Immobilization of Na Ions for Substantial Power Factor Enhancement

Article pubs.acs.org/JPCC

Immobilization of Na Ions for Substantial Power Factor Enhancement: Site-Specific Defect Engineering in Na0.8CoO2 Ping-Han Tsai,† Mohammad H. N. Assadi,† Tianshu Zhang,† Clemens Ulrich,‡,§ Thiam Teck Tan,† Richard Donelson,∥ and Sean Li*,† †

School of Materials Science and Engineering, The University of New South Wales, Sydney, NSW 2052, Australia School of Physics, The University of New South Wales, Sydney, NSW 2052, Australia § The Bragg Institute, ANSTO, Lucas Heights, NSW, 2234, Australia ∥ CSIRO Division of Process Science and Technology, Clayton, Victoria 3168, Australia ‡

ABSTRACT: Simultaneous enhancement of the interdependent Seebeck coefficient and electrical conductivity has been achieved through defect engineering by doping Mg into specific sites of Na0.8CoO2. Results from thermoelectric measurement demonstrate that the power factor was substantially increased by 50% at ambient. Experimental and theoretical analyses show that the occupation of divalent Mg in the disordered Na layer immobilizes the Na ions and thus induces a long-range ordering of Na ions. This phenomenon improves the carrier mobility significantly, giving rise to the observed exotic thermoelectric performance. Moreover, it is predicted that other electronically closed-shell dopants in sodium cobaltate play a similar role in enhancing the thermoelectric conversion efficiency.

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a remarkable power factor enhancement of ∼20% by introducing merely 1% Zn into the crystal.6 While extensive work was performed on partial substitution of magnetic impurities for Co,7−9 doping nonmagnetic elements (i.e., elements with closed-shell configurations) may provide an alternative route for enhancing TE properties of the system by improving carrier transport while maintaining low heat conductivity. In this work, the influence of doping nonmagnetic Mg2+ (2p6) on the TE properties of Na0.8CoO2 was investigated in detail and it may provide new rules for dopant selection for optimizing the TE performance of the NaxCoO2 system.

INTRODUCTION Transition metal oxides exhibit many spectacular properties and have stimulated an upsurge of interest due to the nontrivial physics that underlies their properties. Typical examples are superconductivity in cuprates,1 colossal magnetoresistance in manganites,2 and large thermopower in cobaltates.3 Sodium cobaltate (NaxCoO2) is one of the cobaltate systems that have attracted considerable attention over the decade due to its diverse electronic ground states as a function of Na content x in addition to its superior thermoelectric (TE) properties.3,4 It is believed that some fascinating features of this material are associated with the patterning of Na+ ions, which arises from the delicate interplay of Coulomb forces between Na+ ions or Na+ and its neighboring O2− ions. Typically, the triangular lattice structure of NaxCoO2 also exhibits a unique advantage of electronic frustration. Such frustration prohibits electron− phonon and superexchange interactions from lifting the spin and orbital degrees of freedom in the cobalt oxide layer, giving rise to a high spin entropy and thus large thermopower.5 Moreover, a narrow electron bandwidth, which is characterized by a small Co−O−Co (COC) bond angle, accompanied by a relatively low concentration of heavy fermions (i.e., carriers experiencing strong electron−electron interaction) is also critical for establishing the thermopower of the system.5 One effective approach to further enhance the thermopower in NaxCoO2 is to introduce impurities that alter the crystal structure extrinsically either to reduce the electronic resistivity or to increase the phonon scattering rate. Recent TE measurement on Zn-doped Na0.8CoO2 reveals a synchronized enhancement of thermopower and reduction of resistivity with © 2012 American Chemical Society

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METHODOLOGY Polycrystalline samples with nominal composition Na0.8CoO2:Mgy (0 ≤ y ≤ 0.05) were prepared employing the conventional solid state reaction technique. A powder mixture of Na2CO3, Co3O4, and MgO with stoichiometric molar ratio was directly placed into a furnace for preheating at 850 °C to minimize Na evaporation and sintering for 16 h in air. The powder was then pulverized, pelletized, and sintered again at 870 °C for 20 h. Structural evolution was studied by employing a PANalytical X’Pert Pro MPD in Bragg−Brentano geometry, with monochromated Cu Kα radiation, 0.025° step size, and a scanning rate of 2°/min. Rietveld refinement of the diffraction Received: September 27, 2011 Revised: December 20, 2011 Published: January 22, 2012 4324

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patterns was performed using GSAS code with EXPGUI frontend. The thermopower and resistivity measurement was carried out simultaneously using the ULVAC-ZEM3 system. Phonon excitations were characterized by a Raman spectrometer employing an Ar ion laser (514 nm) as the excitation source. The 6 mW laser beam was focused at a spot 100 μm in diameter. Due to the sensitivity of sodium cobaltates to air/ moisture, the samples were characterized immediately after fabrication. In the theoretical analysis, spin-polarized density functional calculations were performed with the DMol3 package10,11 based on the generalized gradient approximation (GGA) with the Perdew−Wang formalism.12 Brillouin zone sampling was carried out by choosing a 2 × 4 × 2 k-point set within Monkhorst−Park. For geometry optimization, full relaxation was performed until the energy, Cartesian components, and displacement were less than 10−5 eV/atom, 0.01 eV/Å, and 0.005 Å, respectively.

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RESULTS AND DISCUSSION Correlation of Phonon Vibrations and Long Range Ordering of Na+ Ions. X-ray powder diffraction measurement reveals that the solubility limit y* of Mg2+ in Na0.8CoO2:Mgy is ∼0.05. All the samples (i.e., 0 ≤ y ≤ 0.05) crystallize in the hexagonal system (space group P63/mmc). Figure 1 illustrates the doping dependence of the lattice parameters a and c and the cell volume. Lattice parameter a increases and c decreases with increasing y. This may imply that the doped Mg2+ ions are incorporated into the Na layers where the strong in-plane Na+− Mg2+ repulsion and out-of-plane Mg2+−O2− attraction result in the observed increase of a and decrease of c, respectively. Figure 2 shows the unpolarized Raman spectra for polycrystalline Na0.8CoO2:Mgy (0 ≤ y ≤ 0.05) samples obtained in ambient environment. Three peaks were unambiguously identified for the undoped sample (i.e., y = 0). Among these peaks, the ones at 474 and 585 cm−1 are attributed to the E1g and A1g vibrations of oxygen ions, which are consistent with the reported results of freshly cleaved single crystal β-NaxCoO2 (hexagonal space group P63/mmc).13 Another peak at 454 cm−1 may be attributed to the lowerenergy E1g mode of a different NaxCoO2 phase with a particular Na content x. The origin of this peak needs to be further investigated with combination of inductively coupled plasmaoptical emission spectroscopy and high resolution neutron diffraction in the near future. In Mg-doped samples, the incorporation of Mg2+ ions leads to simultaneous suppression of the lower-energy E1g mode, subtle softening of the higherenergy E1g mode, and substantial hardening of the A1g mode. Furthermore, the Mg2+ doping also induces one additional peak and two shoulders at 496, 560, and 634 cm−1, respectively, as pointed out (with arrows) in the Raman spectra of the sample with y = 0.05 (Figure 2). The energy of the additional peak at 496 cm−1 is very close to the in-plane phonon energy for Na0.5CoO2 with long-range texturing of Na+ ions,14 which is usually observed in the lowtemperature regime where highly disordered motion of Na+ ions is almost “f rozen”.13 The broad shoulder at 560 cm−1 corresponds to the E2g mode which is related to the vibrational motions of both sodium and oxygen ions. This mode is also strongly temperature-dependent and should vanish under ambient conditions in undoped samples.13 Furthermore, the higher-energy shoulder (i.e., 634 cm−1) exhibited here is similar to one of the phonon modes in Co3O4. However, the absence

Figure 1. Lattice parameters a and c and unit cell volume V for polycrystalline samples with nominal composition Na0.8CoO2:Mgy are presented as a function of y parts a, b, and c, respectively. The insets in parts a and b are schematic presentations of the top and side view of the primitive cell of the NaCoO2 crystal. There are two Na+ ions in each primitive cell, one at Z = 0.25 and the other at Z = 0.75.

Figure 2. Unpolarized Raman spectra for polycrystalline Na0.8CoO2:Mgy. The vertical dashed lines show the peak positions for the undoped sample (i.e., y = 0).

of the Co3O4 characteristic phonon peak at 700 cm−1 from our spectra rules out the existence of Co3O4 as a secondary phase. Therefore, the higher-energy shoulder at 634 cm−1 may also be attributed to the vibrations of both sodium and oxygen ions. The appearance of the peak at 560 cm−1 and all the shoulders at room temperature implies the immobilization of the Na+ ions 4325

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in the Na layers similar to the undoped samples in low temperatures. The doping dependence of the wavenumber ω of Ramanactive in-plane E1g and out-of-plane A1g vibrations of oxygen atoms is shown in Figure 3 where the A1g mode stiffens and the

Figure 4. (a) The positions of the Na+ ions in the supercell for the Na0.75CoO2 system and (b) the positions of the Mg2+ ion (the green ball) and the Na+ ions in the supercell for the Na0.75CoO2:MgI system are presented. (c) The charge density of the cobalt oxide layer vertical to the Na/Mg layer is presented. The charge density field’s minimum (maximum) value is 0 e/Å3 (0.125 e/Å3). The green ball denotes Mg.

Figure 3. Doping dependence of Raman-active in-plane E1g and outof-plane A1g vibrations of oxygen atoms. The inset illustrates the doping dependence of the intensity ratio between the two phonon modes.

supercell. Thus, four configurations for Na0.75CoO2:Mg were constructed and the formation energy Ef of the Mg2+ ion was calculated for each configuration. The position of Mg2+ ion in each configuration was as follows: (i) Mg2+ substituting a Na(1) marked as MgNa(1), (ii) Mg2+ substituting a Na(2) marked as MgNa(2), (iii) Mg2+ substituting a Co marked as MgCo, and finally (iv) Mg2+ occupying an interstitial site in the Na layer marked as MgI. Since the divalent Mg2+ ion has one oxidation state, only Mg2+ was considered. The Ef of Mg2+ ion in the Na0.75CoO2 host lattice was calculated according to

E1g mode softens with increasing y. The stiffening of the A1g mode is caused by the compression of trigonal oxygen antiprisms along the c-axis resulting from the shrinkage of the unit cell, as illustrated in Figure 1. Similarly, the strong Na+− Mg2+ repulsion expands the unit cell along the ab-axes, leading to the observed softening of the in-plane E1g mode. In contrast to the A1g mode, the in-plane E1g mode couples strongly to the electronic states in the CoO2 plane. Such a good agreement between the X-ray and Raman results suggests that the doped Mg2+ ions effectively trigger a long-range texturing of Na+ ions. There was a considerable suppression of spectral-weight ratio E1g/A1g as Mg2+ ions were incorporated into the system (inset of Figure 3). A similar trend was also observed by increasing the sodium concentration in pure NaxCoO2,13,14 which is directly related to the lower mobility of Na+ ions. To reveal the Na+ patterning behaviors associated with the Mg doping in NaxCoO2, a supercell with 75% Na content was constructed considering the inevitable loss of Na from Na0.8CoO2 during the sintering process. The Na+ patterning in Na0.75CoO2 is presented in Figure 4a, where one Na+ ion in each layer is positioned in the Na(1) site while the other five Na+ ions are positioned in Na(2) sites. However, the ions at Na(2) sites are located slightly off the oxygen axis, exhibiting the H1 structure that is in agreement with XRD and Raman characterizations. Noticeably, no pair of Na+ ions within a layer has a distance shorter than 2.84 Å, indicating that electrostatic repulsion is the major derivative of such patterning. In the Mg-doped Na0.75CoO2, one Mg2+ ion was placed in four different possible incorporation sites in the Na0.75CoO2

E f = Et(Na 0.75CoO2 : Mg) − Et(Na 0.75CoO2 ) + nμn − μMg + qEF

(1)

in which E , μn, μMg, and EF represent the total energy, chemical potential for the removed elements, chemical potential for Mg, and Fermi energy, respectively. q stands for the net number of electrons transferred from the defect to the conduction band. Since Mg2+ ions substitute elements of different oxidation states in different configurations, q varies across the configurations. The chemical composition, Ef, and q of all configurations are presented in Table 1, assuming EF is located at the valence band maximum. It was found that MgI is the most stable form of the Na0.75CoO2:Mg system with the lowest Ef value of 1.34 eV. It was followed by MgNa(1) and MgNa(2) with Ef values of 1.45 and 1.72 eV, respectively. MgCo has the highest Ef value of 3.30 eV. The results clearly indicate that the incorporation of Mg2+ ions in the Na layer is far more stable than that in the cobalt oxide layer. Figure 4b presents the Na+/Mg2+ ion positioning pattern t

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partial density of states of the Mg2+ ion in the most stable configuration (i.e., Na0.75CoO2:MgI) was calculated and compared to the ones of the undoped system, as presented in Figure 6a and b. According to Figure 6a, the majority of the

Table 1. The Chemical Composition, Formation Energy (Ef), and Supercell’s Charge State (q) for the Four Studied Configurations configuration

chemical composition

Ef (eV)

q (e)

MgNa(1) MgNa(2) MgI MgCo

(Na0.6875Mg0.0625)CoO2 (Na0.6875Mg0.0625)CoO2 (Na0.75Mg0.0625)CoO2 Na0.75(Co0.9375Mg0.0625)O2

1.45 1.72 1.34 3.30

1 1 2 −1

in the Na layer of the Na0.75CoO2:MgI system and indicates that the Mg2+ ion is located on the top of Co ions occupying a site equivalent to the Na(1). More noticeably, the patterning of the Na+ ions changes substantially when the Mg2+ ion is incorporated into the supercell. For example, in the top layer where the Mg2+ ion is located, there are two Na+ ions at the Na(1) site in contrast to the undoped counterpart where there is only one Na+ ion occupying that site. Figure 4c, which presents a side view of the Na0.75CoO2:MgI charge density pattern, demonstrates the electrostatic attraction between O2− ions in the CoO2 layer and Mg2+ ion in the Na layer. Such an electrostatic attraction results in a shorter Mg−O separation in comparison to the original Na−O separation, leading to a subtle reduction of COC angle. Consequently, the average COC angle for Mg-doped Na0.75CoO2 appears smaller in crystallographic characterization. The Interplay between Carrier Transport and Power Factor. Figure 5 shows the doping-dependent electrical

Figure 6. Total and partial density of states (DOS) of (a) the Na0.75CoO2 system and (b) the Na0.75CoO2:MgI system are presented. The energy scale is with respect to the Fermi level.

electronic states at the conduction band of the Na0.75CoO2 are Na’s 2s states and are located approximately 1 eV above the valence band maximum. For the Na0.75CoO2:MgI system, Figure 6b clearly demonstrates that the Mg’s 2s states strongly hybridize with Na’s 2s states and are almost distributed in the same subbands. As a result, the Mg2+ ions behave in a similar fashion with the Na+ ions as electron donors. In this case, they are not expected to reduce the hole concentration created by Na+ vacancies in the Na0.75CoO2:MgI system. Therefore, the origin of the observed reduction in the resistivity for y ≥ 0.03 should be attributed to improved carrier mobility rather than higher carrier concentration. Figure 7 illustrates the doping-dependent thermoelectric power (S) as a function of temperature. It demonstrates that S

Figure 5. Temperature dependence of resistivity ρ for NaCo0.8O2:Mgy.

resistivity (ρ) as a function of temperature. It is discernible from Figure 5 that all samples demonstrate a metallic ρ−T behavior and that ρ initially increases with increasing y and then declines when y ≥ 0.03. Doping above the solubility limit y* gives rise to the presence of MgO, resulting in a drastic increment of ρ (not shown). The difference of ρ−T profiles between Mg-doped and undoped samples at intermediate temperature range (i.e., 320−420 K) for the sample with y ≤ 0.02, which corresponds to the electrostatic energy of longrange spatial patterning of Na+ ions,15 infers that the Mg2+ ions reside in the Na layers. The positive ρ(y) relation in lightly doped samples (y ≤ 0.02) can be attributed to the occupation of Mg2+ ions at the vacant Na sites. In either case, Mg2+ serves as an electron donor that introduces electrons into the CoO2 sheets, thus reducing the overall carrier concentration via electron−hole recombination. Consequently, ρ increases with increasing y. However, for the samples with y ≥ 0.03, the doping-dependent behavior of ρ is reversed. To identify Mg2+’s contribution to the electric activity of the system, the total and

Figure 7. Temperature dependence of thermopower S for Na0.8CoO2:Mgy.

increases with increasing y and it also increases with T monotonically for all samples. For the samples with y = 0.01 4327

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0.59 × 10−3 W m−1 K−2. This is about 50% enhancement of PF in comparison with its undoped counterpart at ∼320 K. Thermopower Enhancement. The theoretical analysis suggests that the doped Mg2+ ions always occupy the vacant Na(1) sites in the Na layer acting as an n-type donor. This finding is convincingly consistent with the structural characterization obtained from the X-ray diffraction and Raman scattering measurements. An immediate consequence is a subtle reduction of hole concentration due to electron−hole recombination, as mentioned in the previous section. Therefore, the general reduction of ρ in the doped samples mainly results from the improvement of carrier mobility upon the addition of Mg2+ ions. At higher temperatures, the motion of Na+ ions in the Na layer is highly disordered (i.e., amorphous) due to the high ionic mobility of Na+. Such disordering results in frequent scattering of carriers’ wave functions in the crystal, thus shortening the mean free path of the mobile carriers and raising ρ. However, when a heavier and more positively charged ion is doped in the Na layer, it creates both mass and electrostatic inertia against the mobile Na+ ions at higher temperatures. As a result, the Na+ ions would be forced into their original positions and the overall crystallinity of the system would be preserved even at higher temperatures. Consequently, the mean free path of the carriers is increased, which in turn improves both the carriers’ mobility and the system’s conductivity. This interpretation is reinforced by high resolution Raman spectroscopy which is capable of providing experimental evidence for elucidating the exact mechanism underlying the behavior of ρ as a function of the Mg2+ doping concentration. Such analysis not only offers information on the electronic states but also on the crystal structure of the system. Therefore, the doping-dependent ρ behavior is attributed to the improved mobility of carriers resulting from the amorphous− crystalline (from the highly disordered to ordered Na+ arrangement) transition due to the presence of Mg2+ ions in the Na layers. Since the high S in the cobaltate system is driven from the high spin entropy, the geometrical arrangement of the Co ions is crucial for maintaining high S and thus high thermoelectric performance. Mg ions, by residing in the Na layer, do not jeopardize the antiferromagnetic coupling of the Co ions in the CoO layers. This guarantees that, upon Mg2+ doping, the system does not transform to the spin glass phase with lower spin entropy. The nonmagnetic character of divalent impurities is essential for avoiding any undesired magnetic coupling of the impurities with the host material that, in most cases, lead to compression of the CoO6 octahedral, thus offsetting the enhancement. Additionally, due to the dependence of spin entropy on the indirect hopping integral over intermediate O 2p orbitals,16 the Co−O−Co (COC) bond angle is an important factor in determining S. The inset of Figure 8a shows the schematic illustrations of two edge-sharing CoO6 octahedrals in the CoO2 layers for y = 0.02 and 0.05 samples which demonstrates that the COC bond angle slightly shrinks with increasing y. According to Figure 4c, this shrinkage can be explained by the attractive electrostatic interaction between the O2− and Mg2+ ions. As a consequence, this subtle reduction in COC bond angle also partially contributes to the enhancement of S. It should be emphasized that the incorporation of ions with higher oxidation states (i.e., tri, tetra, pentavalent) in the Na layers may not necessarily lead to an overall enhancement in performance due to higher degree of electron−hole recombination, which is caused by their higher electron contributions to

and 0.02, the S enhancement can arise from the reduced carrier concentration due to the occupation of Mg2+ ions at the vacant Na sites, as demonstrated in the previous section. Here, a lower carrier concentration maintains a strong Hubbard energy U (i.e., strong electron−electron interaction) which is required for obtaining high spin and orbital degrees of freedom and thus a higher S.5 Consequently, the magnitude of S enhancement between the samples with y = 0.00 and 0.01 and between y = 0.01 and 0.02 is equally significant. However, the rate of enhancement of S becomes less momentous from y = 0.02 to 0.03 and afterward, reaching the maximum enhancement of approximately 25% in the sample with y = 0.05. This trend suggests that the mechanism associated with the ρ−y anomaly appears most likely to be insensitive to the carrier concentration Mg content higher than 3%. Figure 8a illustrates the doping-dependent Peltier conductivity (α = S/ρ) as a function of temperature. It

Figure 8. (a) Temperature dependence of Peltier conductivity α for Na0.8CoO2:Mgy. The inset shows the schematic drawing of two edgesharing CoO6 units for y = 0.02 and y = 0.05 samples. (b) Power factor (PF) as a function of temperature for Na0.8CoO2:Mgy.

unambiguously shows the deterioration (y = 0.01 and 0.02) and enhancement (y = 0.03 and 0.05) of α near ambient temperatures. This is different from the Zn-doped sample that exhibits significant improvement in α over the entire temperature range investigated.6 Such behavior suggests that the transport of charge carriers is mainly two-dimensional in nature and mainly takes place in CoO2 layers. The doping-dependent power factor (PF) as a function of temperature is demonstrated in Figure 8b. It is discernible that PF of all Mg-substituted samples decreases with T up to ∼470 K and begins to increase with T afterward. The PF is enhanced with y, and the influence is most prominent at ∼320 K. Although ρ is increased in lightly doped samples (i.e., y = 0.01 and 0.02), the effect is overwhelmed by a larger increment in the S2 term, leading to a net PF enhancement. The simultaneous enhancement of S and the reduction of ρ for the samples with y ≥ 0.03 results in a remarkable PF value of 4328

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(9) Tang, G. D.; Yang, T.; Xu, X. N.; Tang, C. P.; Qiu, L.; Zhang, Z. D.; Lv, L. Y.; Wang, Z. H.; Du, Y. W. Appl. Phys. Lett. 2010, 97, 032108. (10) Delley, B. J. Chem. Phys. 1990, 92, 508−517. (11) Delley, B. J. Chem. Phys. 2000, 113, 7756−7764. (12) Perdew, J. P.; Wang, Y. Phys. Rev. B 1992, 45, 13244−13249. (13) Lemmens, P.; Choi, K. Y.; Gnezdilov, V.; Sherman, E. Y.; Chen, D. P.; Lin, C. T.; Chou, F. C.; Keimer, B. Phys. Rev. Lett. 2006, 96, 167204. (14) Wu, T.; Liu, K.; Chen, H.; Wu, G.; Luo, Q. L.; Ying, J. J.; Chen, X. H. Phys. Rev. B 2008, 78, 115122. (15) Roger, M.; Morris, D. J. P.; Tennant, D. A.; Gutmann, M. J.; Goff, J. P.; Hoffmann, J. U.; Feyerherm, R.; Dudzik, E.; Prabhakaran, D.; Boothroyd, A. T.; Shannon, N.; Lake, B.; Deen, P. P. Nature 2007, 445, 631−634. (16) Mochizuki, M.; Yanase, Y.; Ogata, M. Phys. Rev. Lett. 2005, 94, 147005.

the conduction band. It is interesting to note that the simultaneous reduction of ρ and enhancement of S occurred in both the Na0.8MgyCoO2 (y ≤ 0.03) and Na0.8ZnyCo1‑yO2 systems.6 A prudent examination between Mg and Zn dopings reveals three similarities: (1) both Mg2+ and Zn2+ are uniquely divalent, giving rise to improved carrier mobility without significantly compromising the carrier concentration, (2) the incorporation of both Mg2+ and Zn2+ ions leads to a reduction of COC angle, and (3) both Mg2+ and Zn2+ exhibit closed-shell configurations (i.e., 2p6 for the former and 3d10 for the latter) and thus do not take part in the hopping or superexchange mechanisms. These three features may well be the most decisive factors for the realization of high performance TE materials.

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CONCLUSION In summary, the thermoelectric properties and their associated mechanisms in Mg-doped Na0.8CoO2 were studied in detail. 50% of power factor enhancement resulting from simultaneous reduction in resistivity and enhancement in thermopower at near ambient temperatures has been achieved. The roomtemperature Raman scattering measurement reveals the emergence of three additional peaks which are usually observable at sufficiently low temperature due to the highly disordered nature of Na ions in the system. This suggests that the doped Mg2+ ions are effective in immobilizing the Na+ ions, consistent with first-principle calculation. It was concluded that simultaneous reduction in resistivity and enhancement in thermopower is attributed to the improved mobility of carriers resulting from the amorphous−crystalline transition associated with the presence of Mg2+ ions in the Na layers. The incorporation of Mg2+ induces a narrower Co−O−Co angle. These results suggest that the introduction of divalent impurities which subsequently leads to a reduction in the Co−O−Co angle with electronically closed-shell nature may be the key for the realization of simultaneous enhancement of thermopower and reduction in resistivity.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

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ACKNOWLEDGMENTS This work was supported by the Australian Research Council Discovery Program DP0988687.

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REFERENCES

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