Hidden Rashba Effect

• Hidden Rashba effect is the phenomenon where locally asymmetric Rashba spin polarizations in inversion-partner sectors generate sector-resolved spin textures while maintaining global band degeneracy.
• It arises from strong spin–orbit coupling in locally non-centrosymmetric environments that compete with inter-sector tunneling, leading to spin–layer locking without net bulk spin splitting.
• Materials like BaNiS₂, Si₂Bi₂, and Bi₂O₂Se exemplify this effect, with reported α_R values up to 2.16 eV·Å and clear sector segregation supporting robust hidden spin textures.

Hidden Rashba effect denotes a Rashba-type spin polarization that exists in a crystal whose global space-group symmetry is centrosymmetric, but whose constituent local sectors—such as inversion-partner layers, sublayers, or site environments—are individually non-centrosymmetric. In that setting, spin–orbit coupling generates opposite local Rashba couplings on the inversion-related sectors, so the total band structure remains twofold degenerate while the degenerate partners can carry opposite, sector-resolved spin textures. The central consequence is a “hidden” spin polarization: no net bulk spin splitting in the ordinary band-structure sense, yet a nonzero local spin polarization and, frequently, spin–layer locking. This phenomenon is commonly denoted R-2, in contrast to the conventional Rashba effect R-1 in globally inversion-broken systems (Yuan et al., 2018).

1. Definition and conceptual scope

The conventional Rashba effect arises when spin–orbit coupling acts in a globally inversion-asymmetric environment, producing the standard low-energy Hamiltonian

$H_R=\alpha_R(\sigma_x k_y-\sigma_y k_x),$

or equivalently $H_R=\alpha_R(\sigma\times k)\cdot \hat z$, and lifting spin degeneracy into two nondegenerate branches with opposite helicities. Hidden Rashba differs only in symmetry setting, not in the local spin–orbit structure: the global crystal preserves inversion, but each local sector supports the same Rashba form with opposite sign on the inversion partner (Yuan et al., 2018).

A minimal sector-resolved representation is

$$H(k)=\frac{\hbar^2 k^2}{2m}\,\tau_0+\tau_z\,\alpha_R(\sigma_x k_y-\sigma_y k_x),$$

where $\tau_z=\pm1$ labels the pair of inversion-related sectors. Diagonalization yields

$$E_{\tau,s}(k)=\frac{\hbar^2 k^2}{2m}+s\tau\alpha_R |k|,$$

so each sector separately has the familiar Rashba splitting, but the total crystal remains spin-degenerate because the two sectors contribute opposite helicities at the same $k$ (Yuan et al., 2022).

The same logic extends beyond the specific Rashba form. The literature distinguishes R-2 from the hidden Dresselhaus counterpart D-2, and more generally from “hidden effect X,” meaning a local effect permitted by sector symmetry but canceled by the nominal global symmetry. In this broader sense, hidden Rashba is part of a symmetry-based class of sector-resolved phenomena rather than an anomaly restricted to a few layered compounds (Yuan et al., 2022).

2. Symmetry conditions and microscopic origin

The essential symmetry ingredients are global inversion symmetry, local inversion asymmetry, and a mechanism that prevents the opposite sector contributions from trivially recombining. Global inversion together with time reversal enforces Kramers-like double degeneracy. Local sector symmetry must nevertheless allow a polar axis or an inversion-odd dipole field, so that Rashba SOC is symmetry-allowed within each sector. Hidden Rashba therefore requires not merely “local asymmetry somewhere in the unit cell,” but local non-centrosymmetric sectors that can host opposite internal dipoles (Yuan et al., 2018).

A central development in the microscopic understanding is that hidden Rashba is not explained by local dipoles alone. In BaNiS$_2$, the relevant spin splitting is enforced by specific symmetries, including non-symmorphic operations along X–M, which forbid mixing between states localized on the two inversion-partner sectors. The pertinent Bloch wavefunctions then segregate spatially onto one sector or the other. The segregation measure

$$D(P_k)\equiv \frac{|P_k(S_a)-P_k(S_b)|}{P_k(S_a)+P_k(S_b)},$$

with

$P_k(S_a)=\int_{r\in S_a} |\psi_k(r)|^2\,d^3r,$

reaches $D\simeq 88\%$ along X–M, so each spin branch predominantly samples a single sector’s local dipole field rather than an average over both sectors (Yuan et al., 2018).

A complementary microscopic perspective comes from the competition between local Rashba SOC and inter-sublayer tunneling. In the four-component basis $H_R=\alpha_R(\sigma\times k)\cdot \hat z$0, Si$H_R=\alpha_R(\sigma\times k)\cdot \hat z$1Bi$H_R=\alpha_R(\sigma\times k)\cdot \hat z$2 is described by

$H_R=\alpha_R(\sigma\times k)\cdot \hat z$3

with doubly degenerate branches

$H_R=\alpha_R(\sigma\times k)\cdot \hat z$4

This formulation makes explicit that strong hidden Rashba requires SOC large enough, and sublayer coupling weak enough, for the Rashba term to dominate the recombination tendency induced by inter-sublayer overlap (Lee et al., 2020).

Orbital character can further enhance the effect. In Si$H_R=\alpha_R(\sigma\times k)\cdot \hat z$5Bi$H_R=\alpha_R(\sigma\times k)\cdot \hat z$6, the conduction-band minimum has strong Bi $H_R=\alpha_R(\sigma\times k)\cdot \hat z$7 character, and the layer-resolved orbital angular momentum maps correlate with the large hidden Rashba spin–layer locking. This is described by an “orbital Rashba” contribution

$H_R=\alpha_R(\sigma\times k)\cdot \hat z$8

which reinforces the spin splitting when nonzero in-plane orbital angular momentum accompanies local inversion breaking (Lee et al., 2020).

3. Effective Hamiltonians and spin textures

At the single-sector level, hidden Rashba is governed by the same spin–orbit structure as conventional Rashba. The distinction lies in how the sector degree of freedom is incorporated. For inversion-partner layers with interlayer hopping, a standard bilayer Hamiltonian is

$H_R=\alpha_R(\sigma\times k)\cdot \hat z$9

so that opposite Rashba coefficients on the two layers are hybridized by $$H(k)=\frac{\hbar^2 k^2}{2m}\,\tau_0+\tau_z\,\alpha_R(\sigma_x k_y-\sigma_y k_x),$$0. In Bi$$H(k)=\frac{\hbar^2 k^2}{2m}\,\tau_0+\tau_z\,\alpha_R(\sigma_x k_y-\sigma_y k_x),$$1O$$H(k)=\frac{\hbar^2 k^2}{2m}\,\tau_0+\tau_z\,\alpha_R(\sigma_x k_y-\sigma_y k_x),$$2Se thin films, an equivalent form is written as

$$H(k)=\frac{\hbar^2 k^2}{2m}\,\tau_0+\tau_z\,\alpha_R(\sigma_x k_y-\sigma_y k_x),$$3

with $$H(k)=\frac{\hbar^2 k^2}{2m}\,\tau_0+\tau_z\,\alpha_R(\sigma_x k_y-\sigma_y k_x),$$4 and $$H(k)=\frac{\hbar^2 k^2}{2m}\,\tau_0+\tau_z\,\alpha_R(\sigma_x k_y-\sigma_y k_x),$$5 for a single $$H(k)=\frac{\hbar^2 k^2}{2m}\,\tau_0+\tau_z\,\alpha_R(\sigma_x k_y-\sigma_y k_x),$$6 block. The local Rashba terms on the two Bi monolayers have equal magnitude and opposite sign, so the global band structure remains twofold degenerate even though each monolayer carries a large chiral in-plane spin texture (Wang et al., 2024).

In some systems, the hidden spin texture is not the standard in-plane Rashba helix. Monolayer WSi$$H(k)=\frac{\hbar^2 k^2}{2m}\,\tau_0+\tau_z\,\alpha_R(\sigma_x k_y-\sigma_y k_x),$$7N$$H(k)=\frac{\hbar^2 k^2}{2m}\,\tau_0+\tau_z\,\alpha_R(\sigma_x k_y-\sigma_y k_x),$$8 belongs to space group $$H(k)=\frac{\hbar^2 k^2}{2m}\,\tau_0+\tau_z\,\alpha_R(\sigma_x k_y-\sigma_y k_x),$$9 with point group $\tau_z=\pm1$0, which contains a horizontal mirror $\tau_z=\pm1$1. Because $\tau_z=\pm1$2 forces the spin–orbit field $\tau_z=\pm1$3 to be normal to the layer, the monolayer exhibits full-zone persistent spin texture: $\tau_z=\pm1$4 and $\tau_z=\pm1$5. Along the M–K line, whose little group is $\tau_z=\pm1$6, the low-energy Hamiltonian is

$\tau_z=\pm1$7

with

$\tau_z=\pm1$8

Since $\tau_z=\pm1$9 commutes with $$E_{\tau,s}(k)=\frac{\hbar^2 k^2}{2m}+s\tau\alpha_R |k|,$$0, the spin texture is purely out of plane, $$E_{\tau,s}(k)=\frac{\hbar^2 k^2}{2m}+s\tau\alpha_R |k|,$$1, yielding a persistent spin helix protected by symmetry rather than a conventional in-plane Rashba winding (Sheoran et al., 2022).

This point is significant because “hidden Rashba effect” is often used operationally for any sector-resolved Rashba-like hidden spin polarization, while the actual local spin texture may interpolate among Rashba, Dresselhaus, Zeeman-like, or persistent-spin-texture limits depending on the local point group and the relevant little group in $$E_{\tau,s}(k)=\frac{\hbar^2 k^2}{2m}+s\tau\alpha_R |k|,$$2-space. In the WSi$$E_{\tau,s}(k)=\frac{\hbar^2 k^2}{2m}+s\tau\alpha_R |k|,$$3N$$E_{\tau,s}(k)=\frac{\hbar^2 k^2}{2m}+s\tau\alpha_R |k|,$$4 family, the bulk or even-layer form is centrosymmetric, but each W atom has a local $$E_{\tau,s}(k)=\frac{\hbar^2 k^2}{2m}+s\tau\alpha_R |k|,$$5 site point group. The result is a hidden spin polarization with $$E_{\tau,s}(k)=\frac{\hbar^2 k^2}{2m}+s\tau\alpha_R |k|,$$6 and spin–layer locking rather than an ordinary in-plane Rashba helix (Sheoran et al., 2022).

4. Material realizations and quantitative scales

Hidden Rashba has been identified in chemically and electronically diverse systems, including layered semiconductors, oxides, cuprates, and nanostructured metals. The unifying structure is a centrosymmetric host composed of inversion-related sectors with locally non-centrosymmetric environments.

System	Hidden-Rashba realization	Representative values
BaNiS$$E_{\tau,s}(k)=\frac{\hbar^2 k^2}{2m}+s\tau\alpha_R |k|,$$7	Symmetry-enforced sector segregation along X–M	$$E_{\tau,s}(k)=\frac{\hbar^2 k^2}{2m}+s\tau\alpha_R |k|,$$8; $$E_{\tau,s}(k)=\frac{\hbar^2 k^2}{2m}+s\tau\alpha_R |k|,$$9
Si$k$0Bi$k$1	Centrosymmetric Bi–Si–Si–Bi sublayers with strong SLL	$k$2; $k$3
Bi$k$4O$k$5Se	Hidden Rashba bilayer in $k$6 blocks	$k$7
WSi$k$8N$k$9 family	Hidden spin polarization from local W-site asymmetry	$_2$0 on M–K; $_2$1 at K/K′
YBa$_2$2Cu$_2$3O$_2$4	CuO$_2$5 Rashba bilayers with opposite layer helicities	$_2$6–$_2$7
Ag-in-Au bulk composite	Buried inversion-related Ag/Au interfaces in bulk Au	$_2$8–$_2$9

In Si$$D(P_k)\equiv \frac{|P_k(S_a)-P_k(S_b)|}{P_k(S_a)+P_k(S_b)},$$0Bi$$D(P_k)\equiv \frac{|P_k(S_a)-P_k(S_b)|}{P_k(S_a)+P_k(S_b)},$$1, first-principles fitting to the bilayer model gives $$D(P_k)\equiv \frac{|P_k(S_a)-P_k(S_b)|}{P_k(S_a)+P_k(S_b)},$$2 at full SOC strength and $$D(P_k)\equiv \frac{|P_k(S_a)-P_k(S_b)|}{P_k(S_a)+P_k(S_b)},$$3. The paper characterizes this as the largest hidden-Rashba coefficient reported in any 2D R-2 material among the listed comparisons. The large value is attributed to the joint action of strong SOC, favorable $$D(P_k)\equiv \frac{|P_k(S_a)-P_k(S_b)|}{P_k(S_a)+P_k(S_b)},$$4-derived orbital angular momentum, and weakened sublayer coupling (Lee et al., 2020).

Bi$$D(P_k)\equiv \frac{|P_k(S_a)-P_k(S_b)|}{P_k(S_a)+P_k(S_b)},$$5O$$D(P_k)\equiv \frac{|P_k(S_a)-P_k(S_b)|}{P_k(S_a)+P_k(S_b)},$$6Se provides a particularly clear hidden-Rashba bilayer platform. In inversion-symmetric thick films, DFT yields $$D(P_k)\equiv \frac{|P_k(S_a)-P_k(S_b)|}{P_k(S_a)+P_k(S_b)},$$7 for each sector, yet the global band structure remains degenerate and Shubnikov–de Haas oscillations show a single frequency $$D(P_k)\equiv \frac{|P_k(S_a)-P_k(S_b)|}{P_k(S_a)+P_k(S_b)},$$8 with no beating. In a one-unit-cell Janus film grown on SrTiO$$D(P_k)\equiv \frac{|P_k(S_a)-P_k(S_b)|}{P_k(S_a)+P_k(S_b)},$$9, inversion symmetry is broken and a global Rashba parameter $P_k(S_a)=\int_{r\in S_a} |\psi_k(r)|^2\,d^3r,$0 appears (Wang et al., 2024).

In WSi$P_k(S_a)=\int_{r\in S_a} |\psi_k(r)|^2\,d^3r,$1N$P_k(S_a)=\int_{r\in S_a} |\psi_k(r)|^2\,d^3r,$2, the hidden effect is intertwined with persistent spin texture and coupled spin–valley locking. The monolayer and odd-layer slabs are non-centrosymmetric, whereas bulk and even-layer slabs are centrosymmetric. In the centrosymmetric layered case, the two branches of each Bloch doublet carry opposite $P_k(S_a)=\int_{r\in S_a} |\psi_k(r)|^2\,d^3r,$3 and are spatially segregated on the top and bottom W layers, with spin-texture maps showing $P_k(S_a)=\int_{r\in S_a} |\psi_k(r)|^2\,d^3r,$4 along K–M–K and a nearly layer-pure character $P_k(S_a)=\int_{r\in S_a} |\psi_k(r)|^2\,d^3r,$5 (Sheoran et al., 2022).

YBa$P_k(S_a)=\int_{r\in S_a} |\psi_k(r)|^2\,d^3r,$6Cu$P_k(S_a)=\int_{r\in S_a} |\psi_k(r)|^2\,d^3r,$7O$P_k(S_a)=\int_{r\in S_a} |\psi_k(r)|^2\,d^3r,$8 supplies a cuprate realization. Each unit cell contains a pair of CuO$P_k(S_a)=\int_{r\in S_a} |\psi_k(r)|^2\,d^3r,$9 layers, and the individual layers are non-centrosymmetric because of unequal neighboring charges and oxygen dimpling, enforcing opposite Rashba couplings $D\simeq 88\%$0. The DFT-inspired model predicts a spin splitting of approximately $D\simeq 88\%$1–$D\simeq 88\%$2 along much of the hole-like Fermi surface (Atkinson, 2019).

A distinct route appears in bulk Au containing buried Ag nanoparticles. Here the global solid remains inversion symmetric on average, but each nanoscale Ag/Au interface locally supports a Rashba Hamiltonian. Magnetotransport yields $D\simeq 88\%$3–$D\simeq 88\%$4 near filling fractions $D\simeq 88\%$5–$D\simeq 88\%$6, together with up to a $D\simeq 88\%$7 enhancement in the spin–orbit scattering rate relative to pure Au nanoparticle films (Kumbhakar et al., 3 Sep 2025).

5. Hidden-to-apparent conversion, transport signatures, and experimental probes

A defining property of hidden Rashba systems is that small symmetry perturbations can transform sector-canceled local SOC into an uncompensated global Rashba splitting. In pristine monolayer WSi$D\simeq 88\%$8N$D\simeq 88\%$9, $H_R=\alpha_R(\sigma\times k)\cdot \hat z$00 forbids the linear Rashba term near $H_R=\alpha_R(\sigma\times k)\cdot \hat z$01. Applying an out-of-plane electric field $H_R=\alpha_R(\sigma\times k)\cdot \hat z$02 breaks $H_R=\alpha_R(\sigma\times k)\cdot \hat z$03 but preserves $H_R=\alpha_R(\sigma\times k)\cdot \hat z$04 at $H_R=\alpha_R(\sigma\times k)\cdot \hat z$05, allowing

$H_R=\alpha_R(\sigma\times k)\cdot \hat z$06

For DFT+SOC+EEF$H_R=\alpha_R(\sigma\times k)\cdot \hat z$07, the resulting conventional Rashba ring around $H_R=\alpha_R(\sigma\times k)\cdot \hat z$08 has $H_R=\alpha_R(\sigma\times k)\cdot \hat z$09 and a small splitting $H_R=\alpha_R(\sigma\times k)\cdot \hat z$10 few meV, while the M–K persistent texture remains essentially unaffected up to $H_R=\alpha_R(\sigma\times k)\cdot \hat z$11 because the $H_R=\alpha_R(\sigma\times k)\cdot \hat z$12 term still dominates with $H_R=\alpha_R(\sigma\times k)\cdot \hat z$13 (Sheoran et al., 2022).

The same conversion is explicit in Bi$H_R=\alpha_R(\sigma\times k)\cdot \hat z$14O$H_R=\alpha_R(\sigma\times k)\cdot \hat z$15Se. In a one-unit-cell film on SrTiO$H_R=\alpha_R(\sigma\times k)\cdot \hat z$16, the Bi–O–Ti Janus configuration introduces a net electrostatic potential gradient across the film, modeled by

$H_R=\alpha_R(\sigma\times k)\cdot \hat z$17

with $H_R=\alpha_R(\sigma\times k)\cdot \hat z$18. This breaks inversion so the alternating $H_R=\alpha_R(\sigma\times k)\cdot \hat z$19 fields no longer cancel, producing two nondegenerate spin-split bands with an effective global Rashba parameter $H_R=\alpha_R(\sigma\times k)\cdot \hat z$20. Experimentally, thick symmetric films show only even-integer quantum Hall plateaus $H_R=\alpha_R(\sigma\times k)\cdot \hat z$21 up to $H_R=\alpha_R(\sigma\times k)\cdot \hat z$22, whereas the 1 uc Janus film shows both even- and odd-integer plateaus $H_R=\alpha_R(\sigma\times k)\cdot \hat z$23 and SdH beating with Fourier peaks at $H_R=\alpha_R(\sigma\times k)\cdot \hat z$24 and $H_R=\alpha_R(\sigma\times k)\cdot \hat z$25 (Wang et al., 2024).

Nanoribbon transport offers another diagnostic. In CVD-grown Bi$H_R=\alpha_R(\sigma\times k)\cdot \hat z$26O$H_R=\alpha_R(\sigma\times k)\cdot \hat z$27Se nanoribbons, conductance plateaus at $H_R=\alpha_R(\sigma\times k)\cdot \hat z$28 occur in exact units of $H_R=\alpha_R(\sigma\times k)\cdot \hat z$29 up to $H_R=\alpha_R(\sigma\times k)\cdot \hat z$30, and under magnetic fields up to $H_R=\alpha_R(\sigma\times k)\cdot \hat z$31 no half-integer $H_R=\alpha_R(\sigma\times k)\cdot \hat z$32 plateaus appear. The effective hidden-Rashba bilayer model gives a renormalized $H_R=\alpha_R(\sigma\times k)\cdot \hat z$33 of $H_R=\alpha_R(\sigma\times k)\cdot \hat z$34, so Zeeman splittings remain below the $H_R=\alpha_R(\sigma\times k)\cdot \hat z$35 broadening $H_R=\alpha_R(\sigma\times k)\cdot \hat z$36. Around $H_R=\alpha_R(\sigma\times k)\cdot \hat z$37, the plateau sequence follows the Pascal triangle series $H_R=\alpha_R(\sigma\times k)\cdot \hat z$38, reflecting the interplay of size quantization in two transverse directions (Xiao et al., 7 Jul 2025).

Because hidden Rashba leaves the total spin texture zero while preserving strong layer- or sector-resolved spin polarization, momentum-resolved probes require some degree of sector selectivity. The literature explicitly identifies layer- or depth-sensitive ARPES and spin-resolved scanning probes as methods capable of detecting hidden spin textures, with photon energy or escape depth controlling the relative sector weight (Yuan et al., 2022).

6. Related phenomena, misconceptions, and significance

A common misconception is that hidden Rashba is simply “local Rashba averaged to zero.” The more precise statement is that local inversion asymmetry is necessary but not sufficient. When the Bloch states are evenly delocalized over inversion partners, local spin polarizations compensate trivially and no robust hidden splitting survives. The nontrivial regime requires symmetry-enforced or otherwise stabilized wavefunction segregation onto individual sectors, or sufficiently favorable competition between SOC and inter-sector hybridization, so that the sector-resolved spin texture remains well defined (Yuan et al., 2018).

A second misconception is that hidden Rashba is an artifact of surfaces, disorder, or imperfections. The antiferromagnetic generalization makes the opposite point explicitly: hidden spin polarizations can be intrinsic properties of the perfect crystal, arising because local sectors admit a spin splitting that the global symmetry only conceals rather than forbids microscopically. This broader framework places hidden Rashba alongside hidden Dresselhaus and SOC-independent hidden spin polarization in antiferromagnets (Yuan et al., 2022).

A third misconception is that hidden Rashba must always produce the conventional in-plane helical texture. The WSi$H_R=\alpha_R(\sigma\times k)\cdot \hat z$39N$H_R=\alpha_R(\sigma\times k)\cdot \hat z$40 family shows that hidden spin polarization may instead appear as out-of-plane spin–layer locking and full-zone persistent spin texture when $H_R=\alpha_R(\sigma\times k)\cdot \hat z$41 or local $H_R=\alpha_R(\sigma\times k)\cdot \hat z$42 symmetry constrains the spin–orbit field to the layer normal (Sheoran et al., 2022).

From the standpoint of materials functionality, the recurring themes are spin–layer locking, electrical unmasking of latent SOC, and coexistence with other electronic quantum numbers. In WSi$H_R=\alpha_R(\sigma\times k)\cdot \hat z$43N$H_R=\alpha_R(\sigma\times k)\cdot \hat z$44, hidden spin polarization coexists with coupled spin–valley locking and a large Zeeman-like valley splitting $H_R=\alpha_R(\sigma\times k)\cdot \hat z$45. In Bi$H_R=\alpha_R(\sigma\times k)\cdot \hat z$46O$H_R=\alpha_R(\sigma\times k)\cdot \hat z$47Se, hidden Rashba controls Landau-level degeneracies and the parity of observed quantum Hall plateaus. In YBa$H_R=\alpha_R(\sigma\times k)\cdot \hat z$48Cu$H_R=\alpha_R(\sigma\times k)\cdot \hat z$49O$H_R=\alpha_R(\sigma\times k)\cdot \hat z$50, a hidden Rashba texture is predicted to influence the superconducting and charge-density-wave regimes through a Fermi-wavevector splitting of the underlying CuO$H_R=\alpha_R(\sigma\times k)\cdot \hat z$51 bilayer states (Atkinson, 2019).

These developments suggest a unifying interpretation: hidden Rashba is best viewed not as a weakened version of R-1, but as a sector-resolved SOC phenomenon whose observables depend on whether the experiment couples to the total crystal, to a single sector, or to a perturbation that breaks the equivalence of inversion partners. In that sense, hidden Rashba provides a symmetry-based route to strong spin–orbit functionality in crystals that remain globally centrosymmetric.