Photoinduced Nonequilibrium Topological States in Strained Black Phosphorus

Hang Liu, Jia-Tao Sun, Cai Cheng, Feng Liu, and Sheng Meng

Phys. Rev. Lett. 120, 237403 – Published 8 June 2018

Abstract

Black phosphorus (BP), an elemental semiconductor, has attracted tremendous interest because it exhibits a wealth of interesting electronic and optoelectronic properties in equilibrium condition. The nonequilibrium electronic structures of bulk BP under a periodic field of laser remain unexplored, but can lead to intriguing topological optoelectronic properties. Here we show that, under the irradiation of circularly polarized light (CPL), BP exhibits a photon-dressed Floquet-Dirac semimetal state, which can be continuously tuned by changing the direction, intensity, and frequency of the incident laser. The topological phase transition from type-I to type-II Floquet-Dirac fermions manifests a new form of type-III phase, which exists in a wide range of intensities and frequencies of the incident laser. Furthermore, topological surface states exhibit nonequilibrium electron transport in a direction locked by the helicity of CPL. Our findings not only deepen our understanding of fundamental properties of BP in relation to topology but also extend optoelectronic device applications of BP to the nonequilibrium regime.

Received 10 October 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.237403

Physics Subject Headings (PhySH)

Dirac fermions Optoelectronics Topological phase transition

First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Hang Liu^1,4, Jia-Tao Sun^1,4,*, Cai Cheng¹, Feng Liu^2,3,†, and Sheng Meng^1,3,4,‡

¹Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
²Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, USA
³Collaborative Innovation Center of Quantum Matter, Beijing 100084, People’s Republic of China
⁴University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China

^*jtsun@iphy.ac.cn
^†fliu@eng.utah.edu
^‡smeng@iphy.ac.cn

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 120, Iss. 23 — 8 June 2018

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Schematic illustration of compressed BP irradiated by CPL. The $x$ , $y$ , and $z$ axes are along the armchair, zigzag, and stacking directions, respectively. (b)–(e) Laser-driven phase transitions from Dirac nodal ring to type-I, type-III, and type-II Dirac points in BP. (f)–(i) Evolution of Fermi surface with CPL.
Reuse & Permissions
Figure 2
Topological FDFs induced by laser with photon energy $ℏ ω = 0.5 eV$ . (a) CPL $A (t) = A_{0} (\cos (ω t), \sin (ω t), 0)$ propagates along the stacking direction ( $- z$ ). (b) The laser-induced Floquet-Dirac nodal points (red points) and original nodal ring in equilibrium (dashed circle). Floquet-Bloch band structure and band diagram of BP driven by laser with amplitude $A_{0} = 50 V / c$ (c),(d), $A_{0} = 263 V / c$ (e),(f) and $A_{0} = 300 V / c$ (g),(h). Gray dotted line is the equilibrium electronic structure. The quasienergy of nodal points is marked as $ϵ_{D}$ . Yellow lines on the red plane represent Fermi surfaces. (i)–(k) Fermi contour lines on the $k_{x} = 0$ ( $Γ − Z − W$ ) plane when Fermi energy is at $ϵ_{D} + 1.5 meV$ , $ϵ_{D}$ , $ϵ_{D} - 1.5 meV$ , respectively. The red dots are the positions of projected type-II nodal points on the $k_{x} = 0$ plane. The green closed ellipses and blue open hyperbolas represent the contours of the electron and hole pockets in the plane $k_{x} = 0$ , respectively.
Reuse & Permissions
Figure 3
Laser-induced Floquet phase diagram of compressively strained BP. (a) Counterclockwise CPL propagates on the $y z$ plane with the propagation direction as $θ$ . (b) The gray circle represents equilibrium nodal ring of strained BP. The angle between the connecting line of two Floquet-Dirac nodal points (red dots) and $k_{y}$ direction is $θ^{'}$ . (c) Phase diagram of laser-driven BP (photon energy $ℏ ω = 0.5 eV$ ) on the dependence of laser amplitude $A_{0}$ and incident angle $θ$ . (d) The Floquet phases induced by laser ( $θ = 90 °$ ) with different amplitude $A_{0}$ and frequency $ω$ .
Reuse & Permissions
Figure 4
Origin of the Floquet phase transition of BP driven by CPL propagating along stacking direction ( $- z$ ). (a) The bold and thin gray lines represent $n = 0$ and $n = - 1$ Floquet-Bloch bands, respectively. $Δ^{'}$ is the energy difference between Dirac point on the nodal ring and the crossing of $n = 0$ and $n = - 1$ bands along the $Γ - Z$ direction. The thickness of the line is proportional to the weight of the static ( $n = 0$ ) component. Band gap $Δ$ is induced by the hybridization between bands indexed by $n = 0$ and $n = - 1$ . The distance between the Floquet-Dirac nodal point and the center of the nodal ring is marked as $d$ . (b) The variation of $d$ with laser amplitude $A_{0}$ when the photon energy is set as $ℏ ω = 0.5$ , 1.0, and 2.0 eV, respectively. (c) The dependence of $Δ / 2$ on laser amplitude $A_{0}$ when photon energy is set as $ℏ ω = 0.5$ , 1.0, and 1.5 eV, respectively. Dashed lines represent the value $Δ^{'}$ in three cases. (d) Linear dependence of the photon energy and laser amplitude defining the phase boundary of type-I and type-II Floquet-Dirac phases.
Reuse & Permissions
Figure 5
The locking effect of the transport direction of surface states and laser helicity. (a) The sketch of laser helicity. (b) Surface states along the $\bar{W} − \bar{Z} − \bar{W}$ direction in the SBZ come from left and right surfaces, respectively, which is induced by laser with photon energy $ℏ ω = 0.9 eV$ and amplitude $A_{0} = 150 V / c$ . (c) The opposite direction of topologically protected surface currents on two counter surfaces. LS: left surface; RS: right surface. (d)–(f) Surface states of Floquet-Dirac state when the laser helicity is reversed.
Reuse & Permissions

Physical Review Letters