BiNi Bilayer Superconductivity

• BiNi bilayer is a superconducting epitaxial Bi/Ni heterostructure combining a 10 nm rhombohedral Bi film with a 1 nm Ni layer, exhibiting time-reversal-symmetry breaking.
• Time-domain terahertz spectroscopy and precision polarimetry reveal a finite Kerr rotation and low-frequency Hall conductivity, underscoring its multiband, disorder-driven nature.
• The interplay of strong spin–orbit coupling and interfacial effects in this bilayer opens pathways for exploring topological superconductivity and potential Majorana modes.

BiNi bilayer most commonly denotes a superconducting epitaxial Bi/Ni thin-film heterostructure comprising a 10 nm rhombohedral Bi(110) film on a 1 nm Ni(100) layer grown on a 0.5 mm MgO(100) substrate. In the reported realization, the bilayer is a strongly spin–orbit coupled, highly disordered but metallic, multiband system whose superconducting state exhibits a zero-field terahertz Kerr rotation and a finite terahertz Hall conductivity, both consistent with time-reversal-symmetry-breaking superconductivity rather than with a response of isolated Bi or Ni films (III et al., 11 Aug 2025).

1. Structural definition and material realization

The experimentally studied BiNi bilayer is an epitaxial heterostructure rather than a chemically uniform binary monolayer. A 1 nm Ni(100) layer is first grown on MgO(100) at 300 K, and a 10 nm rhombohedral Bi(110) film is then grown epitaxially on top at 110 K. The active structure is therefore a 10 nm Bi / 1 nm Ni bilayer on MgO. Separate MgO/Ni(1 nm) and MgO/Bi(10 nm) films show no Kerr rotation onset below 4 K, which identifies the bilayer itself as the relevant superconducting and magneto-optic medium rather than either constituent film in isolation (III et al., 11 Aug 2025).

Aspect	Reported value or description	Context
Substrate	0.5 mm MgO(100)	Optical resonator and growth platform
Ni layer	1 nm Ni(100)	First epitaxial layer
Bi layer	10 nm rhombohedral Bi(110)	Superconducting bilayer component
Normal-state THz response	Dirty metal Drude response	Scattering rate larger than the THz window
Superconducting transition	$T_c \approx 3.8\text{–}3.9$ K	Consistent with earlier work
Upper critical field	$H_{c2} \approx 20\,\text{kG}$	Bilayer superconductivity scale

In the terahertz range $0.2\text{–}2$ THz above $T_c$, $\sigma_1(\nu)$ is slightly decreasing with frequency and $\sigma_2(\nu)$ is slightly increasing. This is consistent with a dirty metal Drude response with a scattering rate larger than the THz window, and not like pure Bi or pure Ni. Earlier work cited in the same study showed that superconductivity is bulk-like throughout the bilayer rather than confined to a pure Bi surface layer, an important point because several early interpretations emphasized surface-localized pairing on Bi (III et al., 11 Aug 2025).

2. Normal-state transport and superconducting electrodynamics

The superconducting state was characterized through time-domain terahertz spectroscopy of the complex longitudinal conductivity,

$\tilde\sigma(\nu)=\sigma_1(\nu)+i\sigma_2(\nu).$

At 7 K the response is dirty-metal-like. On cooling through the transition, spectral weight in $\sigma_1(\nu)$ is transferred to a zero-frequency delta function, while $\sigma_2(\nu)$ develops the expected superconducting divergence,

$\sigma_2(\nu)\propto \frac{1}{\nu}.$

The transition temperature is identified as $H_{c2} \approx 20\,\text{kG}$0 K, consistent with earlier values $H_{c2} \approx 20\,\text{kG}$1 K and $H_{c2} \approx 20\,\text{kG}$2 reported by Prashant et al. (III et al., 11 Aug 2025).

Magnetic-field measurements at 1.6 K show progressive suppression of superconductivity, with complete destruction around $H_{c2} \approx 20\,\text{kG}$3. This scale is reported to match expectations for the Bi/Ni bilayer and to be inconsistent with NiBi$H_{c2} \approx 20\,\text{kG}$4, which could form at the interface but is known to be fully gapped and time-reversal-symmetry-preserving. The result is therefore used to argue that the superconducting condensate belongs to the Bi/Ni bilayer itself rather than to an interfacial parasitic phase (III et al., 11 Aug 2025).

The normal-state and superconducting electrodynamics also constrain the microscopic description. The above-$H_{c2} \approx 20\,\text{kG}$5 conductivity does not resemble pure Bi or pure Ni, whereas the superconducting response is sufficiently robust to support a finite low-frequency Hall conductivity in the ordered phase. This combination is consistent with a multiband metallic state with strong disorder, strong spin–orbit coupling, and substantial interfacial reconstruction.

3. Terahertz polarimetry and Kerr–Faraday separation

The decisive measurements were performed with a time-domain THz spectrometer operating from 0.2 to 2.0 THz and using a polarization-resolved detection scheme. A linearly polarized THz pulse passes through or reflects from the sample, and a wire-grid polarizer at $H_{c2} \approx 20\,\text{kG}$6 acts as a polarizing beam splitter so that both orthogonal electric-field components are measured simultaneously. The complex Kerr rotation is extracted as

$H_{c2} \approx 20\,\text{kG}$7

With calibration and antisymmetrization, the reported precision is better than $H_{c2} \approx 20\,\text{kG}$8 (III et al., 11 Aug 2025).

A distinctive technical feature is the use of the thick MgO substrate itself as a Fabry–Pérot–like optical resonator. When the THz pulse enters from the MgO side, the first transmitted pulse acquires a Faraday rotation from the film, whereas the first reflected pulse acquires Kerr rotation at the film surface plus an additional Faraday rotation upon passing again through the bilayer. Comparison of these pulses isolates the film Kerr angle through

$H_{c2} \approx 20\,\text{kG}$9

This referencing strategy avoids moving the sample and suppresses systematic errors from birefringence and alignment drift.

Residual even-in-field artifacts from mirrors, cryostat windows, and the polarizer are removed by antisymmetrization over opposite training fields. Two cooldowns are performed, one with $0.2\text{–}2$0 and one with $0.2\text{–}2$1, and the odd component is isolated. After antisymmetrization, the normal-state Kerr signal is essentially zero, whereas the superconducting state retains a clear training-field-dependent response.

4. Time-reversal-symmetry breaking

The central experimental result is a finite Kerr rotation at zero applied magnetic field in the superconducting state. The signal is trainable by cooling through $0.2\text{–}2$2 in a small magnetic field, reversible in sign with the sign of the training field, independent of the magnitude of the training field as long as $0.2\text{–}2$3, and absent in the normal state and in control Bi-only and Ni-only films. This behavior is interpreted as evidence for a spontaneous time-reversal-symmetry-breaking order parameter with two degenerate chiral domains, with the training field selecting the domain rather than setting the magnitude of the effect (III et al., 11 Aug 2025).

At the lowest measured frequency, $0.2\text{–}2$4, the observed Kerr angle is

$0.2\text{–}2$5

namely a real Kerr rotation of approximately $0.2\text{–}2$6 with negligible imaginary part. Over $0.2\text{–}2$7 THz, the real part decreases monotonically with increasing frequency, roughly consistent with an inverse dependence $0.2\text{–}2$8, while the imaginary part remains very small within error bars. The normal state at 7 K shows no corresponding Kerr signal after antisymmetrization (III et al., 11 Aug 2025).

A common alternative explanation is trapped flux or pinned vortices. The experimental comparison of training fields with different magnitudes directly addresses this point. The Kerr magnitude is essentially unchanged between $0.2\text{–}2$9 G and $T_c$0 G; only the sign flips with the sign of the training field. The response therefore does not scale with the amount of trained flux and is used to rule out trapped vortices as the dominant source. A second alternative, remanent magnetization, is constrained by warming the magnet above its superconducting transition between runs and by the absence of any training-field-dependent normal-state signal.

5. Hall conductivity and multiband interpretation

For a thin conducting film of thickness $T_c$1 on a non-magnetic substrate, with $T_c$2, the measured Kerr rotation is related to the Hall conductivity through

$T_c$3

where $T_c$4. Since $T_c$5 is measured independently by terahertz spectroscopy, the complex Hall conductivity can be extracted directly from the Kerr data (III et al., 11 Aug 2025).

In the superconducting state at 1.6 K, $T_c$6 is positive and decreases with frequency, while $T_c$7 is negative and also decreases in magnitude with frequency. At the lowest frequency,

$T_c$8

At 7 K, the Hall conductivity is essentially zero across the measured range. The low-frequency Hall response is therefore identified as a purely superconducting and time-reversal-symmetry-breaking phenomenon (III et al., 11 Aug 2025).

The same study links the THz Hall response to earlier high-frequency Kerr data at $T_c$9 eV through Kramers–Kronig consistency. Using $\sigma_1(\nu)$0, $\sigma_1(\nu)$1, and $\sigma_1(\nu)$2, the extracted Hall conductivity is

$\sigma_1(\nu)$3

Comparison with the THz value and the asymptotic scaling

$\sigma_1(\nu)$4

yields an effective scale $\sigma_1(\nu)$5. This scale is much larger than the superconducting gap $\sigma_1(\nu)$6 and of the same order, though smaller than, Bi’s inverted gap at the $\sigma_1(\nu)$7 point, $\sigma_1(\nu)$8. The reported interpretation is therefore multiband and interband in character rather than a dirty single-band mechanism (III et al., 11 Aug 2025).

6. Pairing scenarios and microscopic implications

The present interpretation does not fix a unique superconducting order parameter, but it positions BiNi within the broader literature on chiral and multiband superconductivity. Gong et al. had proposed an even-parity $\sigma_1(\nu)$9 state, motivated by pairing on the Bi surface mediated by magnetic fluctuations in Ni. Later work argued that superconductivity is bulk-like throughout the bilayer, weakening a purely surface-confined scenario. The terahertz Hall data add a further constraint: the inferred scale $\sigma_2(\nu)$0 is an order of magnitude larger than the superconducting gap, which is used to argue that the Kerr effect is closely tied to multiband electronic structure and interband transitions rather than to a simple single-band chiral model (III et al., 11 Aug 2025).

Within this framing, two broad mechanisms remain in view. One is an intrinsic multiband mechanism in which interband matrix elements in a time-reversal-symmetry-breaking superconducting state generate a finite anomalous Hall conductivity even in the clean limit. The other is an extrinsic impurity mechanism in a single-band chiral superconductor, where skew scattering produces the Hall response. The reported frequency dependence of $\sigma_2(\nu)$1 and $\sigma_2(\nu)$2, together with the extracted $\sigma_2(\nu)$3, is argued to be more consistent with the intrinsic multiband scenario (III et al., 11 Aug 2025).

A cautious formulation is necessary. The study explicitly stops short of a detailed microscopic model for BiNi and calls for more explicit calculations of the Hall response for possible time-reversal-symmetry-breaking order parameters in BiNi bilayers. The current evidentiary status is therefore strong on the existence of a superconductivity-linked Kerr effect and finite THz Hall response, but open on the precise orbital, band-resolved, and parity structure of the condensate.

7. Relation to other bilayer frameworks and broader significance

The term “BiNi bilayer” also invites comparison with two adjacent bilayer literatures. In the theory of bilayer stacking ferroelectricity, a hypothetical BiNi/BiNi bilayer would be analyzed as two stacked layers of the same 2D material related by a stacking operation $\sigma_2(\nu)$4. Within that framework, if the monolayer were centrosymmetric, pure sliding $\sigma_2(\nu)$5 could not break inversion; rotations, layer flips, or more general stackings would be required to induce ferroelectricity. This is a distinct usage from the experimentally realized Bi/Ni superconducting heterobilayer, but it defines how a same-material BiNi bilayer would be treated in group-theoretical terms (Ji et al., 2022).

Bilayer bismuth provides an additional comparative background. Structure-search calculations predict multiple low-energy phases of bilayer Bi—puckered monoclinic, buckled hexagonal, $\sigma_2(\nu)$6, $\sigma_2(\nu)$7, and $\sigma_2(\nu)$8—with strong spin–orbit coupling, gap renormalization, a Mexican-hat valence dispersion in the buckled hexagonal phase, and symmetry-protected Dirac points in the $\sigma_2(\nu)$9 phase. This suggests that Bi-based bilayers can host structurally tunable multiband and interband-rich electronic structure, a context that is at least qualitatively compatible with the multiband interpretation of the Bi/Ni Hall response, although no direct band-structure reduction from bilayer Bi to Bi/Ni is provided (Singh et al., 2019).

In the broader superconductivity literature, BiNi joins a relatively small set of materials where time-reversal symmetry breaking in the superconducting state is convincingly indicated, alongside systems such as UPt$\tilde\sigma(\nu)=\sigma_1(\nu)+i\sigma_2(\nu).$0, Sr$\tilde\sigma(\nu)=\sigma_1(\nu)+i\sigma_2(\nu).$1RuO$\tilde\sigma(\nu)=\sigma_1(\nu)+i\sigma_2(\nu).$2, and certain noncentrosymmetric and multiband superconductors. What distinguishes BiNi is the combination of a 2D epitaxial heterostructure, strong spin–orbit coupling, interfacial magnetism, lack of inversion symmetry, and a transition temperature near 4 K. It has therefore been treated as a promising candidate for topological superconductivity and associated Majorana zero modes, particularly in chiral pairing scenarios with nonzero phase winding and Chern number. The methodological contribution is likewise significant: terahertz polarimetry with $\tilde\sigma(\nu)=\sigma_1(\nu)+i\sigma_2(\nu).$3rad sensitivity, substrate-resonator Kerr/Faraday referencing, and field-antisymmetrization establishes a route for direct THz spectroscopy of $\tilde\sigma(\nu)=\sigma_1(\nu)+i\sigma_2(\nu).$4 in time-reversal-symmetry-breaking superconductors (III et al., 11 Aug 2025).