Correlated quasiperiodicity enables efficient thermoelectric energy conversion

Heat is often seen as waste, a byproduct of engines and electronics that simply escapes into the air. Yet, for decades, scientists have searched for a way to turn that wasted warmth directly into electricity, a process known as thermoelectricity. Imagine a device that could power a sensor using the heat from a car engine or a computer chip, offering a clean, mechanical-free way to generate power. The efficiency of such a device is measured by a specific number; the higher this number, the better the material is at converting heat into electricity. For a long time, this number has been too low for widespread use, largely because the materials that conduct electricity well also tend to conduct heat well, making it difficult to trap the heat where it is needed to generate power.

Researchers have found that shrinking materials down to the scale of individual atoms changes the rules. In these tiny, low-dimensional systems, the way electrons move can be manipulated to boost electricity generation while keeping heat flow low. However, finding the right arrangement of atoms to achieve this balance has been a challenge. A new study from physicists at the Indian Statistical Institute explores a unique middle ground between perfect order and total chaos. They investigated a specific type of atomic arrangement called a quasiperiodic structure, where the pattern repeats but never quite matches up perfectly, creating a landscape that is neither random nor regular. By carefully tuning this pattern, the team discovered a way to create a highly efficient thermoelectric system, potentially solving the long-standing problem of balancing electrical and thermal flow.

The researchers focused on a one-dimensional chain of atoms, a theoretical model that acts like a tiny wire connecting two heat baths, one hot and one cold. In a perfect, orderly chain, electrons flow freely, carrying both electricity and heat efficiently. This is good for moving current, but bad for generating voltage from a temperature difference, because the heat moves too easily alongside the electricity. The team introduced a specific kind of disorder into this chain, not the random mess found in broken glass, but a "weakly varying" pattern. This pattern is determined by a mathematical rule that shifts the energy levels of the atoms along the chain in a smooth, non-repeating way. This specific type of disorder is known as a weakly varying Aubry-André-Harper potential, a name that describes a special class of incommensurate, or mismatched, arrangements.

When the scientists simulated this system, they found that the weakly varying disorder created a highly uneven landscape for the electrons. Instead of flowing smoothly, the electrons encountered a transmission spectrum that was full of sharp peaks and deep valleys. This irregularity is the key to the system's success. It forces the electrons to behave differently depending on their energy, creating a strong asymmetry. When the researchers placed the system's energy level, known as the Fermi energy, near the edge of these peaks, they observed a dramatic increase in the Seebeck coefficient, a measure of how much voltage is generated by a temperature difference. At the same time, the electrical conductance remained high enough to be useful, and the flow of heat through the electrons dropped significantly. This combination allowed the system to achieve a figure of merit, the number that defines efficiency, that exceeded two, a value considered necessary for practical energy conversion.

The study went further by accounting for the movement of heat through the atoms themselves, known as phonons. In many materials, heat travels as vibrations of the atomic lattice, which can undermine the efficiency of the device. The researchers modeled the chain as a series of masses connected by springs and calculated how these vibrations moved through the disordered pattern. They found that the same irregular pattern that helped the electrons also scattered the heat-carrying vibrations. This scattering reduced the thermal conductance of the lattice, further boosting the overall efficiency. Even when both the electronic and phononic contributions to heat flow were included in the calculations, the system maintained a figure of merit well above two, reaching as high as three in some configurations. This confirmed that the proposed method works even when the full complexity of heat transfer is considered.

The team also tested how sensitive this result was to changes in the system. They varied the strength of the disorder, the size of the chain, and the temperature. They found that the high efficiency was not a fluke of a single setup but appeared across a wide range of conditions. For instance, changing the degree of mismatch in the pattern produced a zigzagging response, with high efficiency appearing at several specific settings. They also checked how the connection between the chain and the electrodes affected the results. While stronger connections generally lowered the efficiency slightly, the system remained robust and effective across different coupling strengths. To ensure their findings were unique to this specific type of disorder, they compared their results with a more conventional, standard version of the same model. The conventional model, which lacks the "weakly varying" feature, produced lower efficiency values, confirming that the specific, smooth variation in their chosen pattern was the critical factor.

The researchers also considered whether this theoretical model could be built in a real laboratory. They noted that similar patterns have already been created using lasers and ultracold atoms, where light creates the necessary energy landscape for atoms. They also suggested that arrays of tiny gates on a nanowire could be used to apply the required voltage profile directly. These possibilities suggest that the system is not just a mathematical curiosity but a feasible design for future devices. By calculating the power output for a realistic temperature difference, the team estimated that their proposed system could generate a measurable amount of power, demonstrating that the high efficiency numbers translate into actual energy conversion potential.

This work highlights a new path forward for thermoelectric materials. Instead of trying to engineer perfect crystals or rely on random imperfections, the study shows that a carefully designed, correlated disorder can be more effective. The weakly varying pattern creates a unique environment where electrons and heat behave differently, allowing for high electrical output and low heat loss simultaneously. The findings suggest that by tuning the specific parameters of this pattern, scientists can design materials that are far more efficient at harvesting waste heat than current technologies. While the study relies on numerical simulations rather than physical experiments, the results are consistent across a broad range of parameters, offering a strong theoretical foundation for future experimental work. The potential applications extend beyond simple power generation, hinting at new ways to control quantum transport and phase transitions in nanoscale systems.