Dirac fermions and superconductivity in the homologous structures $({\mathrm{Ag}}_{x}{\mathrm{Pb}}_{1\ensuremath{-}x}\mathrm{Se}{)}_{5}({\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}{)}_{3m}$ ($m=1,2$)

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Dirac fermions and superconductivity in the homologous structures $({Ag}_{x} {Pb}_{1 - x} Se)_{5} ({Bi}_{2} {Se}_{3})_{3 m}$ ( $m = 1, 2$ )

L. Fang, C. C. Stoumpos, Y. Jia, A. Glatz, D. Y. Chung, H. Claus, U. Welp, W.-K. Kwok, and M. G. Kanatzidis

Phys. Rev. B 90, 020504(R) – Published 9 July 2014

Abstract

A newly discovered topological insulator (TI) $({Ag}_{x} {Pb}_{1 - x} Se)_{5} ({Bi}_{2} {Se}_{3})_{3 m}$ ( $m = 2$ ) has a band gap of 0.5 eV, the largest value reported in topological insulators. We present a magnetotransport study of the Dirac electrons of this compound in the quantum diffusion regime. Two-dimensional weak antilocalization due to the destructive interference of the Dirac electrons was observed. The phase coherence length of the Dirac electrons is independent of doping and disorder levels. This provides an indication of the backscattering immunity under the protection of time reversal invariance of the TI. We further report that the homologous compound $({Ag}_{x} {Pb}_{1 - x} Se)_{5} ({Bi}_{2} {Se}_{3})_{3 m}$ ( $m = 1$ ) is a superconductor with a transition temperature $T_{C} = 1.7$ K. The related structures of these two phases allow lateral intergrowth of crystals to occur naturally, offering a potential platform to observe the Majorana fermion state at the boundary of two intergrown crystals.

Received 30 April 2014

DOI:https://doi.org/10.1103/PhysRevB.90.020504

Authors & Affiliations

L. Fang^1,*, C. C. Stoumpos², Y. Jia³, A. Glatz^2,4, D. Y. Chung², H. Claus², U. Welp², W.-K. Kwok², and M. G. Kanatzidis^1,2,†

¹Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA
²Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
³Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
⁴Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA

^*lei.fang@northwestern.edu
^†m-kanatzidis@northwestern.edu

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Vol. 90, Iss. 2 — 1 July 2014

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Figure 1
(a) Schematic pictures of the crystal symmetry of (PbSe) $_{5}$ (Bi $_{2}$ Se $_{3}$ ) $_{3 m}$ ( $m = 1, 2$ ) and of a Dirac cone in the band structure of the $m = 2$ phase. (b) Structure of two unit cells of the $m = 1$ phase. The thickness of [PbSe] is $\sim$ 2.8 Å. [PbSe] and [Bi $_{2}$ Se $_{3}$ ] are connected by chemical bonds. (c) Structure of one unit cell of the $m = 2$ phase. Bonds between QL-II and QL-III are of van der Waals type. Silver can replace Pb ions in the [PbSe] slabs. (d) Temperature dependent $ρ_{a b}$ of (Ag $_{x}$ Pb $_{1 - x}$ Se) $_{5}$ (Bi $_{2}$ Se $_{3}$ ) $_{6}$ ( $x = 0, 0.2$ ) and (Ag $_{0.2}$ Pb $_{0.8}$ Se) $_{5}$ (Bi $_{2}$ Se $_{3}$ ) $_{3}$ . (e) Temperature dependent $ρ_{c}$ of the $m = 2$ phase. The resistivity anisotropies $Γ = ρ_{c} / ρ_{a b}$ at 2 K are $25 (\pm 3)$ and $28 (\pm 3)$ for doping $x = 0$ and 0.2, respectively.
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Figure 2
(a) Hall coefficient measurements of the $m = 2$ phase at 2 K exhibit a nonlinear field dependence. The inset schematically shows the coexistence of surface (SB) and bulk bands (CB). (b) MR measurement of bulk crystal (PbSe) $_{5}$ (Bi $_{2}$ Se $_{3}$ ) $_{6}$ at 2 K in tilted magnetic fields. (c) 2D scaling of the magnetoconductance of crystal (PbSe) $_{5}$ (Bi $_{2}$ Se $_{3}$ ) $_{6}$ . The inset is a schematic picture of our angle dependent magnetoconductance measurements. (d) The scaled $Δ G$ of two crystals (No. 1, No. 2) of (PbSe) $_{5}$ (Bi $_{2}$ Se $_{3}$ ) $_{6}$ and of a silver-doped crystal ( $m = 2$ , $x = 0.2$ ), in magnetic fields along the $c$ axis. The solid curve is a fitting using the HLN equation.
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Figure 3
(a) Temperature dependent resistivity of (Ag $_{x}$ Pb $_{1 - x}$ Se) $_{5}$ (Bi $_{2}$ Se $_{3}$ ) $_{3}$ ( $x = 0.2, 0.22$ ). Both samples show superconducting transitions below 1.6 K and zero resistances. The inset is a $H_{C 2}$ plot for doping $x = 0.2$ with fields applied in plane and out of plane. The straight solid lines are guides to the eye. (b) Temperature dependent magnetization of crystals (Ag $_{x}$ Pb $_{1 - x}$ Se) $_{5}$ (Bi $_{2}$ Se $_{3}$ ) $_{3}$ ( $x = 0.1$ –0.25). $T_{C}$ varies with the silver doping. ZFC means zero-field cooling. (c) and (d) are temperature dependent resistances of the superconducting sample in fields applied along out of plane and in plane.
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Figure 4
(a) Optical image of a cleaved superconducting crystal. Grain boundaries divide the crystal in two parts. The right part exhibits a more cleavable characteristic than the part on the left. This distinct topography indicates the different structures of these two domains. The domain angles, as shown as the yellow cross, are $\sim$ $90^{\circ}$ , consistent with the solved crystallographic data of (PbSe) $_{5}$ (Bi $_{2}$ Se $_{3}$ ) $_{3 m}$ ( $m = 1, 2$ ). The right domain is ascribed to the $m = 2$ phase and the left part is the $m = 1$ phase. (b) X-ray diffraction of a superconducting crystal along the c axis. The two sets of (00l) peaks unveil that two phases intergrow in the ab plane, consisting well with the image in (a).
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Physical Review B

covering condensed matter and materials physics

Dirac fermions and superconductivity in the homologous structures $({Ag}_{x} {Pb}_{1 - x} Se)_{5} ({Bi}_{2} {Se}_{3})_{3 m}$ ( $m = 1, 2$ )

L. Fang, C. C. Stoumpos, Y. Jia, A. Glatz, D. Y. Chung, H. Claus, U. Welp, W.-K. Kwok, and M. G. Kanatzidis

Phys. Rev. B 90, 020504(R) – Published 9 July 2014

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Physical Review B

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Dirac fermions and superconductivity in the homologous structures (AgxPb1−xSe)5(Bi2Se3)3m (m=1,2)

L. Fang, C. C. Stoumpos, Y. Jia, A. Glatz, D. Y. Chung, H. Claus, U. Welp, W.-K. Kwok, and M. G. Kanatzidis

Phys. Rev. B 90, 020504(R) – Published 9 July 2014

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Dirac fermions and superconductivity in the homologous structures $({Ag}_{x} {Pb}_{1 - x} Se)_{5} ({Bi}_{2} {Se}_{3})_{3 m}$ ( $m = 1, 2$ )