Laser-assisted tunneling in a static tungsten diselenide WSe$_2$ barrier

This study demonstrates that irradiating a static tungsten diselenide (WSe$_2$) barrier with a linearly polarized laser field induces rich Floquet sideband structures and Stark-like confined states, which effectively suppress Klein tunneling and enable dynamic control of quantum transport for potential optoelectronic applications.

The Gist

Imagine a single, ultra-thin sheet of a material called Tungsten Diselenide (WSe2) acting like a microscopic highway for tiny particles called electrons (or "fermions" in physics speak). Usually, these particles zip along easily, but sometimes they hit a wall—a static electric barrier—that they shouldn't be able to cross.

In the world of quantum physics, there's a tricky phenomenon called Klein tunneling. It's like a ghost walking through a brick wall: even when there's a massive barrier, these particles can sometimes pass through it with 100% certainty, which is a problem if you want to build a switch that turns electricity on and off.

This paper explores a clever way to stop these "ghosts" from passing through, using a laser as the tool.

The Setup: A Laser-Soaked Wall

The researchers imagined a scenario where a specific section of this WSe2 sheet is hit by a laser beam. Think of the laser not just as a light, but as a rhythmic, shaking force.

• The Barrier: A wall of electric potential (like a hill the particles must climb).
• The Laser: A shaking motion applied to that hill. The laser is "linearly polarized," meaning it shakes the particles back and forth in a single direction, like a pendulum swinging left and right.

The Magic of "Floquet" Modes: The Time-Traveling Steps

Because the laser is shaking the system back and forth very fast, the rules of the game change. The paper uses a mathematical tool called Floquet theory to describe this.

Think of the particles trying to cross the barrier as a dancer trying to cross a stage.

• Without the laser: The dancer tries to walk straight across. Sometimes, they glide right through the wall (Klein tunneling).
• With the laser: The stage is shaking. To cross, the dancer can't just walk; they have to "dance" in sync with the shaking. This creates Floquet sidebands.

Imagine the dancer has a set of extra shoes. Each pair of shoes represents a different way to interact with the laser:

• Shoe 0: Walking without touching the laser (no photon exchange).
• Shoe +1: Stepping up by absorbing a "kick" of energy from the laser (absorbing a photon).
• Shoe -1: Stepping down by giving a "kick" back to the laser (emitting a photon).

The laser forces the particles to wear these different "shoes," creating multiple parallel paths (channels) to cross the barrier.

What Happens When You Turn Up the Laser?

The paper found that as you increase the intensity of the laser (making the "shaking" stronger):

1. The Ghosts Get Stuck: The perfect "ghost walk" (Klein tunneling) is suppressed. The particles are no longer guaranteed to pass through.
2. Energy Trapping (The Stark Effect): The laser interaction changes the energy levels of the particles, effectively creating new "traps" or confined states inside the barrier. It's like the shaking wall suddenly develops little pockets where the particles get stuck, unable to escape to the other side.
3. Interference: The different paths (the different "shoes" or sidebands) start interfering with each other. Imagine two waves of water crashing into each other and canceling out. The different laser-induced paths cancel each other out, making it even harder for the particles to get through.

The Role of Wall Width

The researchers also looked at how wide the laser-soaked barrier is:

• Narrow Wall: The particles zip through quickly, interacting less with the laser.
• Wide Wall: The particles spend more time in the shaking zone. This gives them more time to get trapped in those energy pockets or to interfere with themselves. The wider the wall, the more the laser suppresses the flow of particles.

The Bottom Line

The main result is that light can control electricity in this material. By adjusting the laser's strength and the width of the barrier, the researchers can tune how easily particles pass through.

• Strong Laser + Wide Barrier: Very little current gets through (the switch is "OFF").
• Weak Laser: More current gets through (the switch is closer to "ON").

The paper concludes that this light-matter interaction offers a way to build new types of electronic devices, such as tunable quantum filters (which only let specific types of particles through) and light-controlled transistors (switches turned on and off by a laser instead of a traditional electrical gate). This is a step toward using light to manage the flow of information in next-generation nanoscale electronics.

Technical Summary

Technical Summary: Laser-assisted tunneling in a static tungsten diselenide WSe2 barrier

Problem Statement
The paper addresses the challenge of controlling quantum transport in two-dimensional (2D) materials, specifically transition metal dichalcogenides (TMDs) like tungsten diselenide (WSe2). While graphene offers high electron mobility, its gapless nature and the resulting Klein tunneling effect (where fermions penetrate high potential barriers with unit probability) limit its utility in electronic switching and confinement. Although TMDs like WSe2 possess an intrinsic bandgap and strong spin-orbit coupling (SOC), the behavior of Dirac fermions in these materials under combined static electrostatic barriers and time-periodic laser fields requires further theoretical investigation. Specifically, the study seeks to understand how linearly polarized laser irradiation modifies the tunneling probability and conductance of fermions traversing a static potential barrier in monolayer WSe2.

Methodology
The authors employ a theoretical framework based on the Floquet formalism to handle the time-periodic nature of the system. The model considers a monolayer WSe2 sheet divided into three regions: two pristine regions (1 and 3) and a central region (2) of width $D$ subjected to a static electrostatic barrier of height $V_0$ and a linearly polarized laser field.

1. Hamiltonian Construction: The system is described using a low-energy effective Hamiltonian that includes the intrinsic bandgap ($\Delta$), spin-orbit coupling terms ($\lambda_c, \lambda_v$), and the static potential. The laser field is incorporated via the minimal coupling (Peierls substitution), replacing the momentum operator $p$ with $p + eA(t)$, where the vector potential $A(t)$ corresponds to a sinusoidal electric field.
2. Floquet Theory: Due to the time-dependent Hamiltonian, the wave functions are expanded into Floquet states. The time-dependent part of the wave function is expressed using Bessel functions $J_m(\alpha)$, where $\alpha = A_0/\omega$ is the driving parameter. This expansion leads to a set of coupled equations involving an infinite number of Floquet sidebands (photon-assisted channels).
3. Boundary Conditions and Matrix Formalism: Continuity conditions for the wave function and its derivatives are enforced at the interfaces ($x=0$ and $x=D$). This results in an infinite system of linear equations relating the reflection and transmission amplitudes of the various Floquet modes. The authors utilize a matrix formalism to solve this system, truncating the infinite series to a finite number of modes (specifically $|l| \le 2$) based on convergence analysis showing that higher-order modes are negligible.
4. Transport Properties: Transmission and reflection coefficients are derived from the solved amplitudes. The total transmission probability is calculated by summing the contributions of all relevant sidebands. Finally, the macroscopic conductance is evaluated using the Landauer-Büttiker formalism, integrating the transmission probability over the transverse wave vector (or incident angle) at zero temperature.

Key Contributions and Results
The numerical analysis of the derived analytical expressions yields several key findings regarding the interplay between the laser field, barrier width, and fermion transport:

• Floquet Sideband Structure: The laser field induces a rich structure of Floquet sidebands. The number and strength of these sidebands increase with the driving parameter $\alpha$. The transmission probability is redistributed among these channels, with the central band (no photon exchange) and sidebands involving photon absorption or emission.
• Suppression of Klein Tunneling: A primary result is the significant suppression of Klein tunneling. In the absence of the laser, perfect transmission can occur for specific barrier widths and angles. However, laser irradiation disrupts this perfect transmission. As $\alpha$ increases, the total transmission decreases, and the system transitions from perfect transmission to a regime where fermions are effectively confined or scattered.
• Role of Barrier Width ($D$): Increasing the width of the irradiated region enhances the interaction between fermions and the laser field. This leads to energy renormalization and the formation of Stark-like confined states. Furthermore, a wider barrier increases the probability of destructive interference between forward and backward Floquet components, further reducing transmission.
• Photon Exchange Dynamics: The study details how transmission channels vary with incidence angle, energy, and laser intensity. For instance, at normal incidence, transmission without photon exchange is often dominant, but as the barrier width or laser intensity increases, channels involving single or multiple photon exchanges become significant. The probability of transmission without photon exchange generally decreases with increasing $\alpha$ and $D$.
• Conductance Modulation: The conductance follows the trend of the transmission probability. It decreases as the laser intensity (parameter $\alpha$) increases and as the barrier width ($D$) increases. This indicates that the laser field acts as an effective external knob to tune the conductance of the WSe2 barrier.

Significance and Claims
The paper claims that the interaction between light and matter in WSe2 provides a mechanism for the dynamic control of quantum transport. Unlike gapless systems like graphene, which require external symmetry breaking to control carriers, the intrinsic bandgap and strong SOC of WSe2 allow for natural confinement and sensitive response to external fields.

The authors assert that their results demonstrate the feasibility of using laser irradiation to:

1. Overcome the limitations of Klein tunneling in 2D materials.
2. Dynamically control the transmission channels (selecting between no-photon, single-photon, or multi-photon exchange processes).
3. Modulate conductance without altering the structural configuration of the device.

These findings are presented as a theoretical foundation for the development of new optoelectronic devices, specifically tunable quantum filters and light-controlled nanoscale transistors, where the electronic current is governed by laser irradiation rather than conventional gate voltages. The study also highlights potential applications in spintronics and valleytronics due to the material's intrinsic spin-valley coupling.