Photocurrents in bulk tellurium

The Gist

Imagine a crystal of Tellurium not as a boring, gray rock, but as a microscopic, three-dimensional spiral staircase. This isn't just any staircase; it's a "chiral" one, meaning it has a specific twist, like a left-handed screw or a right-handed screw. The scientists in this paper decided to shine different colors of invisible light (infrared and terahertz waves) down this spiral staircase to see what happens to the tiny particles (electrons and holes) living inside.

Here is what they discovered, broken down into simple concepts:

1. The Setup: A Spiral Slide

Think of the Tellurium crystal as a long, twisted tube. The researchers shined a laser beam straight down the center of this tube. They also had the ability to twist the "polarization" of the light.

• Linear Polarization: Imagine the light wave shaking back and forth in a straight line, like a jump rope being shaken up and down.
• Circular Polarization: Imagine the light wave spinning like a corkscrew as it moves forward.

When this light hits the crystal, it kicks the particles inside, creating an electric current. The goal was to figure out how the light was kicking them and why the current flowed in specific directions.

2. The Two Different "Kicks" (High vs. Low Energy)

The researchers used two different types of light, which acted like two different kinds of nudges:

• The "High-Energy" Kick (Infrared Light):
  When they used higher-energy light (around 30 THz), it was like giving the particles a strong, direct shove. This energy was just right to lift the particles from one "step" on the spiral staircase to the next step up.

  • The Result: The particles jumped directly to a new level. Because the staircase is twisted, this jump wasn't straight up; it had a sideways component. This created a current that depended on how the light was shaking (its polarization). It's like pushing a ball up a spiral ramp; the ball doesn't just go up, it spirals to the side.

• The "Low-Energy" Kick (Terahertz Light):
  When they used lower-energy light (1 to 3 THz), it wasn't strong enough to make the particles jump to a new step. Instead, it was like a gentle breeze blowing on the particles while they were standing on the same step.

  • The Result: The light transferred its momentum (its "push") directly to the particles, kind of like a photon drag effect. The particles started sliding along the floor. However, because the crystal is a twisted spiral, the particles didn't slide straight; they got scattered in a specific, asymmetric way, creating a current.

3. The Magnetic Field: The "Steering Wheel"

The researchers also turned on a magnetic field, which acted like a steering wheel for the particles.

• The Discovery: When they added the magnetic field, they saw new types of currents appear that didn't exist before.
• The Analogy: Imagine the particles are cars driving on a track. Without the magnetic field, they drive in a pattern determined by the road's shape (the crystal). When you turn on the magnetic field, it's like adding a strong wind that pushes the cars sideways.
  • If the light was spinning (circular polarization), the magnetic field made the cars spin in a specific direction, creating a "circular" current.
  • If the light was shaking straight (linear polarization), the magnetic field tilted the path of the cars, changing the direction of the current.

4. What They Found (The "New" Effects)

Before this study, scientists knew about some of these effects, but they had never seen this specific combination in bulk Tellurium crystals. They identified three main "new" behaviors:

1. The "Twisted" Push (Trigonal Photogalvanic Effect): When the light hits the twisted crystal, it naturally pushes the particles sideways. This happens even without a magnetic field. It's like the crystal itself is biased to push things one way when hit by light.
2. The "Photon Drag": At lower energies, the light literally drags the particles along, transferring its own momentum to them.
3. The Magnetic "Steer": The magnetic field creates new currents that are directly proportional to the strength of the field. If you flip the magnetic field direction, the current flips direction.

5. How They Knew What Was What

The scientists were like detectives. They knew that different "culprits" (mechanisms) leave different "fingerprints."

• Fingerprint 1 (Frequency): If the current changed drastically when they switched from high-energy to low-energy light, they knew it was caused by the "jump" mechanism (high energy) vs. the "drag" mechanism (low energy).
• Fingerprint 2 (Polarization): By rotating the light (changing the angle of the jump rope or the direction of the corkscrew), they could see which part of the current was caused by the crystal's twist and which was caused by the magnetic field.
• Fingerprint 3 (Magnetic Field): Some currents only appeared when the magnet was on, and some grew stronger as the magnet got stronger. This allowed them to separate the "natural" currents from the "magnetic" ones.

Summary

In short, the paper is a detailed map of how light interacts with a twisted, spiral-shaped crystal. The researchers showed that:

1. High-energy light makes particles jump between steps, creating a current based on the crystal's twist.
2. Low-energy light drags particles along, creating a current based on how the light pushes them.
3. Magnetic fields act as a steering wheel, creating new, distinct currents that can be turned on, off, or reversed by flipping the magnet.

They built a mathematical model (a theory) that perfectly predicted exactly how strong these currents would be and in which direction they would flow, confirming that their understanding of the crystal's "spiral staircase" structure was correct.

Technical Summary

Technical Summary: Photocurrents in Bulk Tellurium

Problem and Context
Tellurium (Te) is a chiral semiconductor that has been a subject of study since the early days of semiconductor physics, known for phenomena such as the quantum Hall effect, natural optical activity, and various photoelectric effects arising from the spin-splitting of its valence band. Recently, interest in Te has been revitalized by the emergence of 2D tellurene and theoretical proposals regarding Weyl fermions in strained Te. While recent studies have observed a transverse circular photogalvanic effect (CPGE) in bulk Te attributed to Weyl fermions, alternative explanations involving conventional band structures without significant strain have been proposed. Consequently, there is a critical need to comprehensively understand the bulk photocurrents in unstrained Te that are distinct from 2D states or topological charges, specifically to distinguish between effects driven by Weyl physics and those arising from conventional intersubband transitions and scattering mechanisms.

Methodology
The authors conducted a comprehensive experimental and theoretical study of polarized infrared and terahertz (THz) photocurrents in bulk p-type tellurium single crystals.

• Experimental Setup: Measurements were performed on a 0.8 mm thick Te plate cut perpendicular to the c-axis ($z$-axis), with Ohmic contacts on opposite sides to measure current along the $y$-axis. The experiments utilized two pulsed laser systems covering a frequency range from 1 to 30 THz: a line-tunable TEA CO$_2$ laser (28.3–32.2 THz) and an optically pumped molecular NH$_3$ laser (1.07 and 3.3 THz).
• Variables: The study systematically varied the radiation frequency, polarization state (linear and circular), azimuthal angle of linear polarization, and the strength/direction of an external in-plane magnetic field ($B_x$) up to 1.7 T.
• Theoretical Framework: The authors developed both phenomenological and microscopic theories. The phenomenological approach utilized symmetry analysis based on the $D_3$ point group of Te to identify allowed photocurrent terms. The microscopic theory employed a $k \cdot p$ Hamiltonian for the valence band (including "camel-back" dispersion) and solved the Boltzmann kinetic equation to derive expressions for photocurrents arising from direct intersubband transitions (infrared) and indirect Drude-like intraband transitions (THz).

Key Contributions and Results
The paper reports the observation and theoretical explanation of three distinct photoelectric phenomena in bulk Te, none of which had been previously addressed in this specific combination of conditions:

1. Trigonal Linear Photogalvanic Effect (LPGE):

   • Observation: A photocurrent dependent on the linear polarization angle ($\sin 2\alpha$) was observed at zero magnetic field.
   • Frequency Dependence: At infrared frequencies (~30 THz), this current is driven by direct optical transitions between subbands in the valence band. At lower THz frequencies (1–3 THz), where direct transitions are energetically forbidden, the LPGE arises from indirect Drude-like transitions involving asymmetric scattering of carriers.
   • Mechanism: The infrared contribution is attributed to a shift current mechanism due to the spatial shift of holes during absorption. The THz contribution is attributed to asymmetric scattering (skew scattering) by disorder or phonons.

2. Transverse Linear Photon Drag Effect (PDE):

   • Observation: A photocurrent component proportional to $\cos 2\alpha$ was detected, which is distinct from the LPGE.
   • Mechanism: This effect is observed only at THz frequencies and is caused by the transfer of linear photon momentum to free carriers (Drude absorption). The theory identifies this as a chiral PDE unique to the $D_3$ symmetry of Te, differing from effects in $C_{3v}$ systems.

3. Magnetic Field Induced Photocurrents (Linear and Circular):

   • Observation: The application of an external magnetic field ($B_x$) induces additional photocurrents that depend linearly on the field strength.
     • Linear MPGE/MPDE: A magnetic-field-induced linear photocurrent was observed, modifying the amplitude and phase of the total current.
     • Circular MPGE: A circular photocurrent, reversing sign with radiation helicity ($\sigma^{\pm}$) and magnetic field direction, was detected.
   • Mechanism: The magnetic field modifies the selection rules and scattering probabilities. For intersubband transitions (IR), the circular component arises from magnetic-field-induced spatial shifts. For intraband transitions (THz), it results from magnetic-field-assisted asymmetric scattering.
   • Distinction: The authors explicitly rule out the Lorentz-force-induced suppression of longitudinal CPGE as the source of the observed circular current, confirming a new mechanism of circular magneto-photocurrent.

Significance and Claims
The paper claims to provide a complete and unambiguous identification of photocurrent mechanisms in bulk tellurium. By analyzing the distinct dependencies on radiation frequency, polarization, and magnetic field, the authors demonstrate that:

• All observed effects occur in the bulk of the material and are not related to 2D surface states or topological charges of Weyl points.
• The photocurrents at ~30 THz are driven by direct intersubband transitions, while those at 1–3 THz are driven by Drude absorption.
• The developed phenomenological and microscopic theories successfully explain all experimental data without invoking Weyl fermions, offering an alternative explanation to recent claims of Weyl-induced effects in unstrained Te.
• The study establishes a clear methodology to distinguish between the trigonal LPGE, transverse PDE, and magnetic-field-induced effects, providing a foundational understanding of photoelectric responses in chiral semiconductors.