THz Generation and Detection on Dirac Fermions in Topological Insulators

Abstract

THz radiation is generated from topological insulators using femtosecond laser pulses. Two-channel free carrier absorption with bulk and surface carriers is indispensable to explaining the strong dependence of THz emission power on the carrier concentration. The characteristics of THz emission provide valuable information regarding the fundamental properties of Dirac fermions. Three-dimensional topological insulators (TIs) are characterized by a narrow bandgap in the bulk and a Dirac cone-like conducting surface state.1-3 The surface state is a new state of quantum matter caused by a strong spin–orbit interaction and protected by time-reversal symmetry. The special properties of TIs have applications in spintronics and quantum computations. Certain TIs with a small bandgap are especially useful for terahertz (THz) optoelectronics. One of the key issues regarding TIs has been the identification of the gapless surface electronic states (Dirac fermions) and the characterization of their fundamental properties. Angle-resolved photoemission spectroscopy (ARPES)1, 4-6 and scanning tunneling microscopy (STM)7-10 have successfully confirmed the existence of Dirac fermions in Bi1-xSex, Bi2Se3, and Bi2Te3. Regarding the transport measurements, a metallic channel associated with the protected surface state has been detected by either controlling the gate voltage in TI devices with a sufficiently low bulk carrier density or by using very thin TI films.11-14 However, these experiments used particularly specialized instruments, and their procedures are excessively complex for quick and routine characterizations of Dirac fermions in TIs. Hsieh et al.15 presented an alternative approach using second harmonic generation (SHG) in arsenic-doped Bi2Se3 single crystals associated with Dirac fermions, providing a new venue for examination of Dirac fermions by contact-free optical techniques. However, SHG is highly sensitive to the surface quality of samples and doping. In principle, THz waves with long wavelengths may be an ideal tool for distinguishing Dirac fermions from bulk carriers because they are not sensitive to the surface quality of the samples. Furthermore, THz waves have a photon energy level (approximately 4 meV) that is significantly lower than the bulk gap (approximately 300 meV) of TIs; thus, THz radiation would allow specific characterizations within the Dirac cone. Aguilar et al.16 recently showed the THz responses of Dirac fermions in Bi2Se3 thin films. However, this type of THz experiment can only be applied to thin TIs with several tens of quintuple layers. The present study describes THz generation from pure Bi2Se3 and Cu-doped Bi2Se3 single crystals by femtosecond laser pulse pumping. Dirac fermions were seen to play an indispensable role on the intensity of THz emissions. Moreover, free carrier absorption is a crucial mechanism to the optoelectronic devices of TIs and is revealed by the dependence of the generated THz power on the carrier concentration.17 Single crystals of pure Bi2Se3 and Cu-doped Bi2Se3 were grown using either the Bridgeman, melt growth, or CVT methods.18 Single crystals of CuxBi2Se3 were obtained using a slow-cooling method from 850 to 650 °C at a rate of 2 °C/h followed by quenching in cold water. Scotch tape was used to cleave the (001) surface of the Bi2Se3 crystals to ensure a flat and bright surface for optical measurements. The carrier concentrations of the samples listed on Table 1 were obtained using the Hall measurements. The mobility was measured using the four-probe method. A reflection-type THz generation scheme was used to generate a THz wave on the TIs, as shown in Figure 1a and the inset of Figure 1b. An 800 nm Ti:sapphire laser (FemtoLasers, Inc.) beam with a repetition rate of 5.2 MHz and a pulse duration of 50 fs was incident at θ = 45° (to the surface normal) and focused on the surface of the samples with a diameter of 43 μm. The pumping fluence was tuned by varying the laser output power (the typical value for this study was 0.37 mJ/cm2). Following femtosecond pulse pumping, the generated THz wave was collected using a pair of off-axis parabolic mirrors and focused on a 1-mm-thick ZnTe crystal to allow its detection with electro-optical (EO) sampling.19 The entire generation and detection systems were sealed in a nitrogen-filled plastic box to reduce the humidity to <6.0%. All optical measurements were performed at room temperature. Figure 1b shows the typical THz waveform generated from pure Bi2Se3 and Cu-doped Bi2Se3 single crystals with a reflection-type setup (THz radiation cannot be detected after TIs). The amplitude of the THz wave generated from pure Bi2Se3 single crystals is significantly smaller than that from a Cu0.02Bi2Se3 single crystal. Certain Bi2Se3 crystals, such as sample #1, produce nearly zero amplitude (below the S/N ratio in the detection system). The THz generation intensity is strongly dependent on carrier concentration and doping. In general, the THz waveform is composed of a large single pulse and a damped oscillation, which is due to the optical-group-velocity/THz-phase-velocity mismatching and the dispersive phonon-polariton propagation.20 Time-domain THz waveforms (Figure 1b) can be converted to frequency domain spectra (Figure 2) by using fast Fourier transform (FFT). The central frequency for Cu0.02Bi2Se3 and bandwidth are approximately 1.2 THz and 1.6 THz, respectively. The intensity of pure Bi2Se3 THz spectra is relatively small, corresponding to small THz signals in the time domain. The THz signals were measured at various azimuth angles φ along the surface normal to understand the THz generation mechanism in TIs (inset of Figure 1b). The THz peak amplitude is virtually independent of φ and at odds with the optical rectification simulation curve with six-fold symmetry (see Supporting Information).21 Therefore, optical rectification is not the dominant mechanism for THz generation in TIs, and the nonlinear effect is not the main contributor to THz generation in TIs. The bandgap of 0.3 eV in Bi2Se3 is significantly smaller than the pumping photon energy of 1.55 eV. Free carriers are generated when the femtosecond laser illuminates Bi2Se3 or Cu-doped Bi2Se3 crystals. These excited carriers are located inside the bulk within 100 nm below the surface.22 When an electric field is built inside the crystals, the excited carriers in the bulk are driven and form the currents. Two types of built-in electric fields are normally present in semiconductors. The surface depletion field results from the bending of the conduction band on the semiconductor surface as in GaAs.23 The photo-Dember field is caused by the inhomogeneous distribution of holes and electrons,24 which is usually present in narrow-bandgap semiconductors, such as InAs and InSb with respective bandgaps of 0.35 eV and 0.17 eV. The bandgap is approximately 0.3 eV for Bi2Se3 single crystals, which is close to that of InAs (reference sample in Figure 1). In addition, an intrinsic charge inhomogeneity was found in the vicinity of the surface along with the resulting band-bending effects.25 Consequently, both photo-Dember and surface depletion effects are possible mechanisms for THz generation in Bi2Se3 and Cu-doped Bi2Se3 single crystals. The currents formed by the excited carriers are suppressed within several picoseconds, due to carrier scattering with impurities (e.g., Se vacancies) or with the layer boundary. The transient current further generates THz radiation by ETHz(t)∝∂J(t)/∂t. Higher pumping fluences generate more free carriers, leading to larger changes of the transient current; thus a stronger THz radiation should be generated. The THz peak amplitude increases linearly with the pumping fluences (inset of Figure 2).26 Table 1 shows that the carrier concentration decreases by more than one order of magnitude when Cu is doped into Bi2Se3 crystals (n-type, caused by Se vacancies).27-29 Carrier concentrations from 15.6 ± 10.3 × 1018 cm−3 to 75.5 ± 13.6 × 1018 cm−3 were observed for the pure Bi2Se3 crystals, potentially because of the different growing conditions and methods.The THz signals from pure Bi2Se3 crystals are generally relatively small. Conversely, the Cu0.02Bi2Se3 crystal with a lower carrier concentration produces a stronger THz emission than pure Bi2Se3 crystals. The spectral weight of the FFT spectra in Figure 2 was plotted as a function of the carrier concentration to further quantify these results. Figure 3 clearly shows that the THz output (i.e., the spectral weight of the FFT spectrum) increases as the carrier concentration decreases. The screening of the drift-diffusion current was considered for THz generationin the InAs case.33 However, the bulk carrier mobility in Bi2Se3 (≤1500 cm2/Vs) is much smaller than that in InAs (∼33 000 cm2/Vs). The current screening effect can be neglected in the present case. In summary, THz radiation can be generated from Bi2Se3 and Cu-doped Bi2Se3 single crystals. Dirac fermions of the surface state are indispensable to explaining the strong dependence of the THz emission power on the carrier concentration. Furthermore, the detailed characteristics of the THz emission provide valuable information regarding the fundamental properties of Dirac fermions. This work was supported by the National Science Council of Taiwan under grant: Nos. NSC101–2112-M-009–016-MY2, NSC101–2112-M-009–017-MY2 and NSC 100–2112-M110–004-MY3, and by the MOEATU program at NCTU of Taiwan, R.O.C. Technical help from C. K. Wen and discussions with H. T. Jeng and T. M. Uen are appreciated. 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