{'fraction_non_alphanumeric': 0.028736313688288075, 'fraction_numerical': 0.023321079884580417, 'mean_word_length': 4.954342198164274, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Topological insulator materials for advanced optoelectronic devices

Topological insulators are quantum materials that have an insulating bulk state and a topologically protected metallic surface state with spin and momentum helical locking and a Dirac-like band structure. Unique and fascinating electronic properties, such as the quantum spin Hall effect, quantum anomalous Hall effect, and topological magnetoelectric effect, as well as magnetic monopole images and Majorana fermions, have been observed in the topological insulator materials. With these unique properties, topological insulator materials have great potential applications in spintronics and quantum information processing, as well as magnetoelectric devices with higher efficiency and lower energy consumption. On the other hand, topological insulator materials also exhibit a number of excellent optical properties, including Kerr and Faraday rotation, ultrahigh bulk refractive index, near-infrared frequency transparency, unusual electromagnetic scattering, and ultra-broadband surface plasmon resonances. Specifically, Dirac plasmon excitations have been observed in Bi2Se3 micro-ribbon arrays at THz frequencies. Ultraviolet and visible frequency plasmonics have been observed in nanoslit and nanocone arrays of Bi1.5Sb0.5Te1.8Se1.2 crystals. High transparency has been observed in Bi2Se3 nanoplates. An ultrahigh refractive index has been observed in bulk Bi1.5Sb0.5Te1.8Se1.2 crystals as well as in Sb2Te3 thin films. These excellent optical properties mean that topological insulator materials are suitable for various optoelectronic devices, including plasmonic solar cells, ultrathin holograms, plasmonic and Fresnel lens, broadband photodetectors, and nanoscale waveguides. In this chapter, we focus on the excellent electronic and optical properties of topological insulator materials and their wide applications in advanced optoelectronic devices.


Quantum spin Hall effect
The quantum spin Hall effect in 2D topological insulators was firstly proposed by Kane and Zhang.(18,19) Then, the novel effect was predicted in mercury telluride-cadmium telluride (HgTe/CdTe) semiconductor quantum wells by König et al. in 2006.(4) The HgTe/CdTe quantum wells have well-known strong spin-orbital coupling. When the thickness of the HgTe layer is smaller than 6.3 nm, the 2D electronic states have the normal band order, but when the thickness is larger than 6.3 nm, the 2D bands have an inversion with a quantum phase transition between the trivial insulator and the quantum spin Hall insulator.
Molenkamp et al. experimentally realized the quantum spin Hall effect in HgTe quantum wells in 2007. (20) In the quantum well, two edge states with opposite spin polarization counter propagate at opposite edges. And, the quantum well also has non-local edge channel transport in the quantum spin Hall regime at zero external magnetic field. (21) These measurements confirm that the quantum transport through the helical edge channels is non-dissipative. And the topological protection of the edge states can't be destroyed by weak time reversal symmetric perturbations. The electrons in edge states are the absence of elastic backscattering and robustness against disorder for surface transport.

Topological magnetoelectric effects
Topological magnetoelectric effect is the phenomenon of magnetic polarization induced by applying an external electric field, or electric polarization induced by applying an external magnetic field. To obtain the topological magnetoelectric effect, a time-reversal-symmetry-breaking gap for the side surface is necessary. (22) A ferromagnetic layer with magnetization pointing out of the cylinder's surface induces a gap on the surface of the topological insulator, which has a fixed Hall conductance, σ H = (n +1/2) e 2 /h. When an electric field is applied parallel to the cylinder, a circulating current j can be induced on the interface. This current is identical to the current generated by a constant magnetization M which is anti-parallel to the electric field E. On the contrary, when a magnetic field B is applied parallel to the cylinder, a circulating current is produced parallel to the interface, which induces a Hall current j parallel or anti-parallel to the magnetic field B. As a result, charge density is accumulated on the top and bottom surfaces and induces the charge polarization.(2)

Magnetic monopole image
The topological magnetoelectric effect can be used to generate magnetic monopole image through putting an electric charge near a topological surface state. (23) When an electric charge is put on the surface of a 3D topological insulator with gapped surface states by time-reversal-symmetry breaking, the electric charge will polarize the bulk dielectric, and an image electric charge appears inside the topological insulator. An image magnetic monopole will also appear inside the topological insulator. (23) The magnetic field generated by the image magnetic monopole has been experimentally measured and can be observed by a magnetic force microscope. A scanning magnetic force microscope tip can be applied to detect the magnetic field distribution of the image monopole. The magnetic field contribution from the magnetic monopole can also dominate and be distinguished from the contribution from surface impurities and roughness.

Topological superconductors
When topological insulators connect with ordinary superconductors, topological superconductors appear due to the correlated interface states and the proximity effect.(24) Such topological superconductors are predicted to host Majorana fermion excitations.(1) A Majorana fermion is a fermion that is its own antiparticle and was first predicted in the 1930s. The zero energy Majorana bound state is the simplest non-Abelian excitation and is associated with a vortex in a spinless superconductor. A Majorana zero mode has been proposed that can be realized in a superconducting vortex core by making use of the surface states of 3D topological insulators.(25) Topological protection and non-Abelian exchange statistics make the Majorana fermions promising for quantum computing. Signatures of Majorana fermions have been reported in quantum wires coupled to conventional superconductors. (26)(27)(28) Many experiments have been conducted to observe the elusive Majorana states. (27,29) Recently, chiral Majorana fermion modes was observed in a quantum anomalous Hall insulator-superconductor structure. (30) He et al. demonstrated the existence of one-dimensional chiral Majorana fermion modes in the hybrid system of a quantum anomalous Hall insulator thin film coupled with a superconductor. They conducted the transport measurements and found half-integer quantized conductance plateaus at the locations of magnetization reversals. The transport signature provided a strong evidence of the Majorana fermion modes. The discovery of Majorana fermion could pave a way for producing future topological quantum computing.

Quantum Anomalous Hall effects
The topological surface states of 3D topological insulators are protected by timereversal symmetry and are robust against non-magnetic disorder. Nevertheless, surface states open up a gap in the presence of time-reversal symmetry breaking perturbations, and the Dirac electrons become massive. Magnetic impurities such as Fe, Co, and Mn dopants will induce a surface state gap. Moreover, theoretically, the quantized anomalous Hall effect can emerge in magnetic topological insulators. (31) Such a quantum anomalous Hall effect was observed experimentally soon after it was theoretically predicted in thin films of chromium-doped (Bi,Sb) 2 Te 3 .(32) The gate-tuned anomalous Hall resistance reaches the predicted quantized value of h/e 2 at zero magnetic field. Under a strong magnetic field, the longitudinal resistance vanishes whereas the Hall resistance remains at the quantized value. The realization of the quantum anomalous Hall effect could lead to the development of next generation low-power-consumption electronics.

Giant magnetoresistance effects
Electronic transports are significant not only for the fundamental understanding of electronic properties of materials but also for promoting their applications in practical electronic and optoelectronic devices. (33,34) Giant magnetoresistance was reported in a variety of 3D topological insulators. (35)(36)(37)(38)(39)(40)(41) The Dirac fermions of surface states suggest enhanced quantum corrections of magnetoconductance.(42) Spin-momentum locked surface states always show weak antilocalization effect effects due to strong spin-orbit coupling. Aharonov-Bohm oscillations have also been observed in Bi 2 Se 3 and Bi 1−x Sb x topological insulators. (43,44) Non-saturating positive linear magnetoresistance at high fields was observed in Bi 2 Te 3 films and Bi 2 Se 3 nanoribbons. (45)(46)(47) Room temperature giant and linear MR were observed in the topological insulator Bi 2 Te 3 in the form of nanosheets with a few quintuple layers. (48) The giant, linear magnetoresistance that was achieved was as high as over 600% at room temperature, without any sign of saturation at measured fields up to 13 T. The observed linear magnetoresistance was attributed to the quantum linear magnetoresistance model developed by Abrikosov. (49,50) Actually, the transport behavior of topological insulators reflects the combined contributions of surface states and bulk states due to the metallic bulk. A weak localization effect emerges when the time reversal symmetry is broken and a gap opens in surface states. (51)(52)(53) Competition between weak antilocalization effect and weak localization effect has been observed in the topological insulator thin film Bi 2-x Cr x Se 3 and (Bi 0.57 Sb 0.43 ) 2 Te 3 .(54-56) The weak localization effect has been attributed to the 2D quantized channels of bulk states.(56)

Shubnikov-de Haas (SdH) effects
The surface states of 3D topological insulators have high carrier mobility and the Shubnikov-de Haas effect can appear in the presence of very intense magnetic fields.(57) The Shubnikov-de Haas effect is a macroscopic manifestation of the inherent quantum mechanical nature of matter. The Shubnikov-de Haas effect is a convincing tool for characterizing quantum transport in electronic materials. (58) It can be used to isolate the surface carriers and to determine their mobility and effective mass.(59) Shubnikov-de Haas effects were first observed in 3D topological insulator Bi 2 Te 3 single crystals. (43) The surface mobility of up to 9000 to 10,000 cm 2 /V·s was obtained based on Shubnikov-de Haas quantum oscillations, which is substantially higher than in the bulk. The obtained Fermi velocity of 4 × 10 5 m/s agrees with the results from angle-resolved photoemission measurements. Shubnikov-de Haas quantum oscillations have also been observed in 3D topological insulators, Bi 2 Te 2 Se crystals, Bi 2 Te 3 nanowires, and YPdBi crystals.(57, 60, 61)  In additions, Yue, et al. also discovered that the unequal refractive index in surface and bulk of topological insulator thin films could generate intrinsic resonant cavity. (16,62,63) The multilayer structure of the Sb 2 Te 3 thin film on a Si substrate is schematically shown in Figure 2(a). The dielectric bulk of the Sb 2 Te 3 thin film is sandwiched within the two metallic surface layers. The refractive index n and extinction coefficient k of the surface layers and the bulk are unequal due to different electronic property.(63) With the unequal refractive index, the Sb 2 Te 3 thin film acts as an intrinsic optical resonant cavity.(64) Two surface layers serve as two reflectors. The bulk behaves as an optical resonant cavity. Thus an incident light beam can be reflected multiple times between two surface layers and partially be confined in the bulk. The phase modulation of the reflected light beam from the resonant cavity can be enhanced. Peng, et al. demonstrated near-infrared transparent flexible electrodes based on few-layer Bi 2 Se 3 nanostructures on mica. They found that the Bi 2 Se 3 nanosheets exhibit a transparency of more than 70% over a wide range of wavelengths. Furthermore, the Bi 2 Se 3 nanosheets were used for as transparent electrodes. The electrodes show high chemical and thermal stabilities as well as excellent mechanical durability. These features make the Bi 2 Se 3 nanosheets promising candidates for novel optoelectronic devices. (65)

Faraday rotation and unusual electromagnetic scattering
Faraday rotation was predicted in topological insulator surface. (22) It results from topological magnetoelectric effects in magnetic topological insulators. In principle, it is possible to find a topological insulator with a larger gap which can support an accurate measurement of Faraday rotation. Similar proposals as above can also be worked out for the rotation of reflected wave Kerr effect. In additions, replace the ferromagnetic layers by paramagnetic materials with large susceptibilities and apply an external magnetic field to polarize them. In this case the magnetization is proportional to magnetic field, such that the Faraday rotation contributed by the bulk is also proportional to magnetic field. Unusual electromagnetic scattering was predicted from topological insulator nanoparticles.(66)  scattering-type scanning near-field optical microscopy.(73) They discovered near-field patterns of bright outside fringes also originated from the surfacemetallic plasmonic behavior at mid-infrared frequency.

Ultra-broadband plasmon excitations
With the metallic surface and insulating bulk, topological insulator materials provide an excellent platform for the realization of a new type of nanostructures that could combine the fascinating properties of plasmonic metallic nanostructures and dielectric nanostructures. With these features, the plasmonic topological insulator nanostructures pave a way for designing low-loss and highperformance optical devices, like visible to infrared detectors or sensors.(74)

Polarized light induced photocurrent
Mclver, et al. reported the control of topological insulator photocurrents with light. (75) They showed that illuminating the Bi 2 Se 3 with circularly polarized light generates a photocurrent that originates from topological helical Dirac fermions, and that reversing the helicity of the light reverses the direction of the photocurrent. They also observe a photocurrent that is controlled by the linear polarization of light and argue that it may also have a topological surface state origin. This approach may allow the probing of dynamic properties of topological insulators and lead to novel opto-spintronic devices.

Broadband optical nonlinear response
Chen, et al. studied the nonlinear response of Bi 2 Te 3 at both the optical and microwave band. They demonstrated optical saturable absorption property of Bi 2 Te 3 from 800 nm to 1550 nm. Bi 2 Te 3 shows a saturation intensity of ~12 μW/cm 2 and a normalized modulation depth of ~70%. They argued that the optical saturable absorption in TI is a natural consequence of the Pauli-blocking principle of the electrons filled in the bulk insulating state. (76) Giorgianni, et al. demonstrates an electromagnetic-induced transparency in Bi 2 Se 3 under the application of a strong THz electric field. This effect, concomitantly determined by harmonic generation and charge-mobility reduction, is exclusively related to the presence of Dirac electron at the surface of Bi 2 Se 3 , and opens the road towards tunable THz nonlinear optical devices based on TI materials. (77) The third order nonlinear optical property of Bi 2 Se 3 was investigated under femto-second laser excitation. (78) When excited at 800 nm, the TI Bi 2 Se 3 exhibits saturable absorption with a saturation intensity of 10.12 GW/cm 2 and a modulation depth of 61.2%, and a giant nonlinear refractive index of 10 −14 m 2 /W. This work suggested that the Bi 2 Se 3 is a promising nonlinear optical material and can find potential applications from passive laser mode locker to optical Kerr effect based photonic devices.

Nanometric holograms
Yue, et al. discovered that nanometric topological insulator thin films act as an intrinsic optical resonant cavity due to the unequal refractive indices in their metallic surfaces and bulk. (16,63) The resonant cavity leads to enhancement of phase shifts and thus the holographic imaging. They calculated phase diagram of original images and print on Sb 2 Te 3 thin film using direct laser writing methods, which is often used for 3D printing. (79)(80)(81) They achieved high quality holographic imaging on nanometric holograms. The work paves a way towards integrating holography with flat electronic devices for optical imaging, data storage and information security.

Ultrathin flat lens
An ultrathin double-focusing lens, capable of simultaneously generating a plasmonic focus in the near-field region and a Fresnel-zone-plate based diffraction-limited focal spot in the far-field region, was designed using Sb 2 Te 3 thin films. The Sb 2 Te 3 thin films hold high-index in the bulk and plasmonic excitations on the surface.(82) The double-focusing flat lens opens new opportunities for future compact devices with versatile functionalities, with potential applications ranging from optical imaging and information technology.

Near-infrared photodetector
Photodetectors are sensors of light, which can convert light photons into photocurrent or photovolatge. (83)(84)(85)(86) Topological insulators have an energy gap in the bulk and a gapless surface state consisting of a single Dirac cone. Lowfrequency optical absorption due to the surface state is universally determined by the fine-structure constant. When the thickness of these 3D topological insulators is reduced, they become quasi-two-dimensional insulators with enhanced absorbance. The two-dimensional insulators can be topologically trivial or nontrivial depending on the thickness, and we predict that the optical absorption is larger for topological nontrivial case compared with the trivial case. Since the surface state is intrinsically gapless, we propose its potential application in wide bandwidth, high-performance photodetection covering a broad spectrum ranging from terahertz to infrared. The performance of photodetection can be dramatically enhanced when the thickness is reduced to several quintuple layers with a widely tunable band gap depending on the thickness. (17) Plank et al. demonstrated terahertz/infrared radiation induced photogalvanic effect in 3D TI (Bi 1−x Sb x ) 2 Te 3 .(87) They found that which the observed photogalvanic effect is sensitive to the surface symmetry and scattering details and can be applied to study the high frequency conductivity of the surface states. In particular, measuring the polarization dependence of the photogalvanic current and scanning with a micrometre sized beam spot across the sample, provides access to topographical inhomogeneities in the electronic properties of the surface states and the local domain orientation.
Zheng, et al. fabricated a near infrared (NIR) light photodetector based on a Sb 2 Te 3 thin film, which was grown on sapphire by molecular beam epitaxy (MBE). Electrical analysis reveals that the resistance of the TIdecreases with increasing temperature in the temperature range of 8.5-300 K. Further optoelectronic characterization showed that the as-fabricated photodetector exhibits obvious sensitivity to 980 nm light illumination. The responsivity, photoconductive gain and detectivity were estimated to be 21.7 A/W, 27.4 and 1.22 × 10 11 Jones, respectively, which are much better than those of other topological insulators based devices. This study suggests that the present NIR photodetector may have potential application in future optoelectronic devices. (88) Sharma et al. reported a high performance broadband photodetector based on Bi 2 Se 3 nanowires. (89) They fabricated the Bi 2 Se 3 nanowires using focused ion beam (FIB) and found they can be used for ultrasensitive visible-NIR photodetectors. They observed efficient electron hole pair generation in the Bi 2 Se 3 nanowire under the illumination of visible (532 nm) and IR light (1064 nm). They observed photo-responsivity of up to 300 A/W.

Saturable absorber
Yu, et al. demonstrates that topological insulator can modulate the operation of a bulk solid-state laser by taking advantage of its saturable absorption. Their result suggests that topological insulators are potentially attractive as broadband pulsed modulators for the generation of short and ultrashort pulses in bulk solidstate lasers, in addition to other promising applications in physics and computing.(90) Zhao, et al. showed that the topological insulator material Bi 2 Te 3 is a saturable absorber with high modulation depth at 1.55 μm. The Bi 2 Te 3 based saturable absorber device was fabricated and used as a passive mode locker for ultrafast pulse formation at the telecommunication band.(91) 3-μm mid-infrared pulse was also generated using the Bi 2 Te 3 as the saturable absorber. (92) The Bi 2 Te 3 shows a low saturable peak intensity of 2.12 MW/cm 2 and a high modulation depth of 51.3%. Lee, et al. found that the bulk-structured Bi 2 Te 3 layer can provide sufficient nonlinear saturable absorption for femtosecond mode-locking. (93) They used the Bi 2 Te 3 as an ultrafast mode-locker to generate femtosecond pulses from an all-fiberized cavity. They presented that stable soliton pulses with a temporal width of ~600 femtosecond can be produced at 1.55 μm from an erbium fiber ring cavity.
Large energy, wavelength tunable Q-switched erbium-doped fiber laser was fabricated using the Bi 2 Te 3 .(94) The saturating intensity was ~57 MW/cm 2 and the modulation depth was ~22%. The single pulse energy is ~1.5 μJ and the saturable absorption operation from ~1.51 μm to ~1.58 μm. 2 GHz passively harmonic mode-locked fiber laser was also achieved by a microfiber-based Bi 2 Te 3 saturable absorber. (95) The fiber laser could operate at the pulse repetition rate of 2.04 GHz under a pump power of 126 mW. Bi 2 Te 3 nanoparticles have shown the broadband saturable absorption at 0.8 μm and 1.57 μm. They were employed as nonlinear saturable absorbers to passively mode-lock the erbium-doped fiber lasers for sub-400 fs pulse generations.(96) Xu, et al. reported that the Bi 2 Te 3 exhibited a nonlinear absorption response. (97) They showed that the Bi 2 Te 3 sheets have saturation absorption intensity of 1.1 W/cm 2 at 1.0 μm. A Q-switching pulsed laser was made in a 1.0 μm Nd:YVO 4 laser where the threshold absorbed pump power was 31 mW. A pulse duration of 97 ns was observed with an average power of 26.1 mW. A Q-switched laser at 1.3 μm was also realized with a pulse duration of 93 ns.
Wavelength-tunable picosecond soliton fiber laser was achieved using topological insulator material Bi 2 Se 3 as a mode locker.(98) An optical pulse with ~660 fs was generated at wavelength of 1.55 μm. A modulation depth of 98% and a saturation intensity of 0.49 GW/cm 2 were observed. Femtosecond pulse was also generated from Bi 2 Se 3 mode-locked fiber laser. (99) The used Bi 2 Se 3 saturable absorber has a low saturable optical intensity of 12 MW/cm 2 and a modulation depth of ~3.9%. The mode-locking operation was realized at 25 mW.
Dou, et al. demonstrated a mode-locked ytterbium-doped fiber laser based on the Bi 2 Se 3. (100) The measured modulation depth of the Bi 2 Se 3 film was 5.2%. When the Bi 2 Se 3 film was used in the Yb-doped fiber laser, the mode locked pulses have pulse energy of 0.756 nJ, pulse width of 46 ps and the repetition rate of 44.6 MHz. The maximum average output power was 33.7 mW. When the pump power exceeded 270 mW, the laser can operate in multiple pulse state that six-pulse regime can be realized.
Yu, et al. showed a high-repetition-rate Q-switched fiber laser using the Bi 2 Se 3 film.(101) The Bi 2 Se 3 film had a low saturable optical intensity of 11 MW/cm 2 . By inserting the absorber film into an Erbium-doped fiber laser, a high-repetition Q-switched laser with the repetition rates from 459 kHz to 940 kHz was made. The maximum output power was 22.35 mW with the shortest pulse duration of 1.9 μs.
Luo, et al. demonstrated that a 1.06μm Q-switched ytterbium-doped fiber laser using few-layer Bi 2 Se 3 as a saturable absorber.(101) The few-layer Bi 2 Se 3 has a low saturable optical intensity of 53 MW/cm 2 . By inserting Bi 2 Se 3 into the YDF laser cavity, stable Q-switching operation at 1.06 μm is achieved. The Q-switched pulses have the pulse duration of 1.95 μs, the pulse energy of 17.9 nJ and a tunable pulse-repetition-rate from 8.3 to 29.1 kHz.
Gao, et al. reported a Q-switched mode-locked erbium-doped fiber laser based on the Bi 2 Se 3 deposited fiber taper. (102) Due to the low saturation intensity, stable Q-switched mode-locked fiber lasers centered at 1.56 μm can be generated at a pump power of 10 mW.
These results exhibit that the topological insulator materials Bi 2 Te 3 and Bi 2 Se 3 are promising optical materials for constructing broadband, miniature and integrated high-energy pulsed laser systems with low power consumption.