🔬 mesoscale physics

Engineering Giant Thermoelectric Performance through Electrode-Coupling Geometry and Magnetic Flux in Quasiperiodic Su-Schrieffer-Heeger Rings

This paper demonstrates that combining magnetic flux, quasiperiodicity, and engineered asymmetric electrode-coupling geometry in Su-Schrieffer-Heeger rings can dramatically enhance the thermoelectric figure of merit to approximately 90 by optimizing quantum interference and energy filtering while violating the Wiedemann-Franz law.

Original authors: Sridhar, Souvik Roy, Malay Bandyopadhyay

Published 2026-09-07

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Sridhar, Souvik Roy, Malay Bandyopadhyay

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the quiet corners of modern physics, researchers are learning to harvest energy from heat in ways that were once thought impossible. The goal is simple: turn wasted thermal energy into useful electricity. This process, known as thermoelectric conversion, relies on a delicate balance. To work well, a material must let electricity flow through it easily while simultaneously blocking the flow of heat. In the natural world, these two things usually go hand in hand; if electrons can move freely to carry a current, they also carry heat with them, making it hard to build an efficient device. For decades, scientists have searched for a way to break this link, to filter out the heat while keeping the electricity.

The key to this challenge lies in the quantum world, where particles like electrons behave more like waves than tiny balls. When these waves travel through a material, they can interfere with one another, much like ripples on a pond. Sometimes these ripples add together to make a bigger wave, and sometimes they cancel each other out completely. By designing materials with specific shapes and patterns, scientists can use this interference to create a "traffic jam" for heat-carrying electrons while leaving a clear path for electricity-carrying ones. This paper explores a new way to engineer these quantum waves, not just by changing the material itself, but by changing how the material is connected to the outside world.

The researchers, working at the Indian Institute of Technology Bhubaneswar, focused on a ring-shaped structure made of atoms arranged in a specific, repeating pattern. This ring is threaded by a magnetic field, which adds a subtle twist to the path of the electrons traveling through it. The team used computer simulations to model how electrons move through this ring when it is connected to two metal reservoirs, acting as a source and a drain. The central question was whether the way these connections were made—the geometry of the contact points—could be used as a powerful tool to control the flow of energy. They tested two distinct arrangements: one where the source and drain were connected to the ring at three points each, creating a symmetrical bridge, and another where the source connected to three points but the drain connected to only a single point, creating an asymmetrical bridge.

Without any magnetic field, the simulations showed that the shape of the ring itself mattered most. The researchers found that when the atoms in the ring were arranged in a specific "trivial" pattern, the device worked best. In this state, the asymmetrical connection, where the drain touched only one spot, performed significantly better than the symmetrical one. It managed to boost the efficiency of converting heat to electricity to a level roughly three times higher than the symmetrical setup. This happened because the single-point contact forced the electrons to take a more selective route, filtering out the heat more effectively than the multiple contacts allowed.

However, the story changed dramatically when the researchers introduced a magnetic field. The magnetic field acts like a dial that tunes the quantum interference of the electrons. As the field strength increased, it reshaped the landscape of the electron waves, shifting the most efficient operating mode from the "trivial" pattern to a different "topological" pattern of the ring. In this new state, the electrons behaved differently, and the optimal conditions for energy conversion moved to a different part of the material's structure.

The most striking result emerged when the researchers combined the magnetic field with the asymmetrical connection. In this specific configuration, the efficiency of the device skyrocketed. The simulations predicted a figure of merit, a standard measure of thermoelectric performance, reaching a value of approximately 90. This is an enormous number for such a system, far exceeding the typical values seen in similar studies, which usually hover between 1 and 30. The asymmetrical connection, when paired with the magnetic field, created a situation where the device could filter energy with extreme precision. It allowed electricity to pass through with high efficiency while almost completely blocking the flow of heat.

This massive improvement was linked to a fundamental breakdown in a long-standing rule of physics known as the Wiedemann-Franz law. This law usually states that the ability of a material to conduct electricity is directly tied to its ability to conduct heat. The researchers found that in their optimized setup, this rule was violated. The device managed to conduct electricity well while conducting very little heat, effectively decoupling the two flows. This decoupling is the "holy grail" of thermoelectric research, and the study suggests that the shape of the connection points is just as important as the material itself in achieving it.

The findings suggest that the future of high-performance energy harvesting may not depend solely on discovering new materials, but on how we choose to wire them. By carefully designing the geometry of the contacts and using magnetic fields to tune the quantum interference, it is possible to engineer devices that are far more efficient than previously thought. The study demonstrates that a simple change in the number of connection points, from three to one, can transform a modest device into a giant performer. While these results are currently based on computer simulations, they offer a clear blueprint for building real-world devices, such as quantum dots or molecular circuits, where the arrangement of wires could be the key to unlocking a new era of sustainable energy technology.

Technical Summary: Engineering Giant Thermoelectric Performance through Electrode-Coupling Geometry and Magnetic Flux in Quasiperiodic SSH Rings

Problem Statement
Thermoelectric devices convert waste heat into electrical energy, with performance quantified by the dimensionless figure of merit, $ZT = S^2G T / \kappa$ , where $S$ is the Seebeck coefficient, $G$ is electrical conductance, and $\kappa$ is thermal conductance. Enhancing $ZT$ requires simultaneously promoting energy-selective charge transport and suppressing heat transport. While quantum interference in coherent mesoscopic systems (such as quantum dots and molecular junctions) offers a route to reshape transmission spectra for this purpose, typical thermoelectric figures of merit in such systems remain in the range of $ZT \sim 1-30$ . The authors investigate whether engineering the spatial distribution of electrode contacts—specifically the coupling geometry—can serve as an independent control parameter to further optimize thermoelectric transport in quasiperiodic topological systems, potentially accessing regimes beyond those achievable through intrinsic lattice engineering alone.

Methodology
The study employs the nonequilibrium Green's function (NEGF) formalism within the Landauer-Büttiker framework to analyze coherent thermoelectric transport. The physical system modeled is a finite, quasiperiodic Su-Schrieﬀer-Heeger (SSH) ring threaded by a magnetic flux $\Phi$ . The ring consists of $N=34$ sites with nearest-neighbor hopping amplitudes $t_1$ (intracell) and $t_2$ (intercell), defining trivial ( $t_1 > t_2$ ), homogeneous ( $t_1 = t_2$ ), and topological ( $t_1 < t_2$ ) regimes. Quasiperiodicity is introduced via an Aubry-André-Harper (AAH) onsite potential with modulation strength $W$ .

The core innovation lies in comparing two distinct system-electrode coupling geometries:

Symmetric Coupling: Three lattice sites are connected to both the source and drain reservoirs.
Asymmetric Coupling: Three sites are connected to the source, while only a single site is connected to the drain.

The authors calculate the transmission probability $T_{SD}(E, \phi)$ and derive transport coefficients (electrical conductance, Seebeck coefficient, electronic thermal conductance, $ZT$ , and the normalized Lorenz ratio) by scanning the Fermi energy and magnetic flux. The analysis focuses on the interplay between dimerization, quasiperiodicity, magnetic flux-induced Aharonov-Bohm interference, and the electrode-coupling geometry.

Key Contributions and Results

Role of Coupling Geometry at Zero Magnetic Flux:
- In the absence of magnetic flux, the trivial dimerized phase ( $t_1 > t_2$ ) exhibits the highest thermoelectric efficiency for both geometries.
- Symmetric coupling yields a maximum $ZT \approx 9$ in the trivial regime.
- Asymmetric coupling significantly enhances performance, achieving $ZT \approx 30$ in the trivial regime. This enhancement arises because the asymmetric geometry restricts the number of coherent transmission pathways, creating sharper, more isolated resonances. This leads to stronger energy filtering, which amplifies the Seebeck coefficient while suppressing electronic thermal conductance ( $\kappa_e$ ).
- The study establishes a clear correlation between enhanced $ZT$ and the violation of the Wiedemann-Franz law (indicated by a suppressed Lorenz ratio $R$ ), signifying the decoupling of charge and heat transport.
Impact of Magnetic Flux on Symmetric Coupling:
- Introducing magnetic flux reconstructs the transmission spectrum via Aharonov-Bohm interference.
- For symmetric coupling, the optimal thermoelectric regime shifts from the trivial phase (at zero flux) to the topological dimerized phase ( $t_1 < t_2$ ) under finite flux.
- At optimal flux conditions ( $\phi \approx 0.48$ ), the symmetric configuration achieves a maximum $ZT \approx 12$ in the topological regime.
Synergy of Asymmetric Coupling and Magnetic Flux:
- The most significant finding is the combined effect of asymmetric coupling and magnetic flux. In the topological dimerized phase under finite flux, the asymmetric geometry produces a "giant" thermoelectric response.
- The maximum figure of merit reaches $ZT \approx 90$ near $\phi \approx 0.48$ .
- This represents a dramatic enhancement compared to the symmetric case ( $ZT \approx 12$ ) under the same conditions. The mechanism involves the cooperative interplay of topological dimerization, broken left-right coupling symmetry, and flux-induced quantum interference. This combination reshapes the energy dependence of the transmission to maximize thermopower while strongly suppressing $\kappa_e$ .
- In contrast to the zero-flux case where the trivial phase was optimal, the finite flux combined with asymmetry strongly favors the topological phase.

Significance and Claims
The paper claims that electrode-coupling geometry is not merely a boundary condition but an active design parameter for quantum interference. By engineering the spatial distribution of contacts (specifically using asymmetric coupling), one can tailor the transmission spectrum to achieve energy filtering far more effective than intrinsic lattice properties alone.

The authors demonstrate that the combination of quasiperiodicity, topology, magnetic flux, and electrode-coupling geometry provides a versatile strategy for engineering high-performance coherent thermoelectric devices. The predicted $ZT \approx 90$ suggests that interference engineering can yield thermoelectric efficiencies significantly higher than those typically found in coherent mesoscopic systems. The work highlights that the violation of the Wiedemann-Franz law is a fundamental signature of this enhanced performance, rooted in the selective decoupling of charge and heat transport channels. The authors suggest these effects are relevant to experimentally accessible platforms such as gate-defined quantum-dot arrays, semiconductor nanowire quantum dots, molecular junctions, and cold-atom realizations of SSH systems, where the relevant parameters can be independently controlled.

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