Switchable Surface Linear Photogalvanic Effect in the Magnetic Weyl Semimetal Co3Sn2S2

This paper theoretically demonstrates that the magnetic Weyl semimetal Co3Sn2S2 exhibits a switchable surface linear photogalvanic effect driven by extrinsic contributions from Fermi-arc states, which can be controlled by magnetization flipping and offers a promising platform for symmetry-controlled optoelectronic applications.

The Gist

Imagine a material called Co₃Sn₂S₂ as a bustling, three-dimensional city. Deep inside the city (the "bulk"), the streets are perfectly symmetrical. If you walk down one street and turn around, you see an identical street going the other way. Because of this perfect balance, if you shine a light on the city, the electrons (the city's workers) cancel each other out, and no net movement happens. Nothing flows.

But, every city has a surface, and the surface is different. It's like the edge of a cliff where the symmetry breaks. Here, the rules change. This paper explores what happens when you shine light on this specific "cliff" of the Co₃Sn₂S₂ city.

Here is the breakdown of their discovery using simple analogies:

1. The "Switchable" Light Current

The researchers are studying a phenomenon called the Linear Photogalvanic Effect (LPGE). Think of this as a special kind of traffic jam caused by light.

• The Setup: You shine a laser (light) on the surface of the material.
• The Result: The light pushes the electrons, creating an electric current.
• The Twist: This material is magnetic. The authors found that if you flip the direction of the material's internal magnetism (like flipping a giant compass needle), the direction of the electric current flips too. It's like a traffic light that instantly switches from "Go North" to "Go South" just by changing the magnetic setting.

2. Why the Surface is the Star

In the deep interior of the material, the symmetry is so perfect that the light-induced current is zero. It's like a tug-of-war where both teams are perfectly matched; the rope doesn't move.
However, at the surface, that symmetry is broken. The "tug-of-war" is unbalanced. The paper argues that the massive current they see comes almost entirely from these surface electrons, specifically from special "highways" called Fermi arcs.

• The Analogy: Imagine the interior is a crowded room where everyone is dancing in a circle, canceling out any forward motion. The surface is a slide leading out of the room. When the light hits, everyone slides down the surface, creating a strong, fast flow of people (current) that doesn't happen inside.

3. The "Magic Mirror" Rule

The paper uses complex math to show that the material has a "magic mirror" rule (an antiunitary mirror symmetry).

• The Rule: This rule acts like a strict bouncer. It says, "If the current looks the same when you flip the magnet, you aren't allowed to exist as an 'intrinsic' (natural) effect."
• The Consequence: This forces the natural part of the current to be strictly dependent on the magnet's direction. If you flip the magnet, the natural current must flip.
• The Exception: There is also an "extrinsic" part of the current (caused by electrons bumping into impurities, like cars hitting potholes). The magic mirror rule doesn't stop this part. However, the researchers found a clever trick: by shining the light at specific angles (like 0 degrees or 45 degrees), they can filter out the "pothole" traffic and isolate the "magic mirror" traffic. This allows them to see the pure, switchable current.

4. How Temperature and Frequency Affect the Flow

The researchers tested how the current behaves under different conditions:

• Temperature: As the material gets warmer, the current gets stronger in a straight, predictable line. It's like a car accelerating steadily as you press the gas pedal.
• Light Frequency (Color): When they used lower-frequency light (redder, longer waves), the current got much stronger. The relationship follows a specific mathematical curve (power law), meaning the current drops off sharply as the light gets higher frequency.

5. Why This Matters (According to the Paper)

The paper concludes that Co₃Sn₂S₂ is a perfect playground for studying these effects because:

1. It's controllable: You can turn the current on, off, or reverse it just by changing the magnet.
2. It's strong: The current is surprisingly large because of the unique "Fermi arc" highways on the surface.
3. It's predictable: The behavior follows clear rules based on symmetry.

The authors suggest this material is a promising candidate for magnetically controlled optoelectronic devices. In plain English, this means we could potentially build future gadgets where light and magnets work together to control electricity in new, efficient ways, all based on the unique physics of this specific crystal surface.

Technical Summary

Technical Summary: Switchable Surface Linear Photogalvanic Effect in the Magnetic Weyl Semimetal Co$_3$Sn$_2$S$_2$

Problem Statement
While Weyl semimetals (WSMs) are known for topological surface states (Fermi arcs) and bulk topological responses, the nonlinear optical transport properties of magnetic WSMs, specifically at the surface, remain largely unexplored. In centrosymmetric materials like the kagome ferromagnet Co$_3$Sn$_2$S$_2$, bulk inversion symmetry forbids second-order photogalvanic effects. However, the surface explicitly breaks this symmetry, potentially allowing for significant nonlinear photocurrents. The central challenge is to theoretically characterize the Linear Photogalvanic Effect (LPGE) on the surface of Co$_3$Sn$_2$S$_2$, distinguishing between intrinsic (band-structure driven) and extrinsic (scattering-driven) contributions, and determining how magnetization and symmetry constrain these responses for potential optoelectronic applications.

Methodology
The authors employ a diagrammatic Green's-function formalism to calculate the second-order nonlinear conductivity tensor $\chi^{\mu\alpha\beta}$.

• Model: An effective tight-binding model is constructed based on the $d_{3z^2-r^2}$ Co orbital and $p_z$ interlayer Sn orbital, derived from previous works (Ozawa and Nomura). The model includes nearest- and next-nearest-neighbor Co-Co hopping, interlayer Co-Sn hopping, spin-orbit coupling, and an exchange coupling term for magnetization.
• System Geometry: A slab geometry consisting of 40 alternating Co and Sn layers is used to simulate the surface. The bulk Hamiltonian preserves inversion symmetry, ensuring that any calculated finite response originates solely from the surface where inversion symmetry is broken.
• Calculation: The response is computed using four Feynman diagrams representing the interaction of the system with oscillating electric fields. The integration is performed over a 2D Brillouin zone with a dense $k$-point mesh ($1201 \times 1201$).
• Parameters: Calculations are performed for magnetization directions along $\pm \hat{z}$, varying temperatures, and driving frequencies ($\hbar\omega$). A finite quasiparticle lifetime ($\tau \approx 22$ fs) is included to account for extrinsic scattering contributions.

Key Contributions and Symmetry Analysis
The paper provides a rigorous symmetry analysis of the LPGE in Co$_3$Sn$_2$S$_2$:

1. Symmetry Constraints: The system possesses an antiunitary mirror symmetry ($T \otimes M_y$) when magnetization lies in the $x$-$z$ plane. This symmetry forces the intrinsic contribution to the LPGE to vanish for tensor components with an even number of $y$-indices. Consequently, for magnetization along $\hat{z}$, the intrinsic LPGE is purely odd under magnetization reversal ($m_z \to -m_z$).
2. Intrinsic vs. Extrinsic: While the intrinsic response is strictly constrained by symmetry, the extrinsic contribution (dependent on scattering) is not subject to the antiunitary mirror constraint and can generate both even- and odd-in-magnetization components.
3. Switchability: The authors identify specific polarization angles (e.g., $\phi = 0, \pi/2$ for $j_y$ and $\phi = \pi/4, 3\pi/4$ for $j_x$) where the symmetry-allowed even-in-magnetization contributions are suppressed. At these angles, the total photocurrent is strictly odd under magnetization reversal, enabling a "switchable" photocurrent that flips sign when the magnetization direction is flipped.

Results

• Magnitude and Origin: The calculated LPGE currents are of the order of $O(1)$ A/m. The large magnitude is attributed to the enhanced density of states associated with the Fermi-arc surface states, contrasting with the smaller responses typically seen in topological insulators with isolated Dirac cones.
• Temperature Dependence: The photocurrent exhibits an approximately linear dependence on temperature ($j \propto T$). This linear scaling suggests the response is dominated by low-energy excitations near the Fermi arc. The slope of this dependence weakens as the driving frequency increases.
• Frequency Dependence: In the low-frequency regime, the current magnitude follows a power-law scaling $|j_y| \propto \omega^{-2.2}$. The exponent of this scaling shows weak temperature dependence, indicating robust scaling behavior.
• Angular Dependence: Polar plots of the current versus polarization angle reveal $\pi$-periodic behavior. While the total current generally contains mixed symmetry components, the specific high-symmetry angles identified in the symmetry analysis isolate the magnetization-odd response, resulting in a clean sign reversal upon flipping the magnetization.

Significance and Claims
The paper concludes that Co$_3$Sn$_2$S$_2$ serves as a promising platform for experimentally accessing symmetry-controlled nonlinear transport in realistic magnetic systems. The study identifies that:

1. The surface LPGE is a robust probe of Fermi-arc physics, distinct from bulk responses which vanish due to centrosymmetry.
2. The photocurrent can be magnetically switched (reversed) by controlling the magnetization direction, provided the optical polarization is tuned to specific angles.
3. These findings suggest potential utility for magnetically controlled optoelectronic devices, leveraging the interplay of topology, broken inversion symmetry at the surface, and intrinsic ferromagnetism.

The authors maintain a modest stance, noting that while the effect is large and theoretically accessible, the specific applications are framed as potential directions enabled by the demonstrated symmetry-controlled switching, rather than as immediate commercial implementations.