🔬 mesoscale physics

Terahertz field-driven nonlinear Hall effect and other second order transport phenomena in two-dimensional tellurene

This paper investigates terahertz field-driven second-order nonlinear transport phenomena in two-dimensional tellurene, demonstrating that gate-tunable dc currents arising from skew scattering, side jump, and Berry curvature dipole mechanisms scale quadratically with the electric field and are strongly enhanced at low temperatures and lower frequencies.

Original authors: M. D. Moldavskaya, L. E. Golub, E. Mönch, Chang Niu, Peide D. Ye, J. Wunderlich, S. D. Ganichev

Published 2026-07-13

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: M. D. Moldavskaya, L. E. Golub, E. Mönch, Chang Niu, Peide D. Ye, J. Wunderlich, S. D. Ganichev

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 a tiny, flat sheet of a material called tellurene. It's like a microscopic piece of a shiny, metallic ribbon that's only a few atoms thick. Scientists have been poking this ribbon with invisible waves of energy called terahertz (THz) radiation—think of these as super-fast, invisible wiggles of light that sit between microwaves and infrared on the energy spectrum.

Here's the magic trick they discovered: When they shine this THz light onto the tellurene, it doesn't just heat up; it starts pumping out a steady stream of electricity, like a solar panel that runs on invisible radio waves. But here's the twist: this electricity doesn't just flow in a straight line. It flows sideways, diagonally, and in straight lines all at once, depending on how you tilt the light beam.

The "Wobbly" Sheet

To understand why this happens, imagine the tellurene sheet isn't a perfect, symmetrical tile. Instead, it's a crumpled, lopsided piece of paper. In physics terms, it lacks "inversion symmetry," meaning if you flipped it upside down, it wouldn't look the same. Because of this wobbly shape, when the invisible THz waves hit the electrons inside, they don't bounce off evenly.

Think of the electrons as a crowd of people in a hallway. If you push them with a gentle, rhythmic wind (the THz light), they usually just sway back and forth. But because the hallway is lopsided and full of weird, jagged obstacles (the material's unique atomic structure), the crowd gets pushed unevenly. Some get shoved hard to the left, some to the right, and some get kicked forward.

The scientists found that this "kick" creates a steady current (DC) that is quadratic in strength. That's a fancy way of saying: if you double the strength of the light's push, the electricity doesn't just double—it quadruples! It's like if you pushed a swing twice as hard, it didn't just go twice as high, but four times as high.

The Three Ways the Current Flows

The team measured the electricity flowing in two directions: along the length of the ribbon (the c-axis) and across its width (the a-axis). They found the current is a mix of three different behaviors, which they named with catchy acronyms:

The Nonlinear Hall Effect (NLHE): This is the "sideways" current. Even though the light pushes straight, the electrons get kicked sideways, like a soccer ball curving around a wall.
The Nonlinear Longitudinal (NLL) Current: This is the "straight-ahead" current. The electrons run in the same direction the light is pushing them.
The Nonlinear Diagonal (NLD) Current: This is the "diagonal" current. The electrons run at a 45-degree angle, cutting across the grain.

The paper shows that all three of these happen at the same time. By rotating the direction of the light's electric field (using a special lens called a half-wave plate), the scientists could see which of these three currents was winning. Sometimes the sideways kick was huge; other times, the diagonal cut was the strongest.

The "Gate" and the Temperature Switch

The scientists had a remote control for this experiment: a gate voltage. By applying a small electrical voltage to the back of the tellurene sheet, they could switch the material from conducting electricity with positive "holes" to negative "electrons."

When they flipped this switch, the direction of the current flipped too! If the electrons were flowing left, they suddenly started flowing right. This confirmed that the effect is deeply tied to the type of charge carrier moving through the material.

Then, they turned up the cold. When they cooled the samples from room temperature (about 300 K) down to a frosty 4.2 K (just a few degrees above absolute zero), the electricity didn't just get a little stronger; it exploded. The current grew by two orders of magnitude (that's 100 times bigger!). It's as if the electrons, when frozen in place, suddenly found a superhighway to run on.

The "Why" Behind the Magic

Why does this happen? The paper rules out the idea that it's just one simple cause. Instead, they found it's a team effort from three microscopic mechanisms:

Skew Scattering: Imagine the electrons are billiard balls hitting a table with uneven pockets. They don't bounce straight back; they get deflected at weird angles. This "skew" bounce creates the current.
Side Jump: When an electron hits a bump, it doesn't just bounce; it takes a tiny, sudden step to the side, like a dancer dodging a partner.
Berry Curvature Dipole: This is a bit more abstract. Think of the electrons moving through a landscape that has a hidden "twist" or "curl" in its geometry. This twist pushes them sideways even without hitting anything.

The paper suggests that while the "Berry Curvature" (the twist) is often talked about in other materials, in these tellurene samples, the skew scattering (the uneven billiard table) might actually be the biggest player, especially at room temperature. They also noted that the current gets stronger as the frequency of the light gets lower, which hints that the material's internal "refractive index" (how it bends light) is changing in a way that makes the electric field inside the material stronger.

What They Didn't Find

It's important to note what the paper says doesn't happen. They looked for signs that the current was caused by the material absorbing the light and getting hot (heating effects), but they found that while heating plays a small role, the main driver is the unique way the electrons scatter and move due to the material's shape. They also didn't see any special "magic" happen when the electrons crossed a specific point in the material's energy levels (the Weyl point), suggesting the effect is a general property of the whole sheet, not just a specific spot.

The Bottom Line

In short, the paper shows that tellurene is a playground for a new kind of electricity. By shining invisible terahertz light on it, you can generate a steady current that flows in straight, sideways, and diagonal lines, all controlled by a simple voltage switch and the temperature of the room. It's a discovery that proves even a tiny, crumpled sheet of atoms can do some very complex, very cool tricks when you know how to push it.

Technical Summary: Terahertz Field-Driven Nonlinear Hall Effect and Second-Order Transport in 2D Tellurene

Problem and Motivation
Two-dimensional tellurene, the 2D allotrope of trigonal tellurium, has emerged as a promising elemental semiconductor with a chiral crystal structure lacking inversion symmetry. This broken inversion symmetry, combined with time-reversal invariance, creates a natural platform for studying symmetry-allowed second-order nonlinear transport phenomena. While the nonlinear Hall effect (NLHE) has been observed in various topological and 2D systems, the specific microscopic origins in tellurene remain a subject of debate. Previous interpretations have varied, attributing the effect in gate-tuned 2D tellurene to a large Berry curvature dipole (BCD) near Weyl band edges, while room-temperature thin flakes have shown giant NLHE dominated by extrinsic scattering and surface symmetry reduction. Furthermore, the full spectrum of second-order transport in tellurene—which, due to its low $C_1$ symmetry, permits transverse, longitudinal, and diagonal currents—requires comprehensive experimental resolution. This work addresses the need to characterize these second-order phenomena driven by terahertz (THz) fields and to identify the underlying microscopic mechanisms (skew scattering, side-jump, and BCD).

Methodology
The study utilized Hall bar devices fabricated from hydrothermally grown 2D tellurene flakes (approx. 30 nm thick) transferred onto $p^+$ -Si substrates with a 90 nm $SiO_2$ back gate. The devices were patterned with Ni contacts, and the tellurene was capped with $Al_2O_3$ . Experiments were conducted on two samples (#A and #B) across a temperature range from 300 K down to 4.2 K.

The primary experimental technique involved contactless excitation of the samples using linearly polarized, monochromatic THz radiation (frequencies ranging from 0.6 to 2.54 THz). The orientation of the in-plane electric field vector relative to the tellurene $c$ -axis was controlled via a half-wave plate, defining an azimuth angle $\alpha$ . DC photocurrents were measured along both the $c$ -axis (source-drain) and the $a$ -axis (transverse to $c$ ). The gate voltage was swept to modulate the carrier density and type (electrons vs. holes), allowing the researchers to probe the charge neutrality point (CNP) and the sign dependence of the currents.

Key Contributions and Results

Observation of Second-Order Transport: The authors successfully demonstrated that THz radiation induces a DC current in 2D tellurene that scales quadratically with the radiation electric field ( $J \propto E^2$ ), confirming its nature as a second-order nonlinear transport phenomenon.
Decomposition of Current Components: By varying the azimuth angle $\alpha$ $α$ and gate voltage, the total current was resolved into three distinct contributions described by the phenomenological equations:
- Nonlinear Hall Effect (NLHE): A transverse current component.
- Nonlinear Longitudinal (NLL) Current: A component parallel to the electric field.
- Nonlinear Diagonal (NLD) Current: A newly identified component oriented at $\pm 45^\circ$ to the field, arising from the low $C_1$ symmetry.
  The study established the equivalence between these transport currents and the Linear Photogalvanic Effect (LPGE) contributions induced by linearly polarized THz radiation.
Microscopic Mechanisms: The experimental data were analyzed using both phenomenological and microscopic theories. The results indicate that the photocurrents originate from a combination of three mechanisms:
- Skew Scattering: An extrinsic mechanism where asymmetric scattering off defects leads to a net current. The authors suggest that conventional skew scattering likely dominates in their samples.
- Side-Jump: A scattering-induced correction to carrier velocity.
- Berry Curvature Dipole (BCD): An intrinsic mechanism.
  The theory confirms that all three mechanisms contribute to the NLHE, NLL, and NLD currents.
Gate Voltage and Temperature Dependence:
- Gate Voltage: All current contributions ( $J_{L1}, J_{L2}, J_0$ ) reverse sign when the effective gate voltage crosses the CNP, switching between electron and hole conductivity. This sign reversal is consistent with the theoretical prediction that current density is odd in the carrier charge $q$ .
- Temperature: Cooling the samples from 300 K to 4.2 K resulted in a drastic increase (by two orders of magnitude) in the current magnitude. This is attributed to the increase in scattering time ( $\tau$ ), as the current scales with $\tau^2$ in the relevant frequency regime.
- Frequency: The current magnitude increases as the radiation frequency decreases, consistent with Drude-like absorption behavior, though the authors note that refractive index variations near the reststrahlen band may complicate the exact frequency dependence.

Significance and Claims
The paper claims to provide a comprehensive characterization of THz-driven second-order transport in 2D tellurene, resolving the contributions of NLHE, NLL, and NLD currents. A significant finding is the demonstration that in systems with $C_1$ symmetry, the "chiral axis" of the bulk material does not play an essential role in determining the magnitude of currents excited by linearly polarized radiation; instead, the low symmetry allows for a rich set of independent transport coefficients.

The authors emphasize that their THz approach offers distinct experimental advantages, including contactless field application, direct access to longitudinal currents without a linear DC background, and operation up to room temperature. By linking the observed photocurrents to specific microscopic mechanisms (skew scattering, side-jump, and BCD), the study clarifies that while BCD is often cited as the primary origin of NLHE, extrinsic mechanisms like skew scattering can be dominant, particularly in tellurene-based systems. The work concludes that polarization-dependent THz or GHz photocurrent measurements serve as a robust tool for dissecting the microscopic processes governing nonlinear transport in low-dimensional and bulk semiconductor materials.