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Robust and Pristine Topological Dirac Semimetal Phase in Pressured Two-Dimensional Black Phosphorous Penglai Gong, Bei Deng, Liang-Feng Huang, Liang Hu, Weichao Wang, Dayong Liu, Xingqiang Shi, Zhi Zeng, and Liang-Jian Zou J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b08926 • Publication Date (Web): 08 Sep 2017 Downloaded from http://pubs.acs.org on September 9, 2017
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The Journal of Physical Chemistry
Robust and Pristine Topological Dirac Semimetal Phase in Pressured Two-Dimensional Black Phosphorous Peng-Lai Gong,†,‡,⊥ Bei Deng,†,⊥ Liang-Feng Huang,¶ Liang Hu,† Wei-Chao Wang,‡ Da-Yong Liu,∗,§ Xing-Qiang Shi,∗,† Zhi Zeng,§,∥ and Liang-Jian Zou∗,§,∥ †Department of Physics, South University of Science and Technology of China, Shenzhen 518055, China ‡Department of Electronics and Tianjin Key Laboratory of Photo-Electronic Thin Film Device and Technology, Nankai University, Tianjin 300071, China ¶Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA §Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, P. O. Box 1129, Hefei 230031, China ∥University of Science and Technology of China, Hefei 230026, China ⊥Contributed equally to this work E-mail:
[email protected];
[email protected];
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Abstract
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Very recently, in spite of various efforts in searching for two dimensional topological
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Dirac semimetals (2D TDSMs) in phosphorene, there remains a lack of experimentally
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efficient way to activate such phase transition and the underlying mechanism for the
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topological phase acquisition is still controversial. Here, from first-principles calcula-
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tions in combination with a band-sorting technique based on k·p theory, a layer-pressure
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topological phase diagram is obtained and some of the controversies are clarified. We
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demonstrate that, compared with tuning by external electric-fields, strain or doping by
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adsorption, hydrostatic pressure can be an experimentally more feasible way to acti-
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vate the topological phase transition for 2D TDSM acquisition in phosphorene. More
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importantly, the resultant TDSM state is a pristine phase possessing a single pair of
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symmetry-protected Dirac cones right at the Fermi level, in startling contrast to the
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pressured bulk black phosphorous where only a carrier-mixed Dirac state can be ob-
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tained. We corroborate that the Dirac points are robust under external perturbation as
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long as the glide-plane symmetry preserves. Our findings provide a means to realize 2D
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pristine TDSM in a more achievable manner, which could be crucial in the realization
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of controllable TDSM states in phosphorene and related 2D materials.
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Two dimensional (2D) Dirac semimetals, in which Dirac points cross the Fermi level
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(EF ) being protected by nonsymmorphic crystal symmetries, was first proposed by Young
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and Kane in 2015. 1 Very recent progress on the strain or electric-field modified phosphorene,
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as a representative of the rare candidates, has established a link between Dirac cones and
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the topological nature. 2–4 Given the experimental discovery of three dimensional (3D) topo-
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logical Dirac semimetals (Na3 Bi, 5 Cd3 As2 6 ) and α-Sn on InSb(111) substrate, 7 it is natural
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to ask whether the 2D topological Dirac semimetals (TDSMs) can also be realized in an
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experimentally feasible manner.
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A simple mechanism for a 2D TDSM phase acquisition has been proposed based on the
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Stark effect in phosphorene thin films by applying an external electric field. 3,8 However,
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applying an exceptionally giant electric field on such a system is difficult to realize exper2 ACS Paragon Plus Environment
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imentally (the value of the field required is ∼0.5 V/Å for a four-layer phosphorene 8 ). On
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the basis of the same mechanism, the experimentally observed Dirac semimetal state, from
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potassium doping of few-layer phosphorene, is actually an electron-doped TDSM. 9 However,
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a pristine TDSM in 2D is highly desirable as it can be tuned to be topological insulators
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(TIs) or Weyl semimetals by explicit breaking of symmetries. In this regard, in-plane s-
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train has been proposed as a possible means to induce Dirac cones in monolayer or bilayer
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phosphorene, 10–12 whereas the critical strain (as large as ∼10% uniaxial strain or 5% biaxial
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strain based on the DFT-PBE level 11 ) is difficult to be experimentally realized, particularly
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for the biaxial strain in strong-anisotropic systems such as phosphorene. Furthermore, such
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large uniaxial/biaxial strains could substantially lower the local symmetry of the system,
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resulting in large distortion and structural instability due to the accumulative strain energy.
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Additionally, it remains conflicted in literature about the true phase (i.e., whether the re-
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sultant phase is a TI or a TDSM) in the strain-induced phase transition. 2,4,10 All the above
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issues need to be solved or clarified, and examined by a more achievable way.
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Apart from uniaxial/biaxial strains, the hydrostatic pressures, which to a larger extent
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preserve the crystal symmetry, and also could be free of the typical epitaxial-mismatch
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effect, have been proved as a powerful tool to deal with both fundamental and practical
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issues. Very recently, we have reported that bulk black phosphorous (BP) can convert from
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a normal insulator (NI) into a 3D Dirac semimetal under a certain hydrostatic pressure,
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both experimentally and theoretically, but only a carrier-mixed phase is acquired. 13,14 In
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experiments, hydrostatic pressures can also substantially modify the optical and vibrational
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properties of 2D systems like monolayer or few-layer MoS2 , 15–20 WS2 , 21 and WSe2 . 22 Starting
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from this point, the few-layer phosphorene could be feasibly pressurized like other layered
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2D systems. Therefore, in this Letter, from first-principles methods in conjunction with
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band-sorting technique based on k·p theory (to solve the above mentioned TI or TDSM
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conflict), we study the layer-pressure topological phase diagram of few-layer phosphorene.
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We discovered that hydrostatic pressures can energetically drive the 2D phosphorene from NI
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to TDSM phase, with the topological-phase-transitions (TPTs) depending on the number of
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layers. The resultant 2D TDSM state is characterized to be a pristine phase as a consequence
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of the reduced dimensional effect in the vertical direction. We demonstrate that the Dirac
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points are robust under external perturbation, including strain, pressure or electric field, as
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long as the glide-plane symmetry within each sublayer preserves.
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In order to explore the evolutions of electronic structures of few-layer phosphorene under
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increasing hydrostatic pressures, we first determine their crystal structures (under each pres-
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sure) by DFT calculations. We employed the Vienna Ab initio Simulation Package (VASP) 23
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with the projector augmented wave (PAW) method. 24,25 The interlayer vdW interaction is
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described by the optB88-vdW functional. 26 A previous study on few-layer MoS2 has pro-
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posed an extraction method to obtain the 2D structures under pressures. 27 Based on this
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method, their results reveal that the critical pressure for direct-to-indirect gap transition is
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∼13 GPa, in qualitative agreement with the conclusion drawn from photoluminescence ex-
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perimental measurement of ∼16 GPa. 15 The extraction method is a reasonable and practical
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strategy to mimic the real pressurized procedure for layered systems, because it makes the
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sample feel the pressure from the other parts of the bulk system, which could serve as a
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good approximation to the inert pressure-transmitting medium in experiments. Meanwhile,
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the periodic potential field at the vdW boundary is not such strong that can change the
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geometric and electronic properties of the 2D BP system, as this is further verified by anoth-
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er method, namely, the medium method, in which the very realistic pressure-transmitting
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medium is considered. We find based on a set of comparison test, that basically the two
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method will yield a same structure for the 2D BP under a given pressure (see Table S2),
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suggesting that the extraction method is reliable to the cases in this study. As it is compu-
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tationally much more expensive to consider the medium in each configuration (more than
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800 atoms in the whole system), especially for the cases with the inclusion of spin-orbital
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coupling (SOC) effect, here, we chose the extraction method as an appropriate approach to
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conduct the study. Within the extraction method, in our study the structure of bulk BP was
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Figure 1: (a) Side- and (b) top-views of the crystal structure of a 2-layer phosphorene; (c) 2D first Brillouin zone; (d) anisotropic variation of structural parameters of few-layer phosphorene under pressure. 83
first optimized under a specified hydrostatic pressure, and then these structural parameters
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were used to construct the n−layer phosphorene, with a vacuum space of 20 Å along the z
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direction. Based on the constructed 2D structures, the electronic properties is calculated by
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hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE06) 28 calculations with the inclusion
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of SOC effect.
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Few-layer BP is a layered material, in which each layer stacks together by van der Waals
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(vdW) interactions. Each layer consists of two sublayers and in turn forms a bulking honey-
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comb structure. The structural model of 2-layer phosphorene, as a representative for a finite
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n-layer phosphorene (n denotes the number of layers), is shown in Figures 1a,b, where the
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directions of lattice vectors a and b are along the zigzag (the y axis) and the armchair (the
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x axis) directions, respectively. The 2D rectangular Brillouin zone of n-layer phosphorene is
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typified in Figure 1c.
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With increasing pressure, as shown in Figure 1d, the lattice constant b (armchair direc-
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tion) and the interlayer spacing between two adjacent phosphorene layers (dint ) are signif-
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icantly shortened (by 5.6% and 8.8% for b and dint at 4.0 GPa), while a (zigzag direction)
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and the sublayer distance within one single layer (h) remain almost unchanged. The ther-
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modynamic and lattice-dynamic stabilities of few-layer phosphorene depend on their atomic
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and electronic properties, as well as the environment, such as pressure and temperature, etc.
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In the current work, the stabilities of few-layer phosphorene are in line with that of bulk BP.
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(b)
(a)
TDSM NI
Figure 2: Layer-pressure topological phase diagram of n-layer phosphorene. PC and PT are the critical pressures for electronic phase transition and upper limit of thermodynamic stability, respectively (see main text). NI denotes normal insulator (Figure 3a); and TDSM denotes a pure topological Dirac semimetal with Dirac points locating exactly at EF (Figures 3c,d). (b) Three dimensional band structure for the TDSM bands around Γ point, showing a single pair of Dirac cones. 102
The thermodynamic stability of the bulk BP is considered through the enthalpy-pressure re-
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lationship. We find that the critical pressure of thermodynamic stability PT for bulk BP with
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orthorhombic phase is 4.6 GPa (see Figure S2), very close to the experimental result (4.7
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GPa), 29 which indicates a structural phase transition from a A17 (orthorhombic) phase to a
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A7 (rhombohedral) phase. 30 For few-layer phosphorene, a similar structural phase transition
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is found in accordance to our calculations because of the same mechanism of the structural
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phase transition as the bulk BP. 30 Phonon spectra are then calculated to judge whether or
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not the thermodynamically stable structures (with P ≤ PT ) are lattice-dynamic stable. Our
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results show that all the pressured structures have no imaginary frequencies below PT . 14
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The above results ensure that the pressured structures will not experience a structural phase
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transition below PT ; and this is further confirmed by the medium method, showing that the
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2D structure is indeed stable and does not favor reconstruction below PT (see Table S2 and
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Figure S1).
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Topological phase diagram. The layer-pressure topological phase diagram for few-layer
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phosphorene (below PT , with consideration of SOC) is displayed in Figure 2, where PC and
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PT are the critical pressures for electronic and structural phase transitions, respectively. At
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PC , an electronic phase transition, from NI to TDSM, takes place (see Figure 3b). TDSM
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+ -
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Figure 3: Band structures of 4-layer phosphorene as a representative for the pressured structures at (a) 0.0 GPa, (b) 4.1 GPa, (c) 4.4 GPa and (d) also 4.4 GPa, but around the Dirac point along the kx and ky directions, respectively. The SOC was also included in the calculation. The parity (even: +, odd: -) of the VBM and CBM at Γ point is labeled in (a) and (c). Dirac point (denoted by green point, labeled with "D") was set as the starting point in the band structure plotting in (d). A band-sorting method is used to sort the bands according to their symmetry (see text). 119
denotes a pristine topological Dirac semimetal phase with only Dirac fermions at EF (see
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Figure 3c). No TPTs are observed for n = 2 and 3 layers so they are still NIs below PT
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(dashed red line), this is because of their large band gaps (≥ 0.75 eV) under zero pressure.
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With increasing number of n, their zero-pressure band gaps gradually decrease, and a NI
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to TDSM transition happens to occur in the pressure range of PC
