Inverse CISS: Chiral Spin-to-Charge Conversion

• Inverse CISS is a spin-to-charge conversion phenomenon where chiral molecules leverage spin–orbit coupling and helical geometry for handedness-dependent electron deflection.
• The phenomenon is modeled using a tight-binding NEGF approach that incorporates both Rashba and intra-molecular SOC to capture angular voltage responses and spin dynamics.
• Experimental and simulation results show that ICISS, unlike the conventional ISHE, exhibits a sign reversal with chirality and demonstrates robust performance even in disordered molecular films.

Inverse chiral-induced spin selectivity (inverse CISS, ICISS) is a spin–to–charge conversion phenomenon observed in chiral molecule systems, where the spin of electrons interacts with the helical geometry and spin–orbit coupling (SOC) of the molecular structure, resulting in a handedness-dependent transverse charge response. Unlike the conventional inverse spin Hall effect (ISHE) in metals, where a spin current is converted to a transverse charge current due to intrinsic SOC, ICISS arises from the spin-dependent deflection of electrons along the axis of chiral molecules. This effect—demonstrated in self-assembled molecular films such as helical polyalanine or DNA analogs—offers a chemical control knob for tuning spin–charge conversion efficiency and sign, with conversion ratios that can reach unity within molecular length scales (Zhang et al., 4 Sep 2025, Liu et al., 4 Sep 2025).

1. Physical Origin and Mechanism

ICISS is established when a pure spin current $J_s$ is injected from a ferromagnetic lead (e.g., Ni$_{81}$Fe$_{19}$) into a film of chiral molecules. The essential features are:

• Spin–Orbit Coupling Sources: (1) Rashba-type SOC at the interface (normal electric field $E_x$), (2) intra-molecular SOC from the electrostatic environment of the chiral monomers.
• Helical Geometry: The chiral molecular potential $V(\mathbf{r})$ breaks mirror symmetry along the helix axis $\hat{z}$.
• Spin-Dependent Deflection: Electrons with spin $\sigma_z = \pm1$ are deflected by the SOC term $$\propto \boldsymbol{\sigma}\cdot(\nabla V\times\mathbf{p})$$, yielding opposite charge accumulations ($V_z$) at $\pm\hat{z}$ surfaces.

Reversing the molecular handedness switches which spin state is transmitted preferentially, flipping the sign of the ICISS signal. This mechanism is fundamentally distinct from ISHE, which arises from bulk SOC in metals and is not sensitive to molecular chirality.

2. Theoretical Model and Hamiltonian Structure

The minimal tight-binding model for ICISS employs:

• Lattice Discretization: Cubic lattice ($n_x, n_y, n_z$), size $L_x\times L_y\times L_z$.
• Full Hamiltonian:

$$H = H_{\rm mol} + H_{\rm SOC}^{\rm mol} + H_{\rm hop}^{x,y} + H_{\rm Rashba} + H_{\rm inj} + H_{\rm y\!-\!probes}$$

• $H_{\rm mol}$: Helical chain hopping; $j = 1,2$ are intertwined helices.
• $H_{\rm SOC}^{\rm mol}$: Intra-chain SOC, $\boldsymbol{\Omega}_{n_z}$ encodes helix tangent.
• $H_{\rm Rashba}$: Rashba SOC from $E_x$.
• $H_{\rm hop}^{x,y}$: Inter-chain hopping in transverse directions.
• $H_{\rm inj}$: Spin injector lead; $H_{\rm y\!-\!probes}$: voltage probes (floating, zero net current).

Via non-equilibrium Green’s function (NEGF) formalism, spin-resolved transport and voltage signals are computed subject to realistic boundary conditions.

3. Spin–Charge Conversion Formalism and Distinction from ISHE

The central transport relations are:

• ISHE:

$$V_y^{\rm ISHE} \propto \theta_{\rm SH}\,|\mathbf{J}_s|\,\cos\phi$$

with spin Hall angle $\theta_{\rm SH}$ and angle $\phi$ between spin polarization and $z$ axis. ISHE vanishes under chirality reversal.

• ICISS:

$$V_z^{\rm ICISS} \propto C_{\rm mol}\,|\mathbf{J}_s|\,\cos\phi$$

$C_{\rm mol}=+C_0$ for right-handed molecules, $-C_0$ for left-handed. ICISS flips sign with molecular handedness.

ISHE produces charge currents perpendicular to both spin polarization and spin current direction; ICISS gives deflection strictly along the molecular axis, and $C_{\rm mol}$ can approach unity for long helices ($L_z\gtrsim$ spin diffusion length).

4. Dependence on Molecular Structure, Disorder, and System Geometry

Key dependences established through tight-binding NEGF simulations:

Parameter	ISHE Voltage $V_y$	ICISS Voltage $V_z$
Chirality	Independent	Flips sign with handedness
Film thickness $L_x$	Peaks for thin films; decay $1/L_x$ for $L_x\gg\ell_{\rm sf}$	Similar scaling, saturates for long $L_x$
Width $L_y$	$V_y\propto L_y/L_x$	$V_z$ independent of $L_y$
Length $L_z$	$V_y$~constant	$V_z$ grows and saturates with $L_z$
Disorder $W$	Modest peak broadening, signals robust	Signals robust, even for $W\sim t_1$

Energy dependence: both $V_y$ and $V_z$ only nonzero within molecular bands; peak near band edges; electron-hole symmetry $V_{y,z}(-E)=-V_{y,z}(E)$.

The ICISS effect persists for strong disorder and is therefore robust to misalignment, defects, and impurity in the molecular film (Zhang et al., 4 Sep 2025).

5. Angular Dependence and Separation from Conventional ISHE

Rotation of spin-polarization $\hat{o}_s$ in the $xz$-plane shows:

• ISHE ($y$-voltage): $V_y(\theta) = V_y^{\rm ISHE}\,\cos\theta$, chirality-independent.
• ICISS ($z$-voltage): $V_z(\theta) = V_z^{\rm ICISS}\,\cos\theta$, flips sign with chirality.

Combined analysis in the $yz$-plane demonstrates a phase shift between ISHE and ICISS contributions, which can be fit to $V_y(\varphi)\sim A\,\cos\varphi+B\,\sin\varphi$ and $V_z(\varphi)\sim B\,\cos\varphi + A\,\sin\varphi$, allowing for quantitative extraction of the ICISS term (Zhang et al., 4 Sep 2025).

6. Experimental Observations and Device Implications

Moharana et al. [28] experimentally confirmed ICISS by observing that the inverse spin Hall voltage on Au was asymmetric under field reversal when coated with chiral polyalanine helices. The angular dependence ($\sin2\alpha$), chirality switch, and magnitude are captured quantitatively by the NEGF tight-binding models.

• Achiral or racemic monolayers restore symmetry ($V_H(+B)=V_H(-B)$).
• Effective spin selectivity $S(\alpha)$ (see key equation above) rises from $23\%$ (helix length $20$) to $30\%$ ($L_p=40$).
• The conversion efficiency, robustness to disorder, and chemical tunability of pitch, sequence, and radius suggest applicability in organic spintronic devices (spin diodes, reconfigurable logic) (Zhang et al., 4 Sep 2025, Liu et al., 4 Sep 2025).

7. Significance and Outlook

Inverse CISS represents a distinct, tunable, and highly efficient mechanism for spin-to-charge conversion in chiral molecular materials. Its separation from conventional ISHE, sensitivity to molecular handedness, extended spin diffusion length, and disorder resilience support potential for low-power molecular spintronics, molecular logic gates, and spin-based sensors. Future directions include synthetic optimization of chiral polymers for maximal ICISS efficiency, multichannel devices exploiting chirality control, and integration with ferromagnetic leads for nonvolatile information processing (Zhang et al., 4 Sep 2025).

References:

• "Spin-to-charge conversion driven by inverse chiral-induced spin selectivity" (Zhang et al., 4 Sep 2025)
• "Spin-to-charge conversion modulated by chiral molecules" (Liu et al., 4 Sep 2025)