Christopher Jaworski - Academia.edu (original) (raw)

Papers by Christopher Jaworski

Dynamic Systems and Control, Parts A and B, 2006

Much analysis has been performed on the application of thermoelectrics in automobiles, but the lo... more Much analysis has been performed on the application of thermoelectrics in automobiles, but the low efficiency of the materials has so far limited their use. As a result, little has been done in the physical design of how to most efficiently utilize thermoelectrics in a vehicle's ...

It was recently shown that p-type PbTe-Tl has a significant increase in zT over that PbTe:Nafootn... more It was recently shown that p-type PbTe-Tl has a significant increase in zT over that PbTe:NafootnotetextScience 25 July 2008:Vol. 321. pp. 554 - 557 due to an increase in power factor. Also, a large increase in zT in n-type PbTe was reported when alloyed with PbS due to the reduction in thermal conductivity.footnotetextJ. Am. Chem. Soc., 2007, 129 (31), pp

MRS Proceedings, 2009

ABSTRACT We previously reported the synthesis of nanostructured composite PbTe with excess Pb and... more ABSTRACT We previously reported the synthesis of nanostructured composite PbTe with excess Pb and Sb metal inclusions. The electrical conductivity shows an unusual temperature dependence that depends on the inclusion Pb/Sb ratio, resulting in marked enhancements in power factor and ZT at 700 K. Additional investigation of the transport and structure of these materials is reported here. Measurements of the scattering parameter reveals there is little change in electron scattering with respect to pure PbTe. High resolution electron microscopy was used to determine additional information about the nature of the precipitate phases present in the samples. High temperature transmission electron microscopy reveals that the precipitates begin to dissolve at high temperatures and completely disappear at T > 619K. A qualitative explanation of the unusual transport behavior of these materials is presented.

Physical Review B, 2013

ABSTRACT Experimental evidence is given relevant to the temperature dependence of the valence ban... more ABSTRACT Experimental evidence is given relevant to the temperature dependence of the valence band structure of PbTe and PbTe1−xSx alloys (0.04≤x≤0.12), and its effect on the thermoelectric figure of merit ZT. The x=0.08 sample has ZT∼1.55 at 773 K. The magnetic field dependence of the high-temperature Hall resistivity of heavily p-type (>1019 cm−3) Na-doped PbTe1−xSx reveals the presence of high-mobility electrons. This casts doubts on prior analyses of the Hall coefficient suggesting that temperature induces a rapid rise in energy of the “heavy” hole relative to the “light” hole bands. The electron-like behavior is likely induced by the topology of the Fermi surface when the L- and Σ-bands merge. Negative values for the low-temperature thermopower are also observed. The data show that PbTe continues to be a direct-gap semiconductor at temperatures where the ZT and S2σ of p-type PbTe are optimal, e.g., 700–800 K.

Physical Review B, 2009

We elucidate the amphoteric nature of antimony as a dopant in PbTe. Band-structure calculations s... more We elucidate the amphoteric nature of antimony as a dopant in PbTe. Band-structure calculations show that Sb substituting for Pb is a donor and that Sb on the Te site is an acceptor giving rise to a large excess density of states (DOS). Experimentally, in Te-rich Pb{sub 1-x}SbTe samples, ¹²Te NMR spectroscopy shows that Sb substitutes for Pb and transport

Physical Review B, 2009

ABSTRACT Tin is a known resonant impurity in the valence band of Bi2Te3 that was previously repor... more ABSTRACT Tin is a known resonant impurity in the valence band of Bi2Te3 that was previously reported to enhance the thermoelectric power S of the host material at cryogenic temperatures through resonant scattering. We show here that Sn provides an excess density of states (DOS) about 15 meV below the valence band edge and that it is the increases in DOS itself that enhances S of this technologically important semiconductor even at room temperature. The experimental proof for the existence of this resonant level comes from Shubnikov-de Haas measurements combined with galvanomagnetic and thermomagnetic properties measurements.

Journal of the American Chemical Society, 2011

Thermoelectric heat-to-power generation is an attractive option for robust and environmentally fr... more Thermoelectric heat-to-power generation is an attractive option for robust and environmentally friendly renewable energy production. Historically, the performance of thermoelectric materials has been limited by low efficiencies, related to the thermoelectric figure-of-merit ZT. Nanostructuring thermoelectric materials have shown to enhance ZT primarily via increasing phonon scattering, beneficially reducing lattice thermal conductivity. Conversely, density-of-states (DOS) engineering has also enhanced electronic transport properties. However, successfully joining the two approaches has proved elusive. Herein, we report a thermoelectric materials system whereby we can control both nanostructure formations to effectively reduce thermal conductivity, while concurrently modifying the electronic structure to significantly enhance thermoelectric power factor. We report that the thermoelectric system PbTe-PbS 12% doped with 2% Na produces shape-controlled cubic PbS nanostructures, which help reduce lattice thermal conductivity, while altering the solubility of PbS within the PbTe matrix beneficially modifies the DOS that allow for enhancements in thermoelectric power factor. These concomitant and synergistic effects result in a maximum ZT for 2% Na-doped PbTe-PbS 12% of 1.8 at 800 K.

Journal of Applied Physics, 2009

ABSTRACT A limiting mean free path was considered in order to better understand the temperature a... more ABSTRACT A limiting mean free path was considered in order to better understand the temperature and wire diameter dependence of the resistivity and Seebeck coefficient of bismuth microwire and nanowire samples. The mean free path limited mobility was numerically calculated from experimentally measured mobility in a bulk bismuth sample, and the electron and hole mobilities were dramatically decreased to a 10 μ m mean free path. Therefore, the temperature dependence of resistivity in very thin wire was quite different from that of a bulk sample, which had a positive temperature coefficient. The calculations showed that the temperature coefficient decreased gradually with decreasing mean free path, and the coefficient became negative for a mean free path of less than 1 μ m at about 150 K. The Seebeck coefficient was also calculated, but showed only a weak dependence on mean free path compared with the resistivity. Experimental comparisons were made to previous measurements of bismuth microwire or nanowire samples, and the temperature and wire diameter dependencies of the resistivity and Seebeck coefficient were qualitatively and quantitatively in very good agreement. Therefore, the temperature dependencies of nanowire samples over 850 nm in diameter were well described using the mean free path limitation.

J Am Chem Soc, 2011

Thermoelectric heat-to-power generation is an attractive option for robust and environmentally fr... more Thermoelectric heat-to-power generation is an attractive option for robust and environmentally friendly renewable energy production. Historically, the performance of thermoelectric materials has been limited by low efficiencies, related to the thermoelectric figure-of-merit ZT. Nanostructuring thermoelectric materials have shown to enhance ZT primarily via increasing phonon scattering, beneficially reducing lattice thermal conductivity. Conversely, density-of-states (DOS) engineering has also enhanced electronic transport properties. However, successfully joining the two approaches has proved elusive. Herein, we report a thermoelectric materials system whereby we can control both nanostructure formations to effectively reduce thermal conductivity, while concurrently modifying the electronic structure to significantly enhance thermoelectric power factor. We report that the thermoelectric system PbTe-PbS 12% doped with 2% Na produces shape-controlled cubic PbS nanostructures, which help reduce lattice thermal conductivity, while altering the solubility of PbS within the PbTe matrix beneficially modifies the DOS that allow for enhancements in thermoelectric power factor. These concomitant and synergistic effects result in a maximum ZT for 2% Na-doped PbTe-PbS 12% of 1.8 at 800 K.

N-type Bi100-xSbx alloys have the highest thermoelectric figure of merit (zT) of all materials be... more N-type Bi100-xSbx alloys have the highest thermoelectric figure of merit (zT) of all materials below 200K; here we investigate how filling multiple valence band pockets at T and H-points of the Brillouin zone produces high zT in p-type Sn-doped material. This approach, theoretically predicted to potentially give zT>1 in Bi, was used successfully in PbTe. We report thermopower, electrical and thermal conductivity (2 to 400K) of single crystals with 12<x<37 and polycrystals (x=50-90), higher Sb concentrations than previous studies. We obtain a 60% improvement in zT to 0.13.

AIP Advances, 2015

ABSTRACT AgSbTe2 is a thermoelectric semiconductor with an intrinsically low thermal conductivity... more ABSTRACT AgSbTe2 is a thermoelectric semiconductor with an intrinsically low thermal conductivity and a valence band structure that is favorable to obtaining a high thermoelectric figure of merit zT. It also has a very small energy gap Eg ∼ 7.6 ± 3 meV. As this gap is less than the thermal excitation energy at room temperature, near-intrinsic AgSbTe2 is a two carrier system having both holes (concentration p) and electrons (n). Good thermoelectric performance requires heavy p-type doping (p &gt; &gt; n). This can be achieved with native defects or with extrinsic doping, e.g. with transition metal element. The use of defect doping is complicated by the fact that many of the ternary Ag-Sb-Te and pseudo-binary Sb 2Te3-Ag2Te phase diagrams are contradictory. This paper determines the compositional region most favorable to creating a single phase material. Through a combination of intrinsic and extrinsic doping, values of zT &gt; 1 are achieved, though not on single-phased material. Additionally, we show that thermal conductivity is not affected by defects, further demonstrating that the low lattice thermal conductivity of I-V-VI2 materials is due to an intrinsic mechanism, insensitive to changes in defect structure.

Band structure calculations indicate the formation of an antimony impurity level just above the F... more Band structure calculations indicate the formation of an antimony impurity level just above the Fermi level for Pb1-xSbxTe and just below the Fermi level for PbSbxTe1-x. For experimental verification, we prepare bulk samples of Pb1-xSbxTe and PbSbxTe1-x (x = 0.25, 0.5, 1%). Electrical resistivity, Seebeck, Hall and transverse Nernst-Ettingshausen coefficients of the crystals have been measured in the temperature range 2-580 Kelvin. Thermal conductivity data was measured in the range 80-800 Kelvin. We confirm the ability of antimony to take the place of a lead atom and dope PbTe n-type or take the place of a tellurium atom and dope PbTe p-type. Antimony, however, is not as efficient an acceptor in p-type material as it is a donor in n-type material. The Fermi levels are calculated using experimental data and will be reported here. Also, a phase transition is experimentally observed at 500 K in p-type PbSbxTe1-x.

Dynamic Systems and Control, Parts A and B, 2006

Much analysis has been performed on the application of thermoelectrics in automobiles, but the lo... more Much analysis has been performed on the application of thermoelectrics in automobiles, but the low efficiency of the materials has so far limited their use. As a result, little has been done in the physical design of how to most efficiently utilize thermoelectrics in a vehicle's ...

Bulk samples of (PbS)x(PbTe)1-x have been prepared in the range 4%

The disordered structure of organic conductors results in a naturally low thermal conductivity (k... more The disordered structure of organic conductors results in a naturally low thermal conductivity (kappa) but their ZT is known to be low because of their low thermopower (S) and electrical conductivity (sigma). Here we report an exception, with results obtained from 220 to 320K for the thermopower of V-TCNEx (V-(C2(CN)4)x) thin films deposited on a Si wafer (111). At room temperature S=+21.8 mV/K and increases with decreasing temperature. Those values are matched only by very pure semiconductors such as Si at low temperature, Bi nanowires, or strongly correlated electron systems like FeSb2. The valence band of V-TCNE has a very high density of states over a very narrow energy range, ascribed mostly to vanadium 3d(t2g) orbitals, ootnotetextY-J Yoo et al., Nat. Mat. 9 638 2010 which is consistent with the exceptionally large value of S. The dependence of S and sigma upon illumination will also be shown, alongside preliminary estimates for the ZT.

ABSTRACT A thermoelectric power is reported in a thermocouple in which both arms are made of the ... more ABSTRACT A thermoelectric power is reported in a thermocouple in which both arms are made of the same material (n-type InSb) with the same electron concentration, but the phonons have different mean free paths at cryogenic temperatures. This experiment, inspired by [1], isolates the phonon-drag contribution to the thermopower from the diffusion thermopower. The experiment decouples the behavior of the subthermal phonons that drag the electrons, and the thermal phonons that carry most heat. We add data on the contributions of both to the thermal conductivity. This sheds new light on the details of the physical mechanism behind the giant spin-Seebeck effect (GSSE) recently observed [2] on the same material. The GSSE signal was attributed to a combination of electron-phonon drag that pushes the electrons, which are spin-polarized by Zeeman splitting, far from thermal equilibrium, and strong spin-orbit interactions that make the Zeeman splitting sensitive to the electron momentum. Furthermore, we may have found experimental clues about the nature of the phonon force [3]. 1. T. H. Geballe and G. W. Hull, Conference de physique des basses temperatures, p 460, Paris, 1955 2. C.M. Jaworski et al. Nature 487, 210 (2012) 3. S. E. Barnes and S. Maekawa, Phys. Rev. Lett. 98 246601 (2007)

Dynamic Systems and Control, Parts A and B, 2006

Much analysis has been performed on the application of thermoelectrics in automobiles, but the lo... more Much analysis has been performed on the application of thermoelectrics in automobiles, but the low efficiency of the materials has so far limited their use. As a result, little has been done in the physical design of how to most efficiently utilize thermoelectrics in a vehicle's ...

It was recently shown that p-type PbTe-Tl has a significant increase in zT over that PbTe:Nafootn... more It was recently shown that p-type PbTe-Tl has a significant increase in zT over that PbTe:NafootnotetextScience 25 July 2008:Vol. 321. pp. 554 - 557 due to an increase in power factor. Also, a large increase in zT in n-type PbTe was reported when alloyed with PbS due to the reduction in thermal conductivity.footnotetextJ. Am. Chem. Soc., 2007, 129 (31), pp

MRS Proceedings, 2009

ABSTRACT We previously reported the synthesis of nanostructured composite PbTe with excess Pb and... more ABSTRACT We previously reported the synthesis of nanostructured composite PbTe with excess Pb and Sb metal inclusions. The electrical conductivity shows an unusual temperature dependence that depends on the inclusion Pb/Sb ratio, resulting in marked enhancements in power factor and ZT at 700 K. Additional investigation of the transport and structure of these materials is reported here. Measurements of the scattering parameter reveals there is little change in electron scattering with respect to pure PbTe. High resolution electron microscopy was used to determine additional information about the nature of the precipitate phases present in the samples. High temperature transmission electron microscopy reveals that the precipitates begin to dissolve at high temperatures and completely disappear at T &gt; 619K. A qualitative explanation of the unusual transport behavior of these materials is presented.

Physical Review B, 2013

ABSTRACT Experimental evidence is given relevant to the temperature dependence of the valence ban... more ABSTRACT Experimental evidence is given relevant to the temperature dependence of the valence band structure of PbTe and PbTe1−xSx alloys (0.04≤x≤0.12), and its effect on the thermoelectric figure of merit ZT. The x=0.08 sample has ZT∼1.55 at 773 K. The magnetic field dependence of the high-temperature Hall resistivity of heavily p-type (&gt;1019 cm−3) Na-doped PbTe1−xSx reveals the presence of high-mobility electrons. This casts doubts on prior analyses of the Hall coefficient suggesting that temperature induces a rapid rise in energy of the “heavy” hole relative to the “light” hole bands. The electron-like behavior is likely induced by the topology of the Fermi surface when the L- and Σ-bands merge. Negative values for the low-temperature thermopower are also observed. The data show that PbTe continues to be a direct-gap semiconductor at temperatures where the ZT and S2σ of p-type PbTe are optimal, e.g., 700–800 K.

Physical Review B, 2009

We elucidate the amphoteric nature of antimony as a dopant in PbTe. Band-structure calculations s... more We elucidate the amphoteric nature of antimony as a dopant in PbTe. Band-structure calculations show that Sb substituting for Pb is a donor and that Sb on the Te site is an acceptor giving rise to a large excess density of states (DOS). Experimentally, in Te-rich Pb{sub 1-x}SbTe samples, ¹²Te NMR spectroscopy shows that Sb substitutes for Pb and transport

Physical Review B, 2009

ABSTRACT Tin is a known resonant impurity in the valence band of Bi2Te3 that was previously repor... more ABSTRACT Tin is a known resonant impurity in the valence band of Bi2Te3 that was previously reported to enhance the thermoelectric power S of the host material at cryogenic temperatures through resonant scattering. We show here that Sn provides an excess density of states (DOS) about 15 meV below the valence band edge and that it is the increases in DOS itself that enhances S of this technologically important semiconductor even at room temperature. The experimental proof for the existence of this resonant level comes from Shubnikov-de Haas measurements combined with galvanomagnetic and thermomagnetic properties measurements.

Journal of the American Chemical Society, 2011

Thermoelectric heat-to-power generation is an attractive option for robust and environmentally fr... more Thermoelectric heat-to-power generation is an attractive option for robust and environmentally friendly renewable energy production. Historically, the performance of thermoelectric materials has been limited by low efficiencies, related to the thermoelectric figure-of-merit ZT. Nanostructuring thermoelectric materials have shown to enhance ZT primarily via increasing phonon scattering, beneficially reducing lattice thermal conductivity. Conversely, density-of-states (DOS) engineering has also enhanced electronic transport properties. However, successfully joining the two approaches has proved elusive. Herein, we report a thermoelectric materials system whereby we can control both nanostructure formations to effectively reduce thermal conductivity, while concurrently modifying the electronic structure to significantly enhance thermoelectric power factor. We report that the thermoelectric system PbTe-PbS 12% doped with 2% Na produces shape-controlled cubic PbS nanostructures, which help reduce lattice thermal conductivity, while altering the solubility of PbS within the PbTe matrix beneficially modifies the DOS that allow for enhancements in thermoelectric power factor. These concomitant and synergistic effects result in a maximum ZT for 2% Na-doped PbTe-PbS 12% of 1.8 at 800 K.

Journal of Applied Physics, 2009

ABSTRACT A limiting mean free path was considered in order to better understand the temperature a... more ABSTRACT A limiting mean free path was considered in order to better understand the temperature and wire diameter dependence of the resistivity and Seebeck coefficient of bismuth microwire and nanowire samples. The mean free path limited mobility was numerically calculated from experimentally measured mobility in a bulk bismuth sample, and the electron and hole mobilities were dramatically decreased to a 10 μ m mean free path. Therefore, the temperature dependence of resistivity in very thin wire was quite different from that of a bulk sample, which had a positive temperature coefficient. The calculations showed that the temperature coefficient decreased gradually with decreasing mean free path, and the coefficient became negative for a mean free path of less than 1 μ m at about 150 K. The Seebeck coefficient was also calculated, but showed only a weak dependence on mean free path compared with the resistivity. Experimental comparisons were made to previous measurements of bismuth microwire or nanowire samples, and the temperature and wire diameter dependencies of the resistivity and Seebeck coefficient were qualitatively and quantitatively in very good agreement. Therefore, the temperature dependencies of nanowire samples over 850 nm in diameter were well described using the mean free path limitation.

J Am Chem Soc, 2011

Thermoelectric heat-to-power generation is an attractive option for robust and environmentally fr... more Thermoelectric heat-to-power generation is an attractive option for robust and environmentally friendly renewable energy production. Historically, the performance of thermoelectric materials has been limited by low efficiencies, related to the thermoelectric figure-of-merit ZT. Nanostructuring thermoelectric materials have shown to enhance ZT primarily via increasing phonon scattering, beneficially reducing lattice thermal conductivity. Conversely, density-of-states (DOS) engineering has also enhanced electronic transport properties. However, successfully joining the two approaches has proved elusive. Herein, we report a thermoelectric materials system whereby we can control both nanostructure formations to effectively reduce thermal conductivity, while concurrently modifying the electronic structure to significantly enhance thermoelectric power factor. We report that the thermoelectric system PbTe-PbS 12% doped with 2% Na produces shape-controlled cubic PbS nanostructures, which help reduce lattice thermal conductivity, while altering the solubility of PbS within the PbTe matrix beneficially modifies the DOS that allow for enhancements in thermoelectric power factor. These concomitant and synergistic effects result in a maximum ZT for 2% Na-doped PbTe-PbS 12% of 1.8 at 800 K.

N-type Bi100-xSbx alloys have the highest thermoelectric figure of merit (zT) of all materials be... more N-type Bi100-xSbx alloys have the highest thermoelectric figure of merit (zT) of all materials below 200K; here we investigate how filling multiple valence band pockets at T and H-points of the Brillouin zone produces high zT in p-type Sn-doped material. This approach, theoretically predicted to potentially give zT>1 in Bi, was used successfully in PbTe. We report thermopower, electrical and thermal conductivity (2 to 400K) of single crystals with 12<x<37 and polycrystals (x=50-90), higher Sb concentrations than previous studies. We obtain a 60% improvement in zT to 0.13.

AIP Advances, 2015

ABSTRACT AgSbTe2 is a thermoelectric semiconductor with an intrinsically low thermal conductivity... more ABSTRACT AgSbTe2 is a thermoelectric semiconductor with an intrinsically low thermal conductivity and a valence band structure that is favorable to obtaining a high thermoelectric figure of merit zT. It also has a very small energy gap Eg ∼ 7.6 ± 3 meV. As this gap is less than the thermal excitation energy at room temperature, near-intrinsic AgSbTe2 is a two carrier system having both holes (concentration p) and electrons (n). Good thermoelectric performance requires heavy p-type doping (p &gt; &gt; n). This can be achieved with native defects or with extrinsic doping, e.g. with transition metal element. The use of defect doping is complicated by the fact that many of the ternary Ag-Sb-Te and pseudo-binary Sb 2Te3-Ag2Te phase diagrams are contradictory. This paper determines the compositional region most favorable to creating a single phase material. Through a combination of intrinsic and extrinsic doping, values of zT &gt; 1 are achieved, though not on single-phased material. Additionally, we show that thermal conductivity is not affected by defects, further demonstrating that the low lattice thermal conductivity of I-V-VI2 materials is due to an intrinsic mechanism, insensitive to changes in defect structure.

Band structure calculations indicate the formation of an antimony impurity level just above the F... more Band structure calculations indicate the formation of an antimony impurity level just above the Fermi level for Pb1-xSbxTe and just below the Fermi level for PbSbxTe1-x. For experimental verification, we prepare bulk samples of Pb1-xSbxTe and PbSbxTe1-x (x = 0.25, 0.5, 1%). Electrical resistivity, Seebeck, Hall and transverse Nernst-Ettingshausen coefficients of the crystals have been measured in the temperature range 2-580 Kelvin. Thermal conductivity data was measured in the range 80-800 Kelvin. We confirm the ability of antimony to take the place of a lead atom and dope PbTe n-type or take the place of a tellurium atom and dope PbTe p-type. Antimony, however, is not as efficient an acceptor in p-type material as it is a donor in n-type material. The Fermi levels are calculated using experimental data and will be reported here. Also, a phase transition is experimentally observed at 500 K in p-type PbSbxTe1-x.

Dynamic Systems and Control, Parts A and B, 2006

Much analysis has been performed on the application of thermoelectrics in automobiles, but the lo... more Much analysis has been performed on the application of thermoelectrics in automobiles, but the low efficiency of the materials has so far limited their use. As a result, little has been done in the physical design of how to most efficiently utilize thermoelectrics in a vehicle's ...

Bulk samples of (PbS)x(PbTe)1-x have been prepared in the range 4%

The disordered structure of organic conductors results in a naturally low thermal conductivity (k... more The disordered structure of organic conductors results in a naturally low thermal conductivity (kappa) but their ZT is known to be low because of their low thermopower (S) and electrical conductivity (sigma). Here we report an exception, with results obtained from 220 to 320K for the thermopower of V-TCNEx (V-(C2(CN)4)x) thin films deposited on a Si wafer (111). At room temperature S=+21.8 mV/K and increases with decreasing temperature. Those values are matched only by very pure semiconductors such as Si at low temperature, Bi nanowires, or strongly correlated electron systems like FeSb2. The valence band of V-TCNE has a very high density of states over a very narrow energy range, ascribed mostly to vanadium 3d(t2g) orbitals, ootnotetextY-J Yoo et al., Nat. Mat. 9 638 2010 which is consistent with the exceptionally large value of S. The dependence of S and sigma upon illumination will also be shown, alongside preliminary estimates for the ZT.

ABSTRACT A thermoelectric power is reported in a thermocouple in which both arms are made of the ... more ABSTRACT A thermoelectric power is reported in a thermocouple in which both arms are made of the same material (n-type InSb) with the same electron concentration, but the phonons have different mean free paths at cryogenic temperatures. This experiment, inspired by [1], isolates the phonon-drag contribution to the thermopower from the diffusion thermopower. The experiment decouples the behavior of the subthermal phonons that drag the electrons, and the thermal phonons that carry most heat. We add data on the contributions of both to the thermal conductivity. This sheds new light on the details of the physical mechanism behind the giant spin-Seebeck effect (GSSE) recently observed [2] on the same material. The GSSE signal was attributed to a combination of electron-phonon drag that pushes the electrons, which are spin-polarized by Zeeman splitting, far from thermal equilibrium, and strong spin-orbit interactions that make the Zeeman splitting sensitive to the electron momentum. Furthermore, we may have found experimental clues about the nature of the phonon force [3]. 1. T. H. Geballe and G. W. Hull, Conference de physique des basses temperatures, p 460, Paris, 1955 2. C.M. Jaworski et al. Nature 487, 210 (2012) 3. S. E. Barnes and S. Maekawa, Phys. Rev. Lett. 98 246601 (2007)