Pressure-Induced Electronic Transition in Black Phosphorus

Z. J. Xiang, G. J. Ye, C. Shang, B. Lei, N. Z. Wang, K. S. Yang, D. Y. Liu, F. B. Meng, X. G. Luo, L. J. Zou, Z. Sun, Y. Zhang, and X. H. Chen

Phys. Rev. Lett. 115, 186403 – Published 28 October 2015

Abstract

In a semimetal, both electrons and holes contribute to the density of states at the Fermi level. The small band overlaps and multiband effects engender novel electronic properties. We show that a moderate hydrostatic pressure effectively suppresses the band gap in the elemental semiconductor black phosphorus. An electronic topological transition takes place at approximately 1.2 GPa, above which black phosphorus evolves into a semimetal state that is characterized by a colossal positive magnetoresistance and a nonlinear field dependence of Hall resistivity. The Shubnikov–de Haas oscillations detected in magnetic field reveal the complex Fermi surface topology of the semimetallic phase. In particular, we find a nontrivial Berry phase in one Fermi surface that emerges in the semimetal state, as evidence of a Dirac-like dispersion. The observed semimetallic behavior greatly enriches the material property of black phosphorus and sets the stage for the exploration of novel electronic states in this material.

Received 16 July 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.186403

Authors & Affiliations

Z. J. Xiang¹, G. J. Ye¹, C. Shang¹, B. Lei¹, N. Z. Wang¹, K. S. Yang³, D. Y. Liu³, F. B. Meng¹, X. G. Luo^1,6, L. J. Zou³, Z. Sun^4,6, Y. Zhang^5,6,*, and X. H. Chen^1,2,6,†

¹Hefei National Laboratory for Physical Sciences at Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and Key Laboratory of Strongly-coupled Quantum Matter Physics, Chinese Academy of Sciences, Hefei, Anhui 230026, China
²High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei, Anhui 230031, China
³Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei, Anhui 230031, China
⁴National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei, Anhui 230026, China
⁵State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
⁶Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

^*zhyb@fudan.edu.cn
^†chenxh@ustc.edu.cn

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Vol. 115, Iss. 18 — 30 October 2015

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Figure 1
Longitudinal resistivity $ρ_{x x}$ of black phosphorus versus $T$ at various hydrostatic pressures. Numbers beside the curves represent applied pressures in GPa. Inset: The value of the residual resistivity ratio $ρ_{x x} (300 K) / ρ_{x x} (2 K)$ and the transverse MR $[[(ρ_{x x} (9 T) − ρ_{x x} (H = 0)] / ρ_{x x} (H = 0)$ ], with $H ∥ c$ at $T = 2 K$ as a function of pressure.
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Figure 2
(a) Hall resistivity $ρ_{x y}$ of a black phosphorus single crystal as a function of the magnetic field at various pressures at $T = 2 K$ . Inset: Low-field sign reversal of $ρ_{x y}$ at $P \geq 1.20 GPa$ . The Hall data were antisymmetrized with respect to positive and negative magnetic fields to remove the $ρ_{x x}$ component. (b) Field dependence of transverse MR for $P > 1.1 GPa$ with $H ∥ c$ , and current $I$ applied in the basal plane, at $T = 2 K$ .
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Figure 3
(a) Negative second derivative of resistivity with respect to the magnetic field, $- d^{2} ρ_{x x} / d H^{2}$ , at varying pressures. Magnetic field $H$ was applied along the $c$ direction. Data were collected for a black phosphorus single crystal labeled sample $A$ . (b) The FFT spectra of $- d^{2} ρ_{x x} / d H^{2}$ of sample $A$ . The labels $α$ and $β$ are assigned to the resolved FFT peaks. (c) The oscillation frequencies and corresponding cross-sectional areas of Fermi surfaces of sample $A$ (solid symbols) and sample $B$ (open symbols), plotted as a function of $P$ . The uncertainty is determined by the half width at half height (HWHH) of the FFT peaks. The raw data obtained for sample $B$ are shown in Fig. S6 of the Supplemental Material [11]. (d) Pressure dependence of the cyclotron mass ratio $m^{*} = m / m_{e}$ . $m^{*}$ was calculated based on the Lifshitz-Kosevich formula fitting of the $T$ dependence of the normalized amplitude of the oscillatory component $Δ ρ_{x x} / ρ_{x x}$ (solid symbols) or the normalized FFT amplitude (open symbols). The average inverse fields in the FFT interval are noted beside data points.
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Figure 4
(a) Oscillation patterns of the magnetoconductivity $σ_{x x} (H)$ of pocket $α$ , obtained by subtracting a smooth background from $σ_{x x} = ρ_{x x} / (ρ_{x x}^{2} + ρ_{x y}^{2})$ , at various pressures with $H ∥ c$ . Integer indices are marked at the maxima of $Δ σ_{x x}$ . (b) Landau index $n$ versus $1 / μ_{0} H$ for the SdH oscillation of pocket $α$ . The linear extrapolations of the indices are indicated by solid lines. Inset: Intercepts of the linear extrapolations on $n$ axis, which equal the total SdH phase $- γ + δ$ . The correction terms $δ$ in the 3D limit, $δ = - 1 / 8$ (FS maxima) and $δ = + 1 / 8$ (FS minima), are denoted by dashed lines for the phase of Dirac electrons ( $γ = 0$ ). Error bars represent the uncertainties of linear fitting.
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