Electric field control of third-order nonlinear Hall effect
Abstract: The third-order nonlinear Hall effect (NLHE) serves as a sensitive probe of energy band geometric property, providing a new paradigm for revealing the Berry curvature distribution and topological response of quantum materials. In the Weyl semimetal TaIrTe4, we report for the first time that the sign of the third-order NLHE reverses with decreasing temperature. Through scaling law analysis, we think that the third-order NLHE at high (T > 23 K) and low (T < 23 K) temperatures is dominated by Berry-connection polarizability (BCP) and impurity scattering, respectively. The third-order NLHE response strength can be effectively modulated by an additional applied in-plane constant electric field. At the high temperature region, the BCP reduction induced by the electric field leads to a decrease in the third-order NLHE response strength, while at the low temperature region, the electric field cause both BCP and impurity scattering effects to weaken, resulting in a more significant modulation of the third-order NLHE response strength. At 4 K and an electric field strength of 0.3 kV/cm, the modulated relative response strength could reach up to 65.3%. This work provides a new means to explore the third-order NLHE and a valuable reference for the development of novel electronic devices.
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Overview
This paper explores a special electrical effect in a quantum material called TaIrTe4 (a “type‑II Weyl semimetal”). The effect is the third‑order nonlinear Hall effect (NLHE). In simple terms, when you push electric current through this crystal, a tiny sideways voltage appears. Unlike the usual Hall effect, this sideways signal shows up even without a magnet and grows in a “nonlinear” way (it doesn’t just double when you double the current—here it scales like the current cubed). The authors show that:
- this effect flips sign when the material gets very cold, and
- you can tune (strengthen or weaken) this effect using an extra in‑plane electric field.
Key Questions
The study asks:
- Why does the third‑order NLHE in TaIrTe4 change sign as the temperature drops?
- What physical ingredients control this effect at high temperature vs. low temperature?
- Can an externally applied (constant) electric field adjust the size and behavior of this effect, and how does that depend on temperature and direction?
How They Did It (Methods)
To answer these questions, the researchers built tiny devices from thin flakes of TaIrTe4 and measured their electrical responses from very cold (4 K) to room temperature (about 300 K).
Here are the steps they took:
- Material and device: They peeled thin layers of TaIrTe4 and placed them on a special electrode pattern with 12 contacts, so they could send current along chosen directions and measure sideways voltages.
- Confirming the crystal: They used microscopes (STEM), surface probes (AFM), and laser light (Raman) to make sure the crystal structure and thickness were as expected and to find its main crystal axes (called a‑axis and b‑axis).
- Measuring the “third‑order” signal: They drove an AC current and looked specifically for the third harmonic response (a standard trick to detect signals that scale like current cubed). They carefully checked that the signals weren’t coming from heating or capacitive artifacts.
- Changing conditions: They varied temperature (4–300 K), rotated the current relative to the crystal axes, and applied an extra steady in‑plane electric field with different strengths and directions.
- Simple model/analysis: They used a scaling law that links the third‑order signal to how easily electrons flow (conductivity). This helped them separate two contributions: one from the geometry of the electron bands (called Berry‑connection polarizability, or BCP) and one from impurity scattering (electrons bumping into defects), similar to how traffic is slowed by road layout vs. roadblocks.
Helpful translations of technical terms:
- Hall effect: a sideways voltage that appears when current flows—usually requires a magnetic field, but here it does not.
- “Third‑order” and “nonlinear”: the sideways voltage grows like the cube of the input current, not in a straight proportional line.
- Berry‑connection polarizability (BCP): a way to describe how twisted or “curved” the energy landscape is for electrons inside the crystal. Think of it like the geometry of roads guiding the flow of cars.
- Impurity scattering: electrons bump into imperfections like potholes or rocks in the road, changing how they move.
What They Found (Main Results)
The main results can be summarized as follows:
- Temperature flips the sign: As the temperature drops, the third‑order NLHE switches sign around a critical temperature of about 23 K (without any extra electric field). Above this temperature, the effect is dominated by BCP (the “road geometry”); below it, impurity scattering (the “roadblocks”) takes over.
- Strong directional behavior: The effect depends on the direction of the current relative to the crystal axes and is weakest when current is exactly along the a‑axis or b‑axis. This shows the effect is intrinsic to the crystal’s symmetry.
- Electric field control: Adding a steady in‑plane electric field weakens the third‑order NLHE, but how it works depends on temperature:
- At higher temperatures: the electric field mainly reduces the BCP contribution, so the effect gets smaller.
- At lower temperatures: the electric field weakens both BCP and impurity scattering contributions, leading to an even stronger reduction. The “switch point” (the temperature where the sign flips) moves lower as the electric field increases (for example, from ~23 K down to ~17 K at 0.5 kV/cm).
- Angle tuning of the control: Rotating the direction of the applied electric field changes the effect with a 180° pattern (it repeats every half turn). This control works even up to room temperature.
- Large tunability: At 4 K and an applied field of 0.3 kV/cm, they achieved up to about 65% change in the third‑order NLHE strength—showing strong, practical control.
In their scaling analysis, the authors showed the third‑order signal can be viewed as two parts:
- a BCP‑like part (linked to band geometry), and
- a Drude‑like part (linked to how often electrons scatter). Because conductivity grows as electrons scatter less, the way the signal changes with conductivity reveals which part is in charge at a given temperature and field. This is how they identified the high‑T (BCP‑dominated) and low‑T (impurity‑dominated) regimes.
Why It Matters (Implications)
This work shows a new, all‑electrical way to control a purely quantum, geometry‑based transport effect—no magnets required. That’s useful because:
- It deepens our understanding of how the “shape” of electron bands (their quantum geometry) and impurities compete to set electronic behavior.
- Electric‑field control is fast, compact, and easier to integrate into chips than mechanical methods like strain, opening paths to:
- programmable quantum and topological electronics,
- sensitive angle‑aware sensors,
- low‑power logic or memory elements that exploit nonlinear responses.
In short, the authors demonstrate a “knob” (an in‑plane electric field) to tune a delicate quantum effect (third‑order NLHE) in a promising material (TaIrTe4), map out when different physics dominates (geometry vs. scattering), and show this control works from cryogenic temperatures up to room temperature. This could help engineers design next‑generation electronic components that use the quantum geometry of materials as a functional resource.
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