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Martin-Gonzalez et al. Energy Mater. 2025, 5, 500121 https://dx.doi.org/10.20517/energymater.2025.32 Page 15 of 35

to the bipolar thermal conductivity term (which can be thought as recombination of electrons and holes at
the contacts of the material). For example, in narrow-gap materials such as SnSe, bipolar transport degrades
[144]
the zT at elevated temperatures by introducing such counteracting hole/electron currents . This material-
level challenge necessitates bandgap widening via alloying in SnSe, thereby achieving a significant reduction
in bipolar conduction [145,146] . Another bandgap engineering direction is related to 2D materials. Theoretical
studies have shown that there exists an optimal value for the PF as the bandgap of these materials is reduced
as a consequence of the bands becoming more linear, which benefits the electronic conductivity. For even
lower bandgaps, however, the PF is reduced because bipolar effects gradually diminish the Seebeck
coefficient .
[147]

Resonant states for Seebeck improvement
Another strategy that led to PF improvements in certain cases is the use of resonant levels which result from
interactions between defects and host materials and could lead to an increase in the DOS. This happens in
rare cases where certain defects can introduce resonance states and were first observed for Tl defects in
[148]
PbTe . Typically, the electronic configuration of such dopants is very close to that of the host, as when
using periodic table elements from neighboring columns for doping. The goal is to identify a dopant that
near the Fermi level forms defect states. The main idea is to increase the DOS locally in energy, such that a
broadened delta-function-like feature is added to the underlying DOS of the pristine material. The sharp
increase in the DOS is translated into an increase in the Seebeck coefficient, as this coefficient is
proportional at first order to the energy derivative of the DOS. As this extra DOS appears at elevated
energies into the bands (and assuming that the Fermi level is placed in that vicinity), typically the electronic
conductivity does not suffer significantly, or at least PF improvements can be observed. For instance, Tl-
doped PbTe exhibits a 3-5× reduction in mobility compared to the single crystal, but shows a 1.7-3×
enhancement in the Seebeck coefficient , resulting in an overall increase in PF and zT. Since the initial
[148]
[148]
observation , a few other cases have been reported. Some other examples are the use of IIIA elements for
rock-salt IV-VI structures and functioning as p-type dopants [149-151] and the use of IVA elements in V VI
3
2
compounds . Additionally, cases such as Sb-doping on the Te-site in CuGaTe 2 [153] , Pb doping on the Bi-
[152]
site in BiCuSeO , and even anti-site defects in ZrNiSn , are known for the formation of band edge
[154]
[155]
resonant levels. More lately such effects arising from defect states in Heusler alloys are claimed to provide
significant PF improvements [139,140] .
Other promising and exploratory directions for PF improvements
Other than the mainstream directions for PF improvements described above, it is worth mentioning
exploratory examples based on novel physical phenomena.

One such direction is the increase of band degeneracy in materials with inverted bands in the presence of
spin-orbit-coupling (SOC) (see Figure 4). Upon band inversion beyond a critical degree, and under the
influence of SOC, a bandgap opens, accompanied by an increase in the number of carrier pockets, the band
degeneracy, and as a result it could largely increase the PF. Such effects have for example been predicted
recently for rock-salt IV-VI compounds [156,157] . With regards to further utilization of SOC in TEs, recent
reports also speculate that the Rashba SOC in 2D materials can modify the DOS distribution and result in
[158]
lower-dimensional states, which could positively influence the Seebeck coefficient under certain cases .
A second exploratory direction is that of topological effects, which have recently emerged with possibly
large PF potential. Indeed, a lot of high-performance TE materials are also topological materials.
Topological materials have demonstrated a variety of unconventional TE effects that can lead to very high
performance. Topological insulators have surface states with almost ballistic conductivity, as backscattering
is forbidden by time-reversal symmetry arguments. Although the metallic topological edge states should