## 1. Introduction

Layered cobaltites with CdI_{2}‐type CoO_{2} block provide an excellent platform for investigating thermoelectric properties. A key to unveil mysterious thermoelectric properties lies in the two‐dimensional (2D) conducting CoO_{2} layer. For layered Bi‐*A*‐Co‐O (*A* = Ca, Sr, and Ba), it also contains analogous conducting CoO_{2} layer [1]. In particular, layered Bi_{2}Sr_{2}Co_{2}O* _{y}* (BSC) exhibits a rather large thermoelectric power

*S*(∼100 μV/K) at room temperature, which makes Bi

_{2}Sr

_{2}Co

_{2}O

*one of promising thermoelectric materials from the viewpoint of potential applications, analogous to other misfit‐layered cobaltites, such as NaCo*

_{y}_{2}O

_{4}and Ca

_{3}Co

_{4}O

_{9}[2–5]. However, most studies of Bi

_{2}Sr

_{2}Co

_{2}O

*system are mainly focused on the thermoelectric improvement [2, 3, 6]. The transport mechanism based on resistivity*

_{y}*ρ*and thermoelectric power

*S*has not been clarified. Moreover, large

*S*is totally different from conventional value (<10 μV/K) based on a broad band model [7]. In this chapter, we will show evidence on a narrow band contribution in doped Bi

_{2}Sr

_{2}Co

_{2}O

*[8]. And what's more, exotic enhancement of large*

_{y}*S*is related to local density of states (DOS) near Fermi level (

*E*

_{F}) [9]. It could be effectively modulated thermoelectric performance by utilizing different doping. It is plausible to distinguish, which thermoelectric materials in doped Bi

_{2}Sr

_{2}Co

_{2}O

*could be regarded as potential candidates.*

_{y}On the other hand, ternary chalcogenides serve as an ideal platform for investigating intricate physical and chemical characteristics controlling the efficiency of thermoelectric materials, and also are promising materials for potential applications in photovoltaics, luminescence, as well as thermoelectric and spintronic devices [10–13]. Ternary chalcopyrite‐structured chalcogenides, such as CuFeS_{2}, have attracted particular attention owing to their unique optical, electrical, magnetic, and thermal properties [14–28]. Studies on chalcopyrite (CuFeS_{2}) have primarily focused on its electronic states [14, 15, 29–31]. However, the microscopic mechanism of electronic structure and thermoelectric character in CuFeS_{2}, which presumably arises from some scenarios such as delocalization of the Fe 3*d* electrons, charge‐transfer‐driven hybridization between Fe 3*d* and S 3*p* orbitals, or density of the conduction band electron states, still remains highly controversial [17, 30, 32]. The intrinsic mechanism of good thermoelectric properties is still a vital question which needs to be clarified. Another important issue is that the fabrication of artificial chalcopyrite itself requires expensively complex synthesis procedures and relatively high cost of constituent precursors, thereby potentially limiting the large‐scale applications in the thermoelectric field.

In this chapter, we confirm that an unexpected thermoelectricity can directly be generated in a natural chalcopyrite mineral Cu_{1+x}Fe_{1−x}S_{2} from a deep‐sea hydrothermal vent, and demonstrate that doped carriers have strong coupling with localized antiferromagnetic (AFM) spins, which greatly enhance the thermoelectric power *S* and power factor, revealing the significance of electron‐magnon scattering and large effective mass [33]. This will open up another useful avenue in manipulating low‐cost thermoelectricity or even electron/hole carriers via the natural energy materials abundantly deposited in the earth.

## 2. Thermoelectric properties and narrow band contribution of Bi_{2}Sr_{1.9}*M*_{0.1}Co_{2}O_{y} and Bi_{2}Sr_{2}Co_{1.9}*X*_{0.1}O_{y}

### 2.1. Crystal structure and valence states of Co ions

The crystal structure of Bi_{2}Sr_{2}Co_{2}O* _{y}* is shown in the inset in

**Figure 1**, where conducting CoO

_{2}layer with triangular lattice and insulating rocksalt Bi

_{2}Sr

_{2}O

_{4}block layer are alternatively stacked along

*c*‐axis, similar to the case of high‐temperature superconductors like Bi

_{2}Sr

_{2}CaCu

_{2}O

*. Scanning electron microscopy (SEM) characterization of Bi*

_{y}_{2}Sr

_{2}Co

_{2}O

*indicates surface morphology of plate‐like grains.*

_{y}**Figure 1**shows X‐ray diffraction (XRD) patterns of selected samples Bi

_{2}Sr

_{2}Co

_{2}O

*, Bi*

_{y}_{2}Sr

_{1.9}Ca

_{0.1}Co

_{2}O

*, and Bi*

_{y}_{2}Sr

_{2}Co

_{1.9}Mo

_{0.1}O

*with single phase, in agreement with XRD result of Bi*

_{y}_{1.4}Pb

_{0.6}Sr

_{2}Co

_{2}O

*[34]. The average Co valence was determined based on energy dispersive spectroscopy (EDS) measurement for all samples. For Bi*

_{y}_{2}Sr

_{2}Co

_{2}O

*, average Co valence is +3.330. For Bi*

_{y}_{2}Sr

_{1.9}

*M*

_{0.1}Co

_{2}O

*(*

_{y}*M*= Ag, Ca, and Y), average Co valence is +3.380, +3.330, and +3.280, respectively. For Bi

_{2}Sr

_{2}Co

_{1.9}

*X*

_{0.1}O

*(*

_{y}*X*= Zr, Al, and Mo), average Co valence is +3.295, +3.347, and +3.189, respectively. X‐ray photoemission spectroscopy (XPS) spectra (see

**Figure 4a**) also show the valence states of Co 2

*p*

_{3/2}and 2

*p*

_{1/2}for selected Bi

_{2}Sr

_{1.9}Ca

_{0.1}Co

_{2}O

*sample. Photon energy of Co 2*

_{y}*p*

_{3/2}and 2

*p*

_{1/2}is 779.4 and 794.2 eV, respectively, demonstrating mixed Co valence between +3 and +4.

### 2.2. Resistivity and transport mechanism

**Figure 2a** and **d** shows temperature dependence of resistivity *ρ*(*T*) of all samples. For parent Bi_{2}Sr_{2}Co_{2}O* _{y}* sample, an upturning point at

*T*

_{p}(∼75 K) is observed. Metallic behavior above

*T*

_{p}appears, demonstrating existence of itinerant charge carriers. Compared with Bi

_{2}Sr

_{2}Co

_{2}O

*,*

_{y}*ρ*(

*T*) of all doped samples (except Bi

_{2}Sr

_{1.9}Ca

_{0.1}Co

_{2}O

*) display total increase in view of the disorder effect. Furthermore, enhanced random Coulomb potential because of the doping induces the obvious shift of*

_{y}*T*

_{p}toward higher temperature. On the other hand,

*ρ*(

*T*) of Bi

_{2}Sr

_{1.9}Ca

_{0.1}Co

_{2}O

*presents an overall decrease due to introduction of hole–type charge carriers into conducting CoO*

_{y}_{2}layers.

To get insight into the conduction mechanism below *T*_{p}, dependences of ln *ρ* on *T*^{−1} are plotted in **Figure 2b** and **e**. At the beginning, it is found that thermally activated conduction (TAC) law matches *ρ*(*T*) data well below *T*_{p}, namely [35], *ρ*(*T*) apparently deviates from the TAC behavior with decreasing temperature further, and it follows Mott's variable‐range-hopping (VRH) model described by equation [35]: **Figure 2c** and **f**, obtained values of *T*_{hopping} of Bi_{2}Sr_{1.9}Ca_{0.1}Co_{2}O* _{y}* (0.66 meV and 15.3 K) are the respective minimum, even smaller, than those of parent Bi

_{2}Sr

_{2}Co

_{2}O

*(0.70 meV and 16.2 K), while*

_{y}*T*

_{hopping}of Bi

_{2}Sr

_{2}Co

_{1.9}Zr

_{0.1}O

*(2.75 meV and 63.6 K) are both maximum among all samples.*

_{y}### 2.3. Thermoelectric power and narrow band model

**Figure 3a** and **b** shows temperature dependence of thermoelectric power *S*(*T*) for all samples. Positive values of *S* reflect electrical transport feature dominated by holes. Values of *S* at room temperature for all doped samples produce a substantial increase, especially for Bi_{2}Sr_{2}Co_{1.9}Mo_{0.1}O* _{y}* (∼117 μV/K), compared with pristine Bi

_{2}Sr

_{2}Co

_{2}O

*(∼92 μV/K). Particularly, with decreasing the temperature until below*

_{y}*T*

_{hopping},

*S*(

*T*) behavior follows with VRH model [36]:

*S*

_{VRH}(

*T*) ∼

*aT*

^{1/2}, where

*a*is factor determined by density of localized states at Fermi level

*N*(

*E*

_{F}). The inset in

**Figure 3b**reveals Anderson localization of Bi

_{2}Sr

_{2}Co

_{1.9}Mo

_{0.1}O

*, in correspondence with low‐temperature resistivity.*

_{y}In general, *S* is extremely small (<10 μV/K) and presents a metallic behavior in a broad band [7]. Taking into account the huge difference, large *S* at high temperatures (above 200 K) in a narrow band matches Heikes model [37]: *d* is concentration of Co^{4+}. The enhanced *S* at high temperatures is attributed to the competition between *d* and spin entropy. It is noted that *S*(*T*) is also described by narrow band model at intermediate temperatures. *S*(*T*) follows with Boltzmann formula [38]: *S*(*T*) indicates monotonous increase with increasing *T*, as well as experimental result as plotted in the inset in **Figure 3a**, revealing the validity of narrow band model.

Actually, activation energy *E*_{F}−*E*_{C}, where *E*_{C} is the upper mobility edge. As *k*_{B}*T*/2 >**Figure 3c**. At high temperatures, the majority of acceptor‐like states are fully ionized, that is, occurs complete excitation of holes, that resulting in metallic behavior of *ρ*(*T*)and diffused *S*(*T*) (Heikes formula). As *k _{B}T*/2 is near to

*k*

_{B}

*T*/2 <

**Figure 3d**.

### 2.4. X‐ray photoemission spectroscopy and thermal conductivity

In order to further verify the narrow band model, we carried out XPS spectra for Bi_{2}Sr_{1.9}Ca_{0.1}Co_{2}O* _{y}*. As shown in

**Figure 4b**, XPS spectra present an intense peak at ∼ 0.95 eV, in line with large

*S*and metallic behavior. Between

*E*

_{F}and ∼2.0 eV, Co 3

*d*and O 2

*p*orbitals play an important role, similar to pristine Bi

_{2}Sr

_{2}Co

_{2}O

*[39]. Moreover, strong hybridization between Co 3*

_{y}*d*and O 2

*p*forms [39, 40]. Namely, antibonding

*t*

_{2g}narrow bands contribute to intense peak at ∼0.95 eV, while bonding

*e*

_{g}broad bands are responsible to peak within 3–8 eV. In addition, calculated

*S*(

*T*) is also consistent with experimental value based on magnitude and temperature dependence [39]. Therefore, the narrow band model is very suitable for explaining all experimental and theoretical results.

Temperature dependence of total thermal conductivity *κ*(*T*) for all samples are shown in **Figure 5a** and **d**. *κ*(*T*) can be expressed by the sum of phononic component *κ*_{ph}(*T*) and mobile charge carriers’ component *κ*_{e}(*T*) as *κ*(*T*) = *κ*_{ph}(*T*) + *κ*_{e}(*T*). Value of *κ*_{e}(*T*) can be estimated from the Wiedemann‐Franz law, *κ*_{e}(*T*) = *L*_{0}*T*/*ρ*, where *L*_{0} ∼ 2.44 × 10^{−8} V^{2}/K^{2} stands for Lorenz number. In **Figure 5b** and **e**, *κ*_{ph}(*T*) dominates the thermal conductivity because CoO_{2} layer and Bi‐Sr‐O block layer induces the interface scattering. Dimension less figure of merit *ZT* = *S*^{2}*T*/*ρκ* reflects total thermoelectric performance (see **Figure 5c** and **f**). For pristine Bi_{2}Sr_{2}Co_{2}O* _{y}*,

*ZT*value reaches ∼ 0.007 at 300 K, while

*ZT*value reaches 0.19 at 973 K, indicative of promising thermoelectric material for Bi

_{2}Sr

_{2}Co

_{2}O

*at high temperatures [2]. Especially for Bi*

_{y}_{2}Sr

_{1.9}Ca

_{0.1}Co

_{2}O

*,*

_{y}*ZT*value reaches maximum ∼ 0.012 at 137 K. Therefore, it is reasonable to predict that Bi

_{2}Sr

_{1.9}Ca

_{0.1}Co

_{2}O

*could be considered as one of potential ultra‐high temperature thermoelectric materials, as well as pristine Bi*

_{y}_{2}Sr

_{2}Co

_{2}O

*.*

_{y}## 3. Exotic reinforcement of thermoelectric power in layered Bi_{2}Sr_{2−x}Ca_{x}Co_{2}O_{y}

### 3.1. XRD patterns and electrical transport properties

The crystal structure of Bi_{2}Sr_{2}Co_{2}O* _{y}* is shown in

**Figure 6a**.

**Figure 6b**shows XRD patterns of all Ca-doping samples with single phase in Bi

_{2}Sr

_{2−x}Ca

*Co*

_{x}_{2}O

*(0.0 ≤*

_{y}*x*≤ 2.0). With increasing Ca content, diffraction peak along [003] direction distinctly shifts to higher angle as shown in the inset in

**Figure 6b**, confirming the smaller ionic radius of Ca

^{2+}, than that of Sr

^{2+}. SEM characterization indicates surface morphology of plate‐like grains and regular grain sizes for selected samples with

*x*= 0.0 and 1.0, respectively.

**Figure 7a** and **b** shows resistivity *ρ*(*T*) of all samples in Bi_{2}Sr_{2−x}Ca* _{x}*Co

_{2}O

*. For the present*

_{y}*x*= 0.0 polycrystalline sample, upturning point at

*T*

_{p}(∼150 K) appears. Metallic behavior above

*T*

_{p}is observed, demonstrating the existence of itinerant charge carriers. In comparison, for

*x*= 0.0 single crystal [41], in‐plane resistivity

*ρ*also shows metallic behavior around room temperature, while it arises minimum near 80 K and diverges with further decreasing the temperature. Resistivity

_{ab}*ρ*value of single crystal for

_{ab}*x*= 0.0 at room temperature is ∼4 mOhm×cm and is smaller than that of our polycrystalline sample (∼15 mOhm×cm). On the other hand, compared with

*x*= 0.0,

*ρ*(

*T*) of all Ca‐doped samples produce total increase due to disorder effect. For the samples with

*x*≤ 0.5, enhanced random Coulomb potential because of Ca doping induces the shift of

*T*

_{p}toward higher temperature. Interestingly, for the samples with

*x*≥ 1.0, the signature of transition at

*T*

_{p}completely vanishes and

*ρ*(

*T*) only presents an insulating‐like behavior.

To discern conduction mechanism below *T*_{p}, relationship of ln*ρ* against 1/*T* is plotted in **Figure 7c** and **d**. As for *x* ≤ 0.5, at the beginning, it is found that TAC law matches *ρ*(*T*) data well below *T*_{p}, namely [35], *ρ*(*T*) apparently deviates from TAC behavior with decreasing the temperature further, and it follows Mott's VRH model described by equation [32]: *x* ≥ 1.0, *ρ*(*T*) meets VRH model only, in agreement with the insulating feature of *x* = 2.0 single crystal [1, 42, 43]. Obtained values of *T*_{hopping} are plotted in **Figure 7e**. Basically, *T*_{p} for *x* ≤ 0.5. In comparison, the present value of *x* = 0.0 at 900°C [8], revealing the difference of grain size effect. It is worth noting that values of *T*_{hopping} and *ρ*_{300K} at room temperature first increase and then decrease in whole Ca‐doped range (see **Figure 7e** and **f**).

### 3.2. Enhancement of thermoelectric power driven by Ca doping

**Figure 8a** shows thermoelectric power *S*(*T*) for all samples. Positive values of *S* demonstrate that majority of charge carriers are hole type. In addition, *S* exhibits a nearly *T*‐independent behavior above 200 K, while *S* strongly depends on *T* peculiarly below 150 K. Ca doping obviously boosts *S*_{300K} at room temperature especially for heavy Ca contents (see **Figure 8b**). Large *S*_{300K} value monotonously increases from 105 μV/K(*x* = 0.0) to 157 μV/K (*x* = 2.0). In general, the change of *S* should be related to variation of *n*. For *x* = 0 single crystal [38], Hall coefficient (*R*_{H}) is positive and strongly dependent on the temperature in the range from 300 to 0 K. Increase of *R*_{H} toward the lowest temperature is not simple due to the decrease of *n*, but rather due to anomalous Hall effect. It is noted that variation of *R*_{H} with Pb doping is also similar to that of *ρ _{ab}*. Pb doping slightly reduces the magnitude of

*R*

_{H}, but the increase in number of charge carriers is much smaller than expected from chemical composition [41, 44].

As we know, *S* is rather low (<10 μV/K) with a metallic behavior in a broad band [7]. Taking into account the tremendous discrepancy, large *S* of Bi_{2}Sr_{2−x}Ca* _{x}*Co

_{2}O

*with a nearly*

_{y}*T*-independence at high temperatures in a narrow band should follow the so‐called Heikes formula [37]:

*d*is concentration of Co

^{4+}, and

^{3+}and Co

^{4+}ions, respectively. Concentration

*d*at room temperature can be deduced from charge carriers’ density

*n*. As visible in

**Figure 8c**, as for

*x*< 1.5,

*d*decreases, while

*S*

_{Heikes}(deriving from Heikes formula) increases, which is consistent with the trend of

*S*

_{300K}. But for

*x*≥ 1.5, reduced

*S*

_{Heikes}is reverse to persistent enhancement of

*S*

_{300K}. Thus, we have to consider other possible reason of enhanced

*S*for heavily doped samples.

### 3.3. Specific heat and Sommerfeld coefficient

Next we will check whether the enhanced *S* originates from the increased effective masses through electronic correlation. To test this point, we performed measurement of specific heat *C*(*T*), which is plotted as *C*/*T* versus *T*^{2} (see the inset in **Figure 8d**) for selected samples with *x* = 0.0, 0.5, 1.5, and 2.0. *C*(*T*) at low temperatures can be described as *C*(*T*) = *γT* + *βT*^{3} [45], where *γT* and *βT*^{3} denote electronic and lattice contribution to *C*(*T*), respectively. We can get electronic coefficient *γ* by the linear fitting according to *C*/*T* = *γ* + *βT*^{2} [45]. Here, we need to explicitly interpret Sommerfeld coefficient *γ*. For the present system, unit formula should involve two cobalt atoms. For our polycrystalline sample with *x* = 0.0, a conventional way to get *γ* by extrapolating high‐temperature linear part of *C/T* versus *T* = 0 gives very large value of ∼ 135 mJ mol^{−1} K^{−2} (see **Figure 8d**), comparable with that of *x* = 0.0 single crystal (∼140 mJ mol^{−1} K^{−2}) [41]. However, it is observed that *γ* rapidly decreases with increasing Ca doping. For our sample with *x* = 2.0, value of *γ* is ∼85 mJ mol^{−1} K^{−2}. Differently, it is noted that value of *γ* is only 50 mJ mol^{−1} K^{−2} for Bi‐Ca‐Co‐O system, while such a unit formula merely includes one cobalt atom [45].

Now we discuss the underlying implications of enhanced *S* with Ca doping. As mentioned above, as for *x* < 1.5, decreased *d* based on Heikes formula should be responsible for the enhanced *S*. But for *x* ≥ 1.5, local modification of DOS and band structure near *E*_{F} could play crucial role. *S*(*T*) can be defined by Mott formula [39]: *σ*(*E*) is electrical conductivity with *σ*(*E*) = *n*(*E*)*eυ*(*E*), *υ*(*E*) is mobility, *n*(*E*) is charge carriers’ density with *n*(*E*) = *D*(*E*)*f*(*E*), *D*(*E*) is DOS, and *f*(*E*) is Fermi function. Apparently, in terms of Mott formula, the enhancement of *S* for *x* ≥ 1.5 should be attributed to the increase of local DOS near *E*_{F}. In details, with decreasing A‐site ionic radius (i.e., with increasing Ca content), tolerance factor decreases (not shown here), which leads to changes of lattice distortion in CoO_{2} layer and local band structure near *E*_{F}, reminiscent of layered perovskite cobaltite SrLnCoO_{4} (Ln stands for different rare earth elements) [46]. Ultimately, value of *S* for *x* ≥ 1.5 would be enhanced. Based on all of above results, one should emphasize that Sommerfeld coefficient *γ* is dependent on *n*, and also as function of DOS at *E*_{F}, which leads to continuous enhancement of large *S*.

## 4. Thermoelectricity generation and electron‐magnon scattering in a natural chalcopyrite mineral

### 4.1. Crystal structure and SEM characterization

A series of natural chalcopyrite minerals, Cu_{1+x}Fe_{1−x}S_{2} (*x* = 0.17, 0.08, and 0.02), were obtained from a hydrothermal vent site named Snow Chimney in the Mariner field of Lau Basin [47]. Basically, mineral composition obtained from intact natural sulfide chimneys has no variation. Subsamples with *x* = 0.02 and 0.08 were obtained from the most interior chimney part, whereas subsample with *x* = 0.17 was obtained from the middle chimney wall region. The highly fluctuated and variable physicochemical conditions lead to obvious differences in mineral composition [48]. **Figure 9** shows sketches of its crystal structure and atomic planes, in which chalcopyrite crystallizes in a tetragonal lattice with space group of *I*‐42*d* and produces honeycomb structure characteristic [49]. Each Fe and Cu atom is encircled by tetrahedron of S atom. The highlighted planes indicateatomic zig‐zag pattern, which is likely responsible to phonon scattering. XRD Rietveld refinement of power pattern indicates that three natural samples are single phase with standard chalcopyrite structure. For *x* = 0.08, refined lattice parameters *a* and *c* are 5.278 and 10.402 Å, respectively (see **Figure 10**).

To probe the microstructures of natural Cu_{1+x}Fe_{1−x}S_{2}, we performed SEM characterization (**Figure 11**). SEM analysis revealed that natural chalcopyrite with *x* = 0.08 had layered structure. Three examined natural samples were found to contain morphological diversity, which is characteristic of chalcopyrite minerals, and suggest different physical and chemical behaviors of various microstructures. The SEM observation may provide important insights of the relevance between physical and chemical functions and behaviors of chalcopyrite minerals.

### 4.2. Thermoelectricity generation and electronic states

To examine the functional properties of natural Cu_{1+x}Fe_{1−x}S_{2} samples, we first measured resistivity (*ρ*) as function of temperature (*T*). Three examined natural samples exhibited excellent conductive behavior with semiconductive characteristics (**Figure 12a**). With the reduction of *x*, the overall resistivity decreased due to the emergence of doped charge carriers. Value of *ρ*_{300K} for *x* = 0.17, 0.08, and 0.02 was 4.97, 0.11, and 1.01 Ohm×cm, respectively. Compared with *x* = 0.08, the increase of resistivity for *x* = 0.02 stems from the enhanced random Coulomb potential owing to the natural doping.

In order to track the evolution of electronic states, we carried out thermoelectric power (*S*) measurement (**Figure 12b**), where the sign of *S* changes. For *x* = 0.17, the sign of *S* switches from negative to positive around 235 K with decreasing temperature (**Figure 12b**). It is amazing to observe two unusual peaks: a broad peak (*T*_{m}; 32 μV/K, 186 K) and a sharper peak (*T*_{p}; 215 μV/K, 11 K), indicating the majority of hole carriers (*p-*type). It is of particular interest that, for *x* = 0.08 and 0.02, *T*_{p} peak utterly disappears, while *T*_{m} peak becomes wider and rapidly shifts to a lower temperature, where *S* presents very large negative values, demonstrating the majority of electron carriers (*n-*type), in line with negative Hall coefficient *R*_{H} (**Figure 13**). Large *S*_{300K} reached a remarkable value of −713 and −457 μV/K for *x* = 0.08 and 0.02, respectively. Namely, more electrons are activated at room temperature with increasing Fe concentration. For *x* = 0.08, charge carriers’ mobility *μ*_{300K} and density *n*_{300K} are 1.8 cm^{2} V^{−1} s^{−1} and 3.5 × 10^{19} cm^{−3}, obtained from *R*_{H} = 1/*ne* and *μ*= 1/*neρ*. In addition, Fe magnetic moment may also play an key role to induce large *S*, indicative of strong coupling between magnetic ions and doped charge carriers because synthetic CuFeS_{2} presents AFM ordering at 823 K [15].

### 4.3. Electron‐magnon scattering and large effective mass

The matter of imperative concern is how to understand the origin of *T*_{m} peak and conduction mechanism. According to Mott's formula, *S* can be qualitatively expressed as *k*_{B} is Boltzmann constant, *E*_{F}, and *d*[*E* [35]. If one assumes ^{−1}= *ρ*, then Δ*S*/*S*_{0} Δ*ρ*/*ρ*_{0} can be derived. Plot of Δ*S*/*S*_{0} versus Δ*ρ*/*ρ*_{0} for *x* = 0.17 (**Figure 14**) shows that all experimental data near *T*_{m} at *T*_{0} from 155 to 300 K deviate from the theoretical calculation, the linearity. These results verify that exotic mechanism of *S*(*T*) in natural sample is beyond the framework of conventional thermoelectric picture [50].

To better discern intrinsic transport mechanism of Cu_{1+x}Fe_{1−x}S_{2}, we incorporate spin-wave theory to analyze temperature dependence of *S*. For *x* = 0.08 and 0.02, field‐cooling magnetization and loop hysteresis indicate the localized ferromagnetism (FM) at low temperatures because of additional Fe moments (**Figure 15**). However, strong AFM interaction at high temperatures dominates for three natural samples. Generally speaking, spin waves can scatter electrons for AFM or FM materials, resulting in magnon‐drag effect [12]. To check this issue, we developed magnon‐drag model, *S*=*S*_{0}+*S*_{3/2}*T*^{3/2}+*S*_{4}*T*^{4}, where *S*_{0} is value of *S* at *T* = 0, *S*_{3/2}*T*^{3/2} term stems from electron‐magnon scattering, and *S*_{4}*T*^{4} term is related to spin‐wave fluctuation in AFM phase. Using this model of magnon drag, the predicted values for three samples closely matched *S*(*T*) data (**Figure 16a** and **b**). As the absolute value of *S*_{3/2} is nearly six orders of magnitude larger than that of *S*_{4} (**Table 1**), electron‐magnon scattering dominates *S*(*T*) curve. Thus, *T*_{m} peak is predicted to originate from magnon drag due to the strong electron‐magnon interaction.

Parameter | T_{m}(K) | S_{0}(μVK^{−1}) | S_{3/2}(μVK^{−5/2}) | S_{4} (μVK^{−5}) | ΔE(meV) |
---|---|---|---|---|---|

x = 0.17 | 186 | −6.21 | 0.03 | −3.84×10^{−8} | 60.1 |

x = 0.08 | 68 | −75.45 | −0.08 | −5.47×10^{−8} | 4.9 |

x = 0.02 | 38 | −10.61 | −0.04 | −3.95×10^{−8} | 11.8 |

[i] -
The parameter *T*_{m} represents the peak of magnon drag, which stems from the experimental *S*(*T*) curve. The parameters *S*_{0}, *S*_{3/2}, and *S*_{4} stem from the model of magnon drag, *S*= *S*_{0} + *S*_{3/2}*T*^{3/2} + *S*_{4}*T*^{4}. The parameter Δ*E* is the activation energy, which stems from the TAC model, *ρ*(*T*) = *ρ*_{0} exp (Δ*E*/*k*_{B}*T*).

To gain more insight into the correlation between magnon drag, doped carriers, and *S*, we plotted parameters *S*_{0}, *S*_{3/2}, and *S*_{4} as a function of *x* (**Table 1**). *S*_{0}, *S*_{3/2}, and *S*_{4} for *x* = 0.08 has largest absolute values among three natural samples, in agreement with the largest *S*, smallest *ρ,* and highest power factor. Unlike *S*_{0} and *S*_{4}, dependence of *S*_{3/2} is quite unique (**Figure 16c**). The sign of *S*_{3/2} varies from positive to negative with increasing Fe concentration, suggesting the alternation of *p*‐type and *n*‐type charge carriers and orbital degree of freedom of Fe 3*d* band with AFM ordering. Additionally, electron‐magnon scattering occupies thermoelectric properties, indicating strong coupling between doped charge carriers and AFM spins. Furthermore, *ρ*(*T*) follows TAC model *E* (60.1, 4.9, and 11.8 meV for *x* = 0.17, 0.08, and 0.02, respectively), which verifies the existence of localized Fe spins, is markedly smaller than that of artificial chalcopyrite [21, 29–31]. It is noted that experimental *S*(*T*) result is well described by electron‐magnon scattering up to ∼200 K, while it deviates from theoretical lines for higher temperatures. In particular, power factor *S*^{2}/*ρ* shows an abrupt enhancement above 200 K for *x* = 0.08 (**Figure 16d**), in agreement with that of *R*_{H} and *n* (**Figure 13**). Above 200 K, large effective mass (*m*^{*}) leads to high power factor and large *S* due to low *μ* and high *n*. For *x* = 0.08, it exhibits the largest *m*^{*} value (1.6 *m*_{0}) at room temperature, where *m*_{0} is free electron mass. Therefore, we can conclude that robust electron‐magnon scattering and large *m*^{*} induce unexpected thermoelectricity generation in natural chalcopyrite mineral.

In terms of thermal conductivity *κ*, phononic component *κ*_{ph} dominates for three natural samples owing to negligible electronic component *κ*_{e} (**Figure 17**). For the optimal sample with *x* = 0.08, value of *ZT* can reach 0.03 at room temperature (**Figure 17**), thus indicating that natural chalcopyrite semiconductor is a promising candidate for thermoelectric energy materials. It is quite striking that the spontaneous doping process during deep‐sea hydrothermal vent mineral precipitations led to natural thermoelectric improvement, which is similar to natural mineral tetrahedrites [51].

## 5. Conclusions

Our results of layered cobaltites Bi_{2}Sr_{2}Co_{2}O* _{y}* system based on narrow band model are not only helpful to understand large

*S*and transport mechanism but also differentiate other systems based on a broad band model. In particular, we give the experimental evidence by Hall effect and

*C*(

*T*) measurements, demonstrating that Sommerfeld coefficient

*γ*is dependent on charge carriers’ density

*n*, and also as a function of DOS at

*E*

_{F}, which induces exotic enhancement of large

*S*in Bi

_{2}Sr

_{2−x}Ca

*Co*

_{x}_{2}O

*. Especially for Bi*

_{y}_{2}Sr

_{1.9}Ca

_{0.1}Co

_{2}O

*, it may provide an excellent platform to be regarded as potential candidates for thermoelectric materials.*

_{y}In addition, we demonstrated direct thermoelectricity generation in natural chalcogenides, Cu_{1+x}Fe_{1−x}S_{2}, which was shown to have large *S* value and high power factor in the low *x* region, in which electron‐magnon scattering and large *m*^{*} values were detected. Since doped charge carriers exist in strong coupling with localized spins, the unusual alternation of *p*‐ and *n*‐type carriers should be of paramount importance in understanding charge dynamics arising from 3*d* orbital degrees of freedom. Such a finding of exotic thermoelectric properties in natural but not synthetic chalcopyrite opens a novel research field for manipulating low‐cost thermoelectricity or even electron/hole carriers, providing therefore a new perspective on technical feasibility for designing and pinpointing the surface‐morphology‐engineered devices via the naturally abundant materials.