🔬 mesoscale physics

Anomalous Hall Effect Driven by Chiral Superconductivity

This paper proposes a zero-field Hall drag effect as a direct transport signature of chiral superconductivity, where a finite quasiparticle current in an open-circuit chiral superconductor mediates a transverse voltage in an adjacent normal layer, abruptly appearing below the critical temperature with a sign determined by the order parameter's phase winding.

Original authors: Vladislav Poliakov, Alex Levchenko, Leonid Levitov

Published 2026-07-01

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CC BY 4.0

Original authors: Vladislav Poliakov, Alex Levchenko, Leonid Levitov

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have two layers of material stacked on top of each other, separated by a tiny, invisible wall. The bottom layer is a standard metal (let's call it the "Normal Layer"), and the top layer is a special kind of superconductor that spins in a specific direction, like a corkscrew (the "Chiral Superconductor").

The scientists in this paper propose a clever way to "see" the spinning nature of the top layer without touching it directly. Here is how it works, broken down into simple concepts:

1. The Problem: The Superconductor is a "Short Circuit"

Usually, if you want to measure how electricity behaves in a material, you run a current through it and see how it reacts. But superconductors are tricky. They are like a super-highway where electricity flows with zero resistance. If you try to measure a sideways voltage (the Hall effect) inside a superconductor, the super-highway "short-circuits" the measurement. The electricity just flows straight ahead, hiding any interesting sideways behavior caused by the material's unique "chiral" (spinning) nature.

2. The Solution: The "Drag" Game

Instead of measuring the superconductor directly, the researchers suggest using the Normal Layer as a detective.

The Setup: You push a stream of electrons through the Normal Layer.
The Interaction: Even though the layers are separated by a wall, the electrons in the bottom layer can "bump" into the electrons in the top layer through invisible electric forces (like static electricity). This is called Coulomb Drag.
The Result: When the bottom electrons bump into the top ones, they transfer some momentum. It's like a strong wind (the bottom current) blowing against a sail (the top layer).

3. The Twist: The "Ghost" Current

Here is the magic part. In a normal metal, if you push the electrons, they move. In a superconductor, if you push the electrons, the "superfluid" part of the material immediately creates a counter-flow to cancel out the movement, keeping the total current at zero.

However, the superconductor isn't just one thing; it has two parts:

The Condensate: The superfluid part that cancels the flow.
The Quasiparticles: The "leftover" particles that exist because of heat. These are the ones that actually get bumped by the bottom layer.

Because the superconductor is chiral (it has a built-in spin), these "leftover" particles don't just move forward when bumped; they also drift sideways, like a spinning top wobbling as it moves. This creates a tiny, sideways "ghost current" inside the superconductor.

4. The Payoff: The "Contactless" Signal

Even though the superconductor cancels out its own total movement, that sideways "ghost current" still exists. Because the two layers are connected by that invisible electric force, this sideways movement in the top layer pushes back on the bottom layer.

This push creates a sideways voltage in the Normal Layer (the bottom one).

Why this is great: Since we are measuring the bottom layer (which is a normal metal), the "short circuit" problem doesn't exist. We can clearly see the sideways voltage.
The Signature: This voltage only appears when the top layer becomes superconducting and chiral. If you reverse the "spin" (chirality) of the superconductor, the voltage flips direction.

The Analogy: The Spinning Ice Skater

Imagine a figure skater (the superconductor) standing on a frozen pond next to a person walking on a treadmill (the normal layer).

The person on the treadmill creates a wind (electric current).
The wind hits the skater.
The skater is wearing a special suit that makes them slide perfectly forward, canceling out the wind's push so they don't move across the ice.
BUT, because the skater is also spinning (chirality), the wind makes them wobble to the side.
Even though the skater doesn't move forward, that side-wobble creates a tiny ripple in the air that pushes the person on the treadmill sideways.
By measuring how the person on the treadmill gets pushed sideways, you can tell that the skater is spinning, even though you never touched the skater.

What This Means

The paper claims this "Hall Drag" effect is a direct, clear sign that a material is a chiral superconductor. It turns on abruptly when the material gets cold enough to become superconducting and disappears if the material loses its "spin." This gives scientists a new, reliable tool to identify these exotic states of matter without needing to measure the superconductor directly.

Problem
Direct transport signatures of unconventional, specifically chiral, superconductivity remain scarce. Existing probes typically rely on indirect methods, such as phase-diagram anomalies, responses to external fields, or optical measurements. A fundamental difficulty in diagnosing broken time-reversal symmetry (TRS) in superconductors via transport is that the superconducting condensate short-circuits quasiparticle currents in the dc limit. This obscures both the ordinary Hall effect and any intrinsic anomalous Hall response of thermally excited Bogoliubov quasiparticles, making it challenging to formulate a direct transport diagnostic analogous to the Hall effect in TRS-broken metals.

Methodology
The authors propose a theoretical framework based on Coulomb drag between a chiral superconducting layer (Layer 1) and an adjacent time-reversal-symmetric normal metal layer (Layer 2). The study employs a minimal hydrodynamic theory that accounts for both the normal quasiparticle current and the condensate supercurrent within the superconducting layer.

Key theoretical components include:

Hydrodynamic Extension: The authors extend the nonchiral quasiparticle kinetics derived by Pethick and Smith (PS) to include a transverse, TRS-odd Hall sector. The equation of motion for the quasiparticle current includes a longitudinal Drude term and an anomalous velocity term driven by the Berry curvature of the Bogoliubov–de Gennes (BdG) bands.
Drag Mechanism: A longitudinal current is driven in the normal layer, creating a drag electric field ( $E^{(D)}_1$ ) in the superconducting layer via interlayer Coulomb scattering. This field drives a quasiparticle current in the chiral superconductor.
Counterflow Condition: The analysis imposes an open-circuit boundary condition on the superconducting layer ( $j_{1,tot} = 0$ ). The authors demonstrate that the condensate generates a counterflowing supercurrent ( $j_{1s} = -j_{1n}$ ) to cancel the net current, while the drag-active quasiparticle current ( $j_{1n}$ ) remains finite.
Microscopic Origin: The transverse conductivity ( $\sigma^{qp}_{xy}$ ) is derived from the intrinsic Berry curvature of the chiral quasiparticle bands, calculated using a minimal single-band BdG Hamiltonian with a chiral gap $\Delta_k = |\Delta_k|e^{i\ell\phi_k}$ .
Robustness Check: The model incorporates a minimal normal-condensate conversion process (analogous to Belyaev-like relaxation or quasiparticle recombination) to test the stability of the counterflow picture.

Key Contributions and Results

Zero-Field Hall Drag Effect: The paper identifies a zero-field Hall drag effect as a direct transport signature of chiral superconductivity. The effect manifests as a transverse Hall voltage in the normal layer, induced by the chiral response of the superconducting layer.
Survival of Quasiparticle Current: The authors show that the open-circuit condition does not suppress the drag signal. While the net current in the superconductor vanishes due to the condensate counterflow, the finite quasiparticle current continues to mediate the interlayer drag. Consequently, the anomalous Hall voltage signal appears in the normal layer without being short-circuited by the superconductor.
Temperature Dependence: The induced Hall resistivity ( $\rho^{(2)}_{xy}$ ) is proportional to the square of the interlayer drag coefficient and the chiral quasiparticle Hall conductivity ( $\rho^{(2)}_{xy} \sim \rho_D^2 \sigma^{qp}_{xy}$ ). The signal exhibits a characteristic temperature dependence: it is zero above $T_c$ , rises abruptly below $T_c$ (scaling roughly as $\Delta(T)/T_c$ ), and drops exponentially at lower temperatures.
Chirality Signature: The Hall signal is odd under the reversal of chirality (the sign of the phase winding $\ell$ ). Thus, the sign of the measured voltage directly reflects the sign of the superconducting order parameter's phase winding.
Quantitative Estimate: For a representative graphene double-layer system, the authors estimate a Hall drag resistivity of $\rho_{xy} \sim 20 \, \text{m}\Omega$ , a value deemed detectable by modern lock-in transport measurements.
Robustness to Relaxation: The inclusion of normal-condensate conversion processes renormalizes and damps the response but does not eliminate the Hall drag signal, provided the chiral layer retains an intrinsic Berry-curvature Hall conductivity.

Significance
The paper claims to provide a "contactless" transport diagnostic for time-reversal symmetry breaking in the superconducting state. Unlike previous methods that rely on external fields or indirect probes, this mechanism relies solely on finite-temperature superconducting quasiparticles, interlayer momentum transfer, and the intrinsic chirality of the quasiparticle spectrum. The abrupt onset of the signal below $T_c$ and its reversal upon chirality reversal offer a direct method to probe chiral superconducting phases, such as those recently reported in rhombohedral graphene multilayers. The work distinguishes itself from other drag mechanisms (e.g., those driven by external fields or superconducting fluctuations) by attributing the transverse response to the intrinsic chirality of the superconducting quasiparticle spectrum.