Optical investigation of the thermoelectric topological crystalline insulator ${\mathrm{Pb}}_{0.77}{\mathrm{Sn}}_{0.23}\mathrm{Se}$

Optical investigation of the thermoelectric topological crystalline insulator ${Pb}_{0.77} {Sn}_{0.23} Se$

Anjan A. Reijnders, Jason Hamilton, Vivian Britto, Jean-Blaise Brubach, Pascale Roy, Quinn D. Gibson, R. J. Cava, and K. S. Burch

Phys. Rev. B 90, 235144 – Published 23 December 2014

Abstract

${Pb}_{0.77} {Sn}_{0.23} Se$ is a promising thermoelectric alloy that exhibits a temperature dependent band inversion below 300 K. Recent work has shown that this band inversion also coincides with a trivial to nontrivial topological phase transition. To understand how the properties critical to thermoelectric efficiency are affected by the band inversion, we measured the broadband optical response of ${Pb}_{0.77} {Sn}_{0.23} Se$ as a function of temperature. We find clear optical signatures suggesting the band inversion occurs at $160 \pm 15$ K, and use the extended Drude model to accurately determine a $T^{3 / 2}$ dependence of the bulk carrier lifetime, associated with electron-acoustic phonon scattering. Due to the high bulk carrier doping level, no discriminating signatures of the topological surface states are found, although their presence cannot be excluded from our data.

Received 29 July 2014
Revised 11 October 2014

DOI:https://doi.org/10.1103/PhysRevB.90.235144

Authors & Affiliations

Anjan A. Reijnders^1,*, Jason Hamilton¹, Vivian Britto¹, Jean-Blaise Brubach², Pascale Roy², Quinn D. Gibson³, R. J. Cava³, and K. S. Burch^4,†

¹Department of Physics & Institute for Optical Sciences, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7, Canada
²Synchrotron SOLEIL, L'Orme des Merisiers Saint-Aubin, 91192 Gif-sur-Yvette, France
³Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
⁴Department of Physics, Boston College, 140 Commonwealth Ave, Chestnut Hill, Massachusetts 02467, USA

^*Present address: Montana Instruments, 151 Evergreen Drive, Bozeman, Montana 59715, USA; reijnder@physics.utoronto.ca
^†burchke@bc.edu

Temperature-driven band inversion in ${Pb}_{0.77} {Sn}_{0.23} Se$ : Optical and Hall effect studies

Naween Anand, Sanal Buvaev, A. F. Hebard, D. B. Tanner, Zhiguo Chen, Zhiqiang Li, Kamal Choudhary, S. B. Sinnott, Genda Gu, and C. Martin

Phys. Rev. B 90, 235143 (2014)

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Vol. 90, Iss. 23 — 15 December 2014

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Figure 1
(a) The changing slope in the reflec-tance below the plasma edge (reflectance minimum) indicates a temperature dependent free carrier scattering rate in ${Pb}_{0.77} {Sn}_{0.23} Se$ . (b) The optical conductivity reveals a clear separation $(ω_{c})$ between Drude conductivity below 125 meV, and inter/intra-band transitions above 125 meV. (c) The zero-crossing of the real part of the dielectric function $(ε_{1})$ , indicative of the screened plasma frequency, can be used to determine $ε_{\infty}$ .
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Figure 2
(a) Band structure diagram before or after the band inversion (left panel), and during the inversion (right panel), illustrating the allowed (in)direct transitions when the chemical potential is in the bulk conduction band (as is the case in as-grown ${Pb}_{0.77} {Sn}_{0.23} Se)$ . (b) Signatures of this inversion include a changing free carrier lifetime $τ (T, ω)$ and plasma frequency $ω_{p}$ (region I), spectral weight change for indirect gap transitions (region II), and changes in the size of the direct gap (region III). (c) The plasma frequency of ${Pb}_{0.77} {Sn}_{0.23} Se$ shows a distinct change in temperature dependence around 160 K, deviating from its expected quadratic temperature dependence. (d) $ε_{\infty}$ also shows an abrupt change in its temperature dependence at 160 K, further suggesting 160 K as the band inversion temperature.
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Figure 3
(a) Linear fits of the squared absorption coefficient yield the smallest observable direct band transition energy $(x$ intercept). (b) Direct gap transition extracted from the linear fit. (c) Absorption coefficient (logarithmic scale) below $E_{dir}$ , revealing a distinct change in temperature dependence, uncharacteristic for an Urbach tail.
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Figure 4
(a) Power-law fits of the frequency dependent scattering rate. (b) A $T^{3 / 2}$ fit (red dashed line) of the temperate dependent static scattering rate $1 / τ_{DC}$ illustrates phonon dominated scattering. (c) Fitting parameters $n$ and $β$ . (d) Comparison of ${Pb}_{0.77} {Sn}_{0.23} Se$ resistivity obtained by optical spectroscopy (solid red line), and by standard DC transport methods by Liang et al. [6] (green dotted line), and Dixon et al. [8] (all other data).
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Figure 5
(a) A linear regression of the Seebeck coefficient in the parabolic band assumption, where all changes in $E_{dir}$ are attributed to changes in $E_{F}$ . (b) The power factor indicates minimal (if any) sensitivity to the suggested band inversion at $160 \pm 15$ K, as a result of the high chemical potential.
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Figure 6
(a) Reflectance of ${Pb}_{0.77} {Sn}_{0.23} Se$ at 194 K, and a model of the 194 K reflectance that included a surface state layer with $ω_{p, 2 D} = 0.34$ meV ${cm}^{1 / 2}$ . (b) Ratios of the temperature dependent reflectance above (black), below (green), and across (blue) the topological phase transition. The dotted red line is the ratio of reflectance spectra from (a), illustrating the much larger effect of temperature on $R (ω)$ compared to the introduction of surface states below the topological phase transition.
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Physical Review B

covering condensed matter and materials physics

Optical investigation of the thermoelectric topological crystalline insulator ${Pb}_{0.77} {Sn}_{0.23} Se$

Anjan A. Reijnders, Jason Hamilton, Vivian Britto, Jean-Blaise Brubach, Pascale Roy, Quinn D. Gibson, R. J. Cava, and K. S. Burch

Phys. Rev. B 90, 235144 – Published 23 December 2014

Abstract

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Temperature-driven band inversion in ${Pb}_{0.77} {Sn}_{0.23} Se$ : Optical and Hall effect studies

Naween Anand, Sanal Buvaev, A. F. Hebard, D. B. Tanner, Zhiguo Chen, Zhiqiang Li, Kamal Choudhary, S. B. Sinnott, Genda Gu, and C. Martin

Phys. Rev. B 90, 235143 (2014)

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Physical Review B

covering condensed matter and materials physics

Optical investigation of the thermoelectric topological crystalline insulator Pb0.77Sn0.23Se

Anjan A. Reijnders, Jason Hamilton, Vivian Britto, Jean-Blaise Brubach, Pascale Roy, Quinn D. Gibson, R. J. Cava, and K. S. Burch

Phys. Rev. B 90, 235144 – Published 23 December 2014

Abstract

Authors & Affiliations

See Also

Temperature-driven band inversion in Pb0.77Sn0.23Se: Optical and Hall effect studies

Naween Anand, Sanal Buvaev, A. F. Hebard, D. B. Tanner, Zhiguo Chen, Zhiqiang Li, Kamal Choudhary, S. B. Sinnott, Genda Gu, and C. Martin

Phys. Rev. B 90, 235143 (2014)

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Optical investigation of the thermoelectric topological crystalline insulator ${Pb}_{0.77} {Sn}_{0.23} Se$

Temperature-driven band inversion in ${Pb}_{0.77} {Sn}_{0.23} Se$ : Optical and Hall effect studies