First-principles and tight-binding analysis of thermoelectricity in irradiated WSe$_2$

This study demonstrates that monochromatic irradiation of zigzag monolayer WSe$_2$ nanoribbons, modeled via a tight-binding Floquet framework and density functional theory, significantly enhances the thermoelectric figure of merit ($ZT > 1$) by reshaping electronic band structures and reducing lattice thermal conductivity through anharmonic scattering.

The Gist

Imagine you have a tiny, super-thin sheet of material called WSe2 (Tungsten Diselenide). It's like a piece of graphene, but with heavy atoms that give it some special "superpowers." Scientists are trying to turn this material into a super-efficient machine that can turn waste heat into electricity. This is called thermoelectricity.

Think of thermoelectricity like a heat-powered water wheel. You want hot water (heat) to flow through the wheel to spin it (generate electricity), but you don't want the water to just leak out the sides without turning the wheel. The goal is to get the most spin out of the least amount of heat loss.

This paper is about how the scientists made this tiny water wheel work 10 times better by doing two clever things: shining a specific light on it and understanding how the heavy atoms inside it vibrate.

Here is the breakdown of their discovery:

1. The Problem: The "Symmetric" Traffic Jam

In its natural state, the WSe2 sheet is a bit boring for making electricity. Imagine a highway where cars (electrons) can drive equally well in both directions, and the traffic flow is perfectly smooth and symmetrical.

• The Issue: To generate electricity from heat, you need a "one-way street" effect. You want hot electrons to rush one way and cold ones to stay put. If the traffic is symmetrical, the heat just cancels itself out, and you get very little electricity.
• The Result: Without help, the material is a poor energy converter.

2. The First Trick: The "Laser Traffic Cop" (Light Irradiation)

The scientists shined a specific, high-frequency laser light onto the material.

• The Analogy: Imagine the highway is now being hit by a rhythmic, flashing strobe light. This light doesn't just illuminate the road; it actually changes the road itself. It acts like a traffic cop who suddenly puts up barriers and speed bumps in a very specific pattern.
• What Happened: This "light cop" forced the electrons to become picky. They could only pass through at very specific energy levels, like a toll booth that only lets cars through if they are exactly the right size.
• The Benefit: This created a sharp, jagged traffic pattern instead of a smooth highway. Suddenly, the material became very good at separating hot electrons from cold ones, which skyrocketed the amount of electricity it could generate.

3. The Second Trick: The "Heavy Dancer" (Spin-Orbit Coupling)

The material contains Tungsten, which is a very heavy atom. Heavy atoms have a quirk called Spin-Orbit Coupling (SOC).

• The Analogy: Imagine the atoms in the material are dancers holding hands, passing energy (heat) down the line. Usually, they pass the energy very smoothly and quickly. But because Tungsten is so heavy, it's like the dancers are wearing heavy, clunky boots. When they try to dance, they stumble and bump into each other more often.
• What Happened: These "stumbles" (which scientists call anharmonic scattering) mean the heat energy gets trapped and scattered around instead of flowing straight through.
• The Benefit: This drastically slowed down the heat. In thermoelectricity, you want electricity to flow fast, but heat to stay put. By making the "dancers" stumble, the scientists stopped the heat from leaking away, keeping the temperature difference high and the electricity generation strong.

4. The Grand Result: A Super-Efficient Machine

When they combined these two tricks:

1. The Light made the electricity flow very efficiently.
2. The Heavy Atoms made the heat flow very poorly (which is good here!).

The result is a material that is incredibly efficient at turning heat into power. The scientists measured a number called ZT (the score for how good a thermoelectric material is).

• Before: The score was very low (less than 1).
• After: The score jumped to over 28 in some cases!

Why This Matters

This is a big deal because:

• No Permanent Damage: Unlike other methods that require drilling holes or adding chemicals (which can break the material), this method uses light. You can turn the light on to make it work and turn it off to stop. It's like a remote control for energy efficiency.
• Waste Heat Recovery: Imagine your car engine, your laptop, or even your body heat. This technology could one day turn that wasted warmth into useful electricity to power your devices, making everything more energy-efficient.

In a nutshell: The scientists took a piece of heavy-metal fabric, shined a laser on it to create a "one-way street" for electricity, and used the heavy atoms to block the flow of heat. The result? A tiny, controllable machine that turns waste heat into power better than almost anything we've seen before.

Technical Summary

1. Problem Statement

Thermoelectric materials convert waste heat into electricity, but their efficiency is limited by the interdependence of electrical conductivity ($\sigma$), the Seebeck coefficient ($S$), and thermal conductivity ($\kappa$). Optimizing the dimensionless figure of merit ($ZT = \sigma S^2 T / \kappa$) is challenging because enhancing one parameter often degrades another.

• Specific Challenge: In pristine monolayer Tungsten Diselenide ($WSe_2$), the electronic transmission function is nearly symmetric around the Fermi energy, which suppresses the Seebeck coefficient. Conventional methods to break this symmetry (e.g., chemical doping) introduce disorder that degrades carrier mobility.
• Gap in Knowledge: While Spin-Orbit Coupling (SOC) is known to affect electronic band splitting in $WSe_2$, its specific role in phonon-mediated heat transport (lattice thermal conductivity) remains unclear. Additionally, there is a need for reversible, non-destructive methods to engineer thermoelectric properties.

2. Methodology

The authors employ a multi-scale theoretical approach combining Tight-Binding (TB) models for electronic transport and Density Functional Theory (DFT) for lattice thermal properties.

A. Electronic Transport (Tight-Binding & Floquet Theory)

• Model: A six-orbital tight-binding model (3 W $d$-orbitals + 3 Se $p$-orbitals) is constructed for zigzag monolayer $WSe_2$ nanoribbons.
• Spin-Orbit Coupling (SOC): Explicitly included in the onsite Hamiltonian for both W and Se atoms.
• Light Irradiation: Modeled using Floquet theory and the Peierls substitution. The system is subjected to monochromatic, time-periodic electromagnetic irradiation (high-frequency limit, $\hbar\Omega \gg$ bandwidth).
  • This maps the time-dependent system to an effective static Floquet Hamiltonian.
  • Light induces renormalization of hopping parameters, making them polarization-dependent and anisotropic.
• Transport Calculation: Coherent electronic transport is calculated using the Landauer-Büttiker formalism via the Kwant package. Key quantities (Conductance $G$, Seebeck $S$, Electronic thermal conductance $\kappa_{el}$) are derived from Landauer integrals of the transmission probability $T(E)$.

B. Lattice Thermal Conductivity (First-Principles DFT)

• Framework: Density Functional Theory (DFT) using the Quantum Espresso package with PBE-GGA functionals and fully relativistic pseudopotentials (to include SOC).
• Phonon Transport:
  • Phonon dispersion and group velocities are calculated using Density Functional Perturbation Theory (DFPT).
  • Lattice thermal conductivity ($\kappa_{latt}$) is solved iteratively using the ShengBTE package, which solves the phonon Boltzmann transport equation.
  • Scattering Mechanisms: Includes Normal and Umklapp three-phonon scattering processes. Anharmonicity is characterized by Gruneisen parameters and three-phonon phase space.
• Comparison: Calculations are performed with SOC (WSOC) and without SOC (WOSOC) to isolate the impact of spin-orbit interactions on phonon transport.

3. Key Contributions

1. Floquet Engineering of Thermoelectrics: Demonstrates that high-frequency light irradiation can reversibly engineer the electronic band structure of $WSe_2$, breaking transmission symmetry without chemical doping.
2. SOC Role in Phonon Transport: Provides a first-principles clarification that SOC in heavy-element TMDs (like $WSe_2$) significantly suppresses lattice thermal conductivity by enhancing phonon scattering, a mechanism often overlooked in previous studies.
3. Unified $ZT$ Optimization: Combines optically tunable electronic transport with intrinsic phonon suppression to achieve a high thermoelectric figure of merit.

4. Key Results

A. Electronic Transport under Irradiation

• Transmission Spectrum: In the absence of light, $T(E)$ shows broad, continuous plateaus. Under irradiation, the spectrum transforms into narrow, well-separated resonant peaks.
• Conductance vs. Seebeck:
  • Electrical Conductance ($G$): Significantly suppressed (by a factor of ~4) due to the narrowing of conducting channels.
  • Seebeck Coefficient ($S$): Dramatically enhanced (from 60 $\mu$V/K to **600 $\mu$V/K**) due to the strong asymmetry and energy selectivity of the transmission function near the Fermi level.
  • Electronic Thermal Conductance ($\kappa_{el}$): Strongly suppressed, reducing heat leakage via electrons.
• Mechanism: The light-induced renormalization of hopping creates an energy-filtering effect, favoring high thermopower.

B. Lattice Thermal Conductivity and SOC

• Phonon Softening: Including SOC causes a slight softening of the out-of-plane flexural (ZA) acoustic mode near the $\Gamma$ and $K$ points.
• Avoided Crossings: SOC induces avoided crossings between acoustic branches, leading to strong mode hybridization.
• Scattering Enhancement:
  • Gruneisen Parameter ($\gamma$): Increases significantly (up to 6) in the WSOC case compared to WOSOC (4.5), indicating stronger anharmonicity.
  • Scattering Rate: The WSOC system exhibits substantially higher phonon scattering rates, particularly for ZA and TA modes below 100 cm$^{-1}$.
• Thermal Conductivity ($\kappa_{latt}$):
  • WSOC: ~15 W/mK at 300 K.
  • WOSOC: ~35 W/mK at 300 K.
  • The WSOC result aligns closely with experimental data, validating the necessity of including SOC for accurate predictions.

C. Thermoelectric Figure of Merit ($ZT$)

• Performance: The combination of enhanced $S$, reduced $\kappa_{el}$, and suppressed $\kappa_{latt}$ leads to a massive increase in $ZT$.
• Magnitude: Under irradiation, $ZT$ exceeds unity and reaches a peak of ~28 at room temperature (300 K) for specific Fermi energy tuning ($E_F \approx 0.6-0.8$ eV).
• Robustness: High $ZT$ values are maintained across different ribbon lengths (10–30 nm), widths, and a broad temperature range (100–600 K), with $ZT$ increasing monotonically with temperature.

5. Significance

• Reversible Control: The study proposes a non-invasive, reversible method (light irradiation) to optimize thermoelectric performance, avoiding the disorder issues associated with doping.
• Material Design: It establishes monolayer $WSe_2$ as a superior platform for tunable thermoelectrics, leveraging both its intrinsic heavy-atom SOC and external Floquet engineering.
• Fundamental Insight: The work resolves the debate on SOC's effect on phonons in TMDs, proving that SOC is a critical factor in reducing lattice thermal conductivity through enhanced anharmonic scattering, which is essential for high-efficiency thermoelectric devices.
• Application Potential: The ability to achieve $ZT > 1$ (and up to 28 in the model) suggests that irradiated $WSe_2$ nanoribbons could be viable for next-generation solid-state cooling and waste-heat recovery systems.