Stacking-dependent thermoelectric transport in layered Sc_2Si_2Te_6 from first principles

This study reveals that the stacking sequence (AA, AB, or ABC) in layered Sc₂Si₂Te₆ significantly modulates its electronic band degeneracy and lattice thermal conductivity, ultimately determining that the ABC and AB structures offer superior thermoelectric performance compared to the AA structure.

The Gist

Imagine a building made of identical, flat floors stacked on top of each other. In the world of materials science, this is a "layered material." Usually, these floors are stacked in a perfect, repeating pattern, like a neat tower of pancakes. But sometimes, the floors get shifted, or the pattern changes slightly. This is called "stacking polymorphism."

This paper investigates a specific material called Sc₂Si₂Te₆ (a mix of Scandium, Silicon, and Tellurium). The researchers wanted to know: Does the way we stack these atomic "floors" change how well the material can turn heat into electricity?

Here is the breakdown of their findings using simple analogies:

1. The Three Stacking Patterns (The "Floor Plans")

The scientists looked at three different ways to stack the atomic layers:

• ABC: The pattern shifts every time (Floor A, then B, then C, then A again). This is the pattern found in nature.
• AA: The floors are perfectly aligned, like a stack of identical plates where every edge matches the one below it.
• AB: The floors shift in a two-step pattern (A, then B, then A again).

The Stability Test:
The researchers found that all three patterns are almost equally stable. It's like having three different ways to arrange furniture in a room that all feel equally comfortable. The energy required to slide one layer over another to change the pattern is tiny (about the weight of a single grain of sand). This explains why, in real life, this material often has "stacking faults" (mixed-up patterns) because it's so easy for the layers to slip around.

2. The Electronic Highway (How Electricity Flows)

Think of electricity moving through the material like cars on a highway.

• The "Valley" Effect: In the ABC pattern, the highway splits into 12 different lanes that are all at the same height. This is great for traffic flow because cars can spread out.
• The "AA" Pattern: Here, the highway only has 2 lanes. It's much more crowded and restrictive.
• The "AB" Pattern: This one has 8 lanes.

The Result: Because the ABC and AB patterns have more "lanes" (a concept called band degeneracy), they allow electricity to flow much more efficiently than the AA pattern, especially when the material is lightly doped (like having fewer cars on the road). However, if you pack the highway with a lot of cars (heavy doping), the difference between the patterns becomes less noticeable.

3. The Heat Traffic Jam (How Heat Moves)

Now, imagine heat moving through the material as a crowd of people trying to walk through a hallway.

• The "AA" Hallway: The crowd moves relatively freely.
• The "AB" Hallway: This layout creates the most obstacles. The "people" (phonons, or heat vibrations) bump into each other more often and move slower. This makes the AB pattern the best at stopping heat from flowing.
• The "ABC" Hallway: This is in the middle. It stops heat well, but not quite as well as the AB pattern.

The researchers found that the AB pattern is the "champion" at blocking heat, while the AA pattern is the "worst" at it.

4. The Final Score: Turning Heat into Power

The goal of a thermoelectric material is to have lots of electricity flowing but very little heat leaking through. The score for this is called ZT.

• The Winner: The AB stacking pattern scored the highest (ZT ≈ 1.74). It had a great balance of good electricity flow and excellent heat blocking.
• The Runner-up: The ABC pattern (the natural one) was very close behind (ZT ≈ 1.72).
• The Loser: The AA pattern scored significantly lower (ZT ≈ 1.33). Even though it wasn't terrible, it was much worse than the other two.

The Bottom Line

The paper concludes that how you stack the layers matters a lot.

• If you want the best performance, you want the AB or ABC patterns.
• You want to avoid the AA pattern.

The researchers suggest that when scientists try to make this material in a lab, they need to be careful to prevent the layers from stacking in the "AA" way, because that specific arrangement acts like a traffic jam for electricity and a clear path for heat, ruining the material's ability to generate power.

In short: The material is like a puzzle. If you put the pieces together in the "AA" way, it's a weak puzzle. If you use the "AB" or "ABC" ways, it becomes a powerhouse for converting waste heat into electricity.

Technical Summary

Technical Summary: Stacking-dependent thermoelectric transport in layered Sc2Si2Te6 from first principles

Problem and Motivation
Van der Waals (vdW) layered materials frequently exhibit stacking polymorphism, where different stacking sequences of atomic layers can substantially modify physical properties. While the thermoelectric performance of the $A_2Si_2Te_6$ family ($A = \text{Sb, Bi, Sc}$) has attracted attention, particularly following reports of high performance in $Sb_2Si_2Te_6$ and theoretical predictions for $Sc_2Si_2Te_6$, current research has primarily focused on the experimentally observed ABC stacking configuration. However, experimental studies indicate that the $A_2Si_2Te_6$ family is prone to stacking faults during synthesis, leading to various stacking configurations. The impact of alternative high-symmetry stacking sequences (specifically AA and AB) on the thermodynamic stability, electronic structure, and thermoelectric performance of $Sc_2Si_2Te_6$ remains unclear. Understanding these dependencies is crucial for optimizing synthesis strategies to achieve high thermoelectric efficiency.

Methodology
The authors performed a systematic first-principles investigation combining density functional theory (DFT) with electron and phonon transport theories.

• Electronic Structure: Calculations were conducted using the Vienna Ab initio Simulation Package (VASP) with the PBEsol functional and projector augmented-wave (PAW) pseudopotentials. To accurately determine band gaps, the modified Becke–Johnson (mBJ) exchange potential with spin–orbit coupling (SOC) was employed.
• Transport Coefficients: Electronic transport properties (electrical conductivity $\sigma$, Seebeck coefficient $S$, and electronic thermal conductivity $\kappa_e$) were evaluated using the AMSET code within the momentum relaxation time approximation (MRTA). This approach accounted for acoustic deformation potential (ADP), polar optical phonon (POP), and ionized-impurity (IMP) scattering mechanisms.
• Lattice Thermal Conductivity ($\kappa_L$): Second-, third-, and fourth-order force constants were calculated using the finite-displacement method and the compressive sensing lattice dynamics (CSLD) method, respectively. Finite-temperature effects were included via self-consistent phonon (SCPH) theory. The Peierls–Boltzmann transport equation was solved using the FourPhonon package to obtain $\kappa_L$, incorporating both three-phonon and four-phonon scattering processes as well as coherent phonon contributions.
• Structures Investigated: Three high-symmetry stacking sequences were analyzed: the experimentally reported ABC phase (space group $R\bar{3}$), and two alternative phases, AA (space group $P\bar{3}$) and AB (space group $P\bar{3}$).

Key Contributions and Results

1. Thermodynamic Stability and Sliding Barriers:
   The study reveals that the AA- and AB-stacked structures are nearly degenerate in energy with the ABC phase. The energy difference between the AA and ABC structures is approximately 7.4 meV/f.u., while the AB structure is virtually identical in energy to ABC. The maximum sliding barrier required to transform between these stacking sequences is only about 10 meV/atom. This low barrier explains the experimentally observed stacking faults in $Sc_2Si_2Te_6$ and suggests that multiple stacking configurations can coexist.

2. Electronic Structure and Band Degeneracy:
   Despite similar total energies, the three stacking sequences exhibit distinct electronic structures. The valence-band maximum (VBM) is located at the $\Gamma$ point for all three. However, the conduction-band minimum (CBM) is highly sensitive to the stacking sequence:

   • ABC: CBM is located along $L-B_1$ and $\Gamma-X$, resulting in a valley degeneracy of 12.
   • AA: CBM is at the $K$ point, with a valley degeneracy of 2.
   • AB: CBM appears at the $H$ point (6 meV lower than $K$), with a total conduction-band degeneracy of 8 due to band folding and degeneracy at both $K$ and $H$ points.
     Consequently, the band gaps differ slightly: 0.73 eV for ABC and AB, and 0.66 eV for AA.

3. Electronic Transport Properties:
   Under heavily doped conditions (carrier concentration $\approx 2 \times 10^{20} \text{ cm}^{-3}$), the differences in electronic transport properties among the three sequences diminish. However, at lower carrier concentrations ($5 \times 10^{19} \text{ cm}^{-3}$), the stacking sequence significantly influences the power factor (PF). The high band degeneracy in the ABC and AB structures leads to larger densities of states and higher Seebeck coefficients compared to AA. Under n-type doping, the in-plane power factor is markedly superior to the out-of-plane direction for all structures, with the ABC structure achieving the highest maximum PF (78.5 $\mu$W cm$^{-1}$ K$^{-2}$), followed closely by AB (76.1) and AA (69.9).

4. Lattice Thermal Conductivity:
   The lattice thermal conductivity is governed primarily by three-phonon scattering, with four-phonon scattering providing additional reduction, particularly in the ABC stacking. The AB stacking exhibits the lowest $\kappa_L$ due to stronger three-phonon scattering rates and lower phonon group velocities. The order of $\kappa_L$ is AB < ABC < AA. All structures show pronounced anisotropy, with out-of-plane $\kappa_L$ being significantly lower than in-plane $\kappa_L$ due to weak interlayer vdW interactions.

5. Thermoelectric Figure of Merit ($ZT$):
   The maximum $ZT$ values are achieved at 800 K.

   • n-type doping: The highest $ZT$ is achieved along the in-plane direction. The order of performance is AB ($ZT \approx 1.74$) > ABC ($ZT \approx 1.72$) > AA ($ZT \approx 1.33$).
   • p-type doping: High $ZT$ values are obtained along the out-of-plane direction due to ultralow $\kappa_L$. The order is AB ($ZT \approx 1.59$) > ABC ($ZT \approx 1.46$) > AA ($ZT \approx 1.04$).
     In both doping scenarios, the AA stacking consistently yields the lowest thermoelectric performance.

Significance and Claims
The paper concludes that the stacking sequence exerts a non-negligible influence on the thermoelectric performance of $Sc_2Si_2Te_6$. While the AB and ABC stacking sequences exhibit comparable and high thermoelectric performance, the AA stacking structure shows substantially reduced values. The authors suggest that suppressing the formation of the AA stacking sequence through appropriate synthesis strategies is important for achieving high thermoelectric performance in $Sc_2Si_2Te_6$. The study highlights that stacking disorder, while common in vdW materials, can be detrimental to thermoelectric efficiency if it leads to the formation of the less favorable AA phase.