Electrodynamic properties of the semimetallic Dirac material $\mathrm{SrMnB}{\mathrm{i}}_{2}$: Two-carrier-model analysis

Electrodynamic properties of the semimetallic Dirac material $SrMnB i_{2}$ : Two-carrier-model analysis

H. J. Park, Byung Cheol Park, Min-Cheol Lee, D. W. Jeong, Joonbum Park, Jun Sung Kim, Hyo Seok Ji, J. H. Shim, K. W. Kim, S. J. Moon, Hyeong-Do Kim, Deok-Yong Cho, and T. W. Noh

Phys. Rev. B 96, 155139 – Published 26 October 2017

Abstract

The electrodynamics of free carriers in the semimetallic Dirac material $SrMnB i_{2}$ was investigated using optical spectroscopy and first-principles calculations. Using a two-carrier-model analysis, the total free-carrier response was successfully decomposed into individual contributions from Dirac fermions and non-Dirac free carriers. Possible roles of chiral pseudospin, spin-orbit interaction (SOI), antiferromagnetism, and electron-phonon $(e − p h)$ coupling in the Dirac fermion transport were also addressed. The Dirac fermions possess a low scattering rate of $\sim 10 meV$ at low temperature and thereby experience coherent transport. However, at high temperatures, we observed that the Dirac fermion transport becomes significantly incoherent, possibly due to strong $e − p h$ interactions. The SOI-induced gap and antiferromagnetism play minor roles in the electrodynamics of the free carriers in $SrMnB i_{2}$ . We also observed a seemingly optical-gap-like feature near 120 meV, which emerges at low temperatures but becomes filled in with increasing temperature. This gap-filling phenomenon is ascribed to phonon-assisted indirect transitions promoted at high temperatures.

Received 21 April 2017
Revised 11 September 2017

DOI:https://doi.org/10.1103/PhysRevB.96.155139

Physics Subject Headings (PhySH)

Dirac fermions Electron-phonon coupling

Dirac semimetal

Optical spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

H. J. Park^1,2, Byung Cheol Park^1,2, Min-Cheol Lee^1,2, D. W. Jeong^1,2, Joonbum Park³, Jun Sung Kim^3,4, Hyo Seok Ji⁵, J. H. Shim^5,6, K. W. Kim⁷, S. J. Moon⁸, Hyeong-Do Kim^1,2, Deok-Yong Cho^1,2,9, and T. W. Noh^1,2,*

¹Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul 08826, Republic of Korea
²Department of Physics and Astronomy, Seoul National University, Seoul 08826, Republic of Korea
³Department of Physics, Pohang University of Science and Technology, Pohang 37673, Republic of Korea
⁴Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang 37673, Korea
⁵Department of Chemistry, Pohang University of Science and Technology, Pohang 37673, Republic of Korea
⁶Division of Advanced Nuclear Engineering, Pohang University of Science and Technology, Pohang 37673, Republic of Korea
⁷Department of Phyisics, Chungbuk National University, Cheongju 28644, Republic of Korea
⁸Department of Physics, Hanyang University, Seoul 04763, Republic of Korea
⁹IPIT & Department of Physics, Chonbuk National University, Jeonju 54896, Republic of Korea

^*Corresponding author: twnoh@snu.ac.kr

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Vol. 96, Iss. 15 — 15 October 2017

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Figure 1
(a) Crystal structure of $SrMnB i_{2}$ , composed of a SrBi(1)-square net and an edge-shared MnBi(2) layer. (b) Schematic diagram of the electronic structure of $SrMnB i_{2}$ [bottom, based on band calculation (see Methods section), transport, and optical data], which possesses both an anisotropic Dirac cone (α) and semimetallic parabolic bands (β and γ). The constant energy surface [top, sliced at the Fermi level μ $(T)]$ consists of two hole pockets (α and β pockets), respectively, in the middle of the Γ- $M$ line and near the Γ point, while an electron pocket (γ pocket) originates from near the $X$ point. The Dirac-like state possesses a small energy gap $Δ_{SOC}$ induced by sizable spin-orbit coupling (SOC). The semimetallic bands allow both direct and indirect optical transitions, represented by red and blue arrows in (b), respectively.
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Figure 2
(a) Temperature $(T)$ -dependent evolution of reflectivity $R$ (ω) and (b) the calculated optical conductivity $σ_{1} (ω)$ spectra of $SrMnB i_{2}$ over the photon energies 7 − 1000 meV. The screened plasma frequency $ω_{p}^{*}$ , a signature of metallic properties here, is presented at the dip in $R$ (ω). The value of $ω_{p}^{*}$ is well defined only in the low- $T$ regime $(T < 100 r m K)$ and broadens out at higher $T$ $(T > 100 K)$ . $σ_{1} (ω)$ in (b) shows the free-carrier response in the low-energy (far-infrared, FIR) regime and the gaplike feature in the high-energy (mid-IR) region.
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Figure 3
(a) Temperature $(T)$ -dependent change in the optical conductivity $σ_{1} (ω)$ of $SrMnB i_{2}$ at low photon energies below 75 meV. The markers (solid circles) correspond to dc conductivity values measured from our complementary transport experiments. The inset in (a) shows the result of the two-carrier-model fit to our low-energy $σ_{1} (ω)$ , representatively performed on our 20-K data, giving rise to highly separable broad and narrow Drude features. (b) The peak in the energy-loss function −Im{1/ $\hat{ɛ} (ω)$ } indicates the screened plasma frequency $ω_{p}^{*}$ of $SrMnB i_{2}$ . The value of $ω_{P}^{*} \sim 120 meV$ is much lower than that of a typical metal, suggesting its semimetallic nature. (c) The Drude spectral weight ${ω_{p}}^{2}$ and (d) the scattering rate $1 / τ$ were extracted through the two-carrier-model fit. (e, f) $T$ -dependent dc transport properties. As shown in (e), the dc transport conductivity $σ_{dc}$ can be explained when the dc limits of optical conductivity $σ (ω \to 0)$ for the Dirac and semimetallic Drude band contributions are included. The different transport behavior of both bands is evidenced, especially below $T = 100 K$ . The overall $T$ -linear behavior (with two distinct regimes) of the optical resistivity $ρ (ω \to 0)$ for Dirac fermions in (f) implies the presence of strong electron-phonon interactions. In addition, the deviation (shaded red region) from the linear trend near $T_{N} \approx 290 K$ presumably indicates the interplay between Dirac fermions and magnetism.
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Figure 4
(a) Optical conductivity $σ_{1, inter} (ω)$ spectra dominated by the interband transitions after excluding the free-carrier contribution from the entire conductivity $σ_{1} (ω)$ . The theoretical $σ_{1, inter} (ω)$ at $T = 0 K$ (labeled by LSDA, a black solid line) was also obtained from density functional calculations with band renormalization by a factor of $Z = 0.59$ . Here, the dashed background shows our estimation for the universal absorption expected for the Dirac state. The absorption edge is less pronounced as $T$ increases due to thermal redistribution of the Dirac fermion population. (b) The band structure along the $M$ -Γ- $X$ direction includes both the linear Dirac-conic (along the $M$ -Γ) and parabolic semimetallic bands (Γ- $X)$ . The electronic bands relevant for direct interband transitions are represented by both the red and blue lines while a blue arrow indicates the indirect interband transition possibly assisted by phonons at high $T$ . (c) The partial density of states (PDOS) integrated over $k$ space also identifies the optical interband transitions (represented by two black arrows), corresponding to the double-peak structure in the $σ_{1, inter} (ω)$ .
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Physical Review B

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Electrodynamic properties of the semimetallic Dirac material $SrMnB i_{2}$ : Two-carrier-model analysis

H. J. Park, Byung Cheol Park, Min-Cheol Lee, D. W. Jeong, Joonbum Park, Jun Sung Kim, Hyo Seok Ji, J. H. Shim, K. W. Kim, S. J. Moon, Hyeong-Do Kim, Deok-Yong Cho, and T. W. Noh

Phys. Rev. B 96, 155139 – Published 26 October 2017

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Electrodynamic properties of the semimetallic Dirac material SrMnBi2: Two-carrier-model analysis

H. J. Park, Byung Cheol Park, Min-Cheol Lee, D. W. Jeong, Joonbum Park, Jun Sung Kim, Hyo Seok Ji, J. H. Shim, K. W. Kim, S. J. Moon, Hyeong-Do Kim, Deok-Yong Cho, and T. W. Noh

Phys. Rev. B 96, 155139 – Published 26 October 2017

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Electrodynamic properties of the semimetallic Dirac material $SrMnB i_{2}$ : Two-carrier-model analysis