Diameter and Temperature Dependences of Phonon-Drag Magnetothermopower in Bismuth Nanowires
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Diameter and Temperature Dependences of Phonon-Drag Magnetothermopower in Bismuth Nanowires Naomi Hirayama1 , Akira Endo2 and Naomichi Hatano3 1 Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510 Japan 2 Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan 3 Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro, Tokyo 153-8505 Japan ABSTRACT We present theoretical calculations of the phonon-drag contribution to the Nernst thermoelectric power Syx in Bismuth nanowires. We investigate the thermopower Syx with diameters L ranging from 22 to 900 nm at low temperatures (0.1 - 4.0 K) and high magnetic fields (up to 16 T). We find that the peak of thermopower Syx around 14.75 T exhibits the size effect in two different ways: for wires with L ≥ 200 nm, the peak height increases with decreasing L; for wires with L 0, Qz > 0 in Fig. 2(a) superposed with the discretized phonon states for L = 500 nm.
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The mechanism of the size dependence of Syx is schematically illustrated in Fig. 3. When the phonon mode near the origin (ny = nz = 1) moves passing through the peak of U(qy, qz) with decreasing L, the voltage Syx rises while approaching the peak of U(qy, qz) (Fig. 3(a)), reaches the maximum when the mode hits the peak (Fig. 3(b)), and then decreases with the further decrease in L (Fig. 3(c)). This explains the size-dependent behavior mentioned above.
Qy
Qy
π / L1 π / L1
π / L3 π / L2 π / L3
Qz (a)
Qy
π / L2
Qz
Qz
(b)
(c)
Figure 3. (a)-(c) Schematic diagram explaining the increase and the decrease of the peak height with decreasing L, L1 > L2 > L3.
Syx [V/K]
Syx [V/K]
Figures 4(a) and 4(b) show the temperature dependence of Syx for the sample with L = 500 nm. The Nernst thermopower Syx monotonically decreases with decreasing T. This drop of Syx is caused by the suppression of phonon drag due to the reduction of the number of phonons at low temperatures. Similar temperature dependence has been also reported for a bismuth bulk in experimental [6] and theoretical [2] studies.
1/B [1/T]
1/B [1/T]
(a)
(b)
Figure 4. Nernst voltage Syx at the temperatures (a) T = 0.5 – 4.0 K and (b) T = 0.1 – 0.8 K.
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CONCLUSIONS We have investigated the phonon-drag Nernst electromotive force Syx of Bismuth nanowires assuming that the acoustic phonons are quantized owing to the confinement into the wire geometry, such that the wave-vector components in the y- and z-directions are given by qy = nyʌ/L and qz = nzʌ/L (ny, nz = 0, 1, 2, …). We found that the peak of the thermopower Syx around 14.75 T (where a Landau level of the holes with n = 1 and ı = +1 crosses the Fermi energy) exhibits the non-trivial size effect; the peak becomes higher with decreasing L down to ~200 nm; for smaller L, on the other hand, the peak shrinks with decreasing L. The increase and decrease of the peak height can be explained by the passing of the phonon mode (ʌ/L, ʌ/L) through the peak in the integrand U(qy, qz) with decreasing wire thickness L.
ACKNOWLEDGMEN
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