 2 Sep 2025). Several papers identify missing coherence peaks, strong broadening, surface sensitivity, and termination dependence as important limitations (Besproswanny et al., 14 Jul 2025). Majorana language is common in this literature, but in the STM-based chiral-pairing work it remains inferential: the strongest direct evidence is the coexistence of a homogeneous surface gap and extended in-gap Andreev states whose line shape is reproduced by a phase-resolved chiral model, rather than a direct observation of isolated Majorana zero modes (Huang et al., 18 Jul 2025).

5. Pairing symmetry and microscopic theories

The superconducting pairing problem in PtBi$_x$91 has been attacked from symmetry, effective-model, and microscopic weak-coupling viewpoints. ARPES-based symmetry analysis assigns the experimentally observed arc-center node to the $_x$92 irreducible representation of $_x$93, with a gap form

$_x$94

identified as nodal $_x$95-wave pairing. In this picture, each gapped Fermi arc carries a sign change and produces one Majorana cone centered at the nodal point; six arcs then yield six Majorana cones per surface and zero-energy Majorana flat bands at hinges or step edges (Changdar et al., 2 Jul 2025). A symmetry-adapted four-band model further shows that, because inversion is absent, the allowed surface pairing on the arcs naturally mixes an $_x$96-wave singlet channel with $_x$97-wave Ising-triplet and $_x$98-wave Rashba-triplet components, and that a $_x$99-phase difference between the two superconducting surfaces produces zero-energy Andreev bound states in the intrinsic superconductor–semimetal–superconductor geometry (Vocaturo et al., 2024).

A Kohn–Luttinger treatment addresses the same surface states from purely electronic repulsion. In a 12-patch model of the six Fermi arcs, the effective pairing problem is written as

$_2$00

with $_2$01 and $_2$02 denoting intra- and inter-chirality scattering channels (Dsouza et al., 29 May 2026). In that framework, strong repulsion between opposite-chirality surface sectors favors a leading $_2$03-wave instability with an intra-arc node at the midpoint of each Fermi arc; for $_2$04, the $_2$05-wave state dominates for approximately $_2$06, while a fully gapped $_2$07-wave state takes over at larger $_2$08, with a narrow nodal $_2$09-wave regime in between (Dsouza et al., 29 May 2026). This theory is explicit that it identifies likely pairing symmetry rather than a quantitatively reliable $_2$10.

A later microscopic theory instead combines anisotropic electron–phonon coupling on the Fermi-arc surface states with statically screened Coulomb repulsion. In that work, the antisymmetrized interaction enters the linearized gap equation

$_2$11

and the competition between strongest Coulomb repulsion at the arc center and strongest phonon attraction between the center and the endpoints drives a nodal solution (Mæland et al., 10 Dec 2025). The experimentally relevant criterion is that the surface-state bandwidth $_2$12 is comparable to the maximum phonon energy $_2$13, so the usual Morel–Anderson reduction of Coulomb repulsion becomes ineffective (Mæland et al., 10 Dec 2025). In that regime, the theory obtains a nodal state whose absolute value reproduces the experimental i-wave-like arc profile, and estimates $_2$14 values of $_2$15, $_2$16, $_2$17, and $_2$18 K for $_2$19-, $_2$20-, $_2$21-, and $_2$22-wave channels, respectively, for one representative parameter set (Mæland et al., 10 Dec 2025). It also predicts that stronger surface Coulomb screening should drive the gap nodeless and increase $_2$23 (Mæland et al., 10 Dec 2025). Taken together, these theories converge on the central point that the Fermi-arc geometry and noncentrosymmetric spin texture of PtBi$_2$24 naturally favor highly anisotropic, often nodal surface pairing states.

6. Spintronic and transport functionalities beyond equilibrium superconductivity

The Pt–Bi family is also a functional materials platform for nonequilibrium transport and spin–charge conversion. In spintronic terahertz emitters, the only PtBi composition directly measured in one comparative study is a $_2$25 nm Pt$_2$26Bi$_2$27 nonmagnetic layer in fused silica / CoFeB / Pt$_2$28Bi$_2$29. At the optimum CoFeB thickness of about $_2$30 nm, this emitter yields a THz amplitude of $_2$31 aVs and central frequency $_2$32 THz, compared with $_2$33 aVs and $_2$34 THz for Pt(2 nm); thus PtBi sacrifices amplitude for a $_2$35 THz upward shift in central frequency and the broadest bandwidth in the measured set, about $_2$36 THz broader than the others (Winkel et al., 2023). THz time-domain spectroscopy further shows that $_2$37, a non-Drude behavior identified as a distinctive carrier-dynamics signature (Winkel et al., 2023).

In spin–orbit-torque devices, dilute PtBi alloys provide a bulk spin Hall enhancement over pure Pt. In Co$_2$38Fe$_2$39B$_2$40(3 nm)/Pt$_2$41Bi$_2$42(4 nm) heterostructures, room-temperature resistivities rise from $_2$43 for Pt to $_2$44 and $_2$45 for Pt$_2$46Bi$_2$47 and Pt$_2$48Bi$_2$49, while dc-bias ST-FMR yields $_2$50 for Pt, $_2$51 for Pt$_2$52Bi$_2$53, and $_2$54 for Pt$_2$55Bi$_2$56 (Shashank et al., 14 Jul 2025). The enhancement is assigned to bulk-dominated extrinsic side-jump scattering through the scaling $_2$57 (Shashank et al., 14 Jul 2025). In $_2$58 nm spin Hall nano-oscillators, the threshold current decreases from $_2$59 mA for Pt to $_2$60 mA for Pt$_2$61Bi$_2$62 and $_2$63 mA for Pt$_2$64Bi$_2$65, corresponding to $_2$66 and $_2$67 reductions (Shashank et al., 14 Jul 2025). This establishes PtBi alloying as a practical route to stronger bulk spin–orbit torque in a Pt-based platform.

The trigonal PtBi$_2$68 crystal itself supports rich magnetotransport. Planar Hall and AMR measurements show not only the expected low-order forms

$_2$69

but also reproducible high-order structures near $_2$70 and $_2$71, strongest at low temperature and high field, with the onset boundary governed by $_2$72 and $_2$73 (Cai et al., 19 Jul 2025). In the same phase, Hall and Nernst measurements indicate a field- and temperature-dependent evolution of hole-like pockets, rather than a transport response dominated straightforwardly by Weyl-node Berry curvature (Caglieris et al., 18 Apr 2025).

At the monolayer limit, first-principles work predicts still another PtBi functionality: intrinsic two-dimensional ferroelectric metallicity with a pronounced Edelstein effect. Monolayer PtBi$_2$74 is predicted to have space group No. $_2$75, point group $_2$76, lattice constant $_2$77, Rashba parameter $_2$78, and a normalized Edelstein coefficient

$_2$79

with the sign coupled to ferroelectric polarization reversal (Pan et al., 23 Jan 2026). An upward Fermi-level shift can reverse the sign of the effect, and a $_2$80 compressive biaxial strain suppresses it by about $_2$81 (Pan et al., 23 Jan 2026). This extends the Pt–Bi materials space from topological semimetals and superconductors to nonvolatile charge–spin conversion in metallic ferroelectrics.

Across these apparently disparate results, a single materials principle recurs: PtBi compounds are unusually sensitive to symmetry lowering, termination, and dilute Bi-induced scattering. In ordered intermetallics that sensitivity generates compensated semimetals, Weyl nodes, and surface superconductivity; in substitutional PtBi films it generates enhanced bulk spin Hall conversion and tunable high-frequency response. The major open issue is therefore not whether PtBi alloys are electronically active, but which structural realization of the Pt–Bi motif is being probed.