Anomalous Anisotropic Magnetoresistance in Topological Insulator Films

Transcription

1 Nano Res. 2012, 5(10): ISSN DOI /s z CN /O4 Research Article Anomalous Anisotropic Magnetoresistance in Topological Insulator Films Jian Wang 1,2 ( ), Handong Li 3,4, Cuizu Chang 5,6, Ke He 5, Joon Sue Lee 2, Haizhou Lu 3, Yi Sun 1, Xucun Ma 5, Nitin Samarth 2, Shunqing Shen 3, Qikun Xue 5,6, Maohai Xie 3, and Moses H. W. Chan 2 ( ) 1 International Center for Quantum Materials, School of Physics, Peking University, Beijing , China 2 The Center for Nanoscale Science and Department of Physics, The Pennsylvania State University, University Park, Pennsylvania , USA 3 Physics Department, The University of Hong Kong, Pokfulam Road, Hong Kong, China 4 State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu, Sichuan , China 5 Institute of Physics, Chinese Academy of Sciences, Beijing , China 6 Department of Physics, Tsinghua University, Beijing , China Received: 28 July 2012 / Revised: 10 September 2012 / Accepted: 13 September 2012 Tsinghua University Press and Springer-Verlag Berlin Heidelberg 2012 ABSTRACT Topological insulators are insulating in the bulk but possess spin-momentum locked metallic surface states protected by time-reversal symmetry. The existence of these surface states has been confirmed by angleresolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). Detecting these surface states by transport measurements, which might at first appear to be the most direct avenue, was shown to be much more challenging than expected. Here, we report a detailed electronic transport study in high quality Bi 2 Se 3 topological insulator thin films. Interestingly, measurements under an in-plane magnetic field, along and perpendicular to the bias current show anomalous opposite magnetoresistance. KEYWORDS Topological insulator, Bi 2 Se 3 film, transport property, magnetoresistance, low temperature 1. Introduction Topological insulators (TIs), materials constituting a new class of quantum matter, have recently attracted much attention in condensed matter physics and materials science [1 23]. In a TI, a finite energy gap in the bulk is crossed by the two gapless surface state branches with opposite spins which are protected from backscattering by time reversal symmetry at the Dirac points. The electron spins in the surface states are perpendicular to their momenta due to the strong spin orbit interaction. In addition to fundamental scientific interest, the topological protection of the surface states can be of interest for spintronics and quantum computation applications [2]. Bi 2 Se 3, a narrow gap semiconductor and thermoelectric material, has been shown to be a three-dimensional (3D) TI with a single Dirac cone [1, 2]. This simple Dirac cone together with the large bulk band gap (0.3 ev, equivalent to 3600 K), make Bi2Se3 a good reference Address correspondence to Jian Wang, jianwangphysics@pku.edu.cn; Moses H. W. Chan, chan@phys.psu.edu

2 740 Nano Res. 2012, 5(10): material for 3D TIs [2]. In spite of existing transport measurements on 3D TIs [12 18], a key feature of the surface state, namely the locking of the spin, and momentum of the conduction electrons [4, 24], has not been directly confirmed. 2. Experimental Recent progress in thin film growth of TIs by molecular beam epitaxy (MBE) [25 37] has made planar TI devices possible. In this work, we measured the transport properties of the MBE-grown high quality Bi 2 Se 3 films at low temperatures under magnetic fields up to 8 T. Our single crystal Bi 2 Se 3 films were grown under Se-rich conditions on high resistivity silicon and sapphire substrates in ultrahigh-vacuum (UHV) MBE systems [27, 29]. More than 10 samples were studied and we will show in this paper data from four typical samples. Results from the other samples show similar and consistent behavior. Sample 1, 2, and 3 are 200 quintuple layers (QLs) Bi 2 Se 3 films grown on high resistivity silicon substrates. Among them, samples 2 and 3 came from same film but with Hall bars patterned along perpendicular crystal axes. Sample 4 is a 45 QL Bi 2 Se 3 film covered by 20 nm thick Se protection layer on the sapphire substrate. Under a field perpendicular to the sample, a large magnetoresistance (MR) was observed. Surprisingly, under an in-plane field parallel to the film sample, the MR was small and positive when the field was perpendicular to the excitation current but negative when the field was parallel to the excitation current. To our knowledge this is a new phenomenon. resistances as a function of magnetic field are shown in Fig. 1(b). The two curves at 1.8 K and 100 K are almost identical. In the low field regime, the Hall resistances are linear. Above 35 koe, the deviation from the linear behavior is obvious. The nonlinear Hall result is likely the consequence of the presence of two channels of carriers in TIs, one from bulk and the other from the surface state [17, 32, 38]. The 3D electron carrier density of sample 1 is ~ cm 3 (2D electron density: cm 2 ) and the electron mobility is cm 2 /Vs at both 1.8 K and 100 K according to the low field Hall results. It is however difficult for us to estimate the ratio between the 3. Results and discussion The resistance of sample 1 (200 nm thick Bi 2 Se 3 ) as a function of temperature is shown in Fig. 1(a). The resistivity of the sample decreases from 125 K to 30 K. Below 30 K, the resistivity increases with decreasing temperature, consistent with previous observations [32]. A high resolution scanning electron microscope (SEM) image of a typical MBE-grown Bi 2 Se 3 film with a thickness of 200 QL is shown in the inset of Fig. 1(a). The inset of Fig. 1(b) is an optical image of the Hall bar measurement structure of sample 1. The Hall Figure 1 Transport property of the sample 1 (200 nm thick Bi 2 Se 3 film). (a) Resistance versus temperature of the sample 1. The left inset is a scanning electron microscope (SEM) image of the Bi 2 Se 3 film. (b) Hall resistance versus magnetic field at 1.8 K and 100 K. The curves at 1.8 K and 100 K are nearly identical. The inset is the optical image of the Hall bar structure. The width of the Hall strip is 400 μm and the distance between two adjacent Hall bars is 650 μm

3 Nano Res. 2012, 5(10): actual 2D surface state carrier density and the 3D bulk carrier density. The MR properties of sample 1 under an in-plane field are shown in Fig. 2. When the field is perpendicular to the current and crystal axis [110] (inset of Fig. 2(a)), the MR is positive (Figs. 2(a) and 2(b)) but ~10 times smaller than the MR when the field is perpendicular to the film. When the in-plane field is aligned along the current direction and crystal axis [110] (the inset of Fig. 2(c)), other than the MR dip around zero field due to weak anti-localization effects [30, 32 34], the MR is negative (Figs. 2(c) and 2(d)). Comparing the MR behavior in perpendicular field, this negative MR effect is ~30 times smaller. Figures 2(b) and 2(d) show a surface plot that summarizes the MR of sample 1 as a function of both the in-plane field (from 80 koe to 80 koe) and temperature (from 1.8 K to 80 K). When the field is transverse to the current (Fig. 2(b)), the MR dip [30, 32 34] at small field decreases with increasing temperature and disappears around 20 K. At larger field, the MR is positive. This positive MR effect weakens gradually with temperature. On the other hand, negative MR is clearly seen when the in-plane field is along the direction of the current (Fig. 2(d)). In this situation, the positive MR dip at low field that exists at low temperature also disappears above 20 K. Near and above 50 K, a gradual positive MR is found at low field which evolves to negative MR at higher fields near and above 40 koe. In order to determine if this anisotropic MR phenomenon is related to the orientation of the crystal axes, a control experiment was carried out with samples 2 Figure 2 In plane magnetoresistance of sample 1 (200 nm thick Bi 2 Se 3 film). (a) The magnetic field is perpendicular to the current direction and crystal axis [110] of sample 1 at 1.8 K. (b) Three-dimensional image of the magnetoresistance at different temperatures when the field is perpendicular to the current. (c) The magnetic field is parallel to the current direction and crystal axis [110]. (d) Threedimensional image of the magnetoresistance at different temperatures when the field is parallel to the current

4 742 Nano Res. 2012, 5(10): and 3, which are from same 200 QL Bi 2 Se 3 film on a silicon substrate. The 3D carrier density of sample 2 is cm 3 (2D density: cm 2 ) and the mobility is 3240 cm 2 /Vs at 1.8 K. For sample 3, the 3D carrier density calculated by low field Hall resistance is cm 3 (2D density: cm 2 ) and the mobility is 2490 cm 2 /Vs. In sample 2, the current is along the crystal axis [110] and perpendicular to [110] (see insets of Figs. 3(a) and 3(b)). In sample 3, the current is along [110] and perpendicular to [110] (see insets of Figs. 3(c) and 3(d)). Irrespective of the crystal orientation, when the field is perpendicular to the current, the MR is positive and when the field is parallel to the current, the MR is negative (see Fig. 3). Thus, we found that the transition from positive MR to negative MR is not due to the different crystal axis but the relative direction between the field and current directions. In order to ascertain if our observations are universal, we measured a 45 QL Bi 2 Se 3 film grown on sapphire (instead of Si) substrate covered by 20 nm thick Se protection layer (sample 4) see Fig. 4. A scanning tunneling microscope (STM) study of the film exhibits atomically flat terraces with 1 QL layer thick steps, which demonstrates the high crystal quality of the film (see Fig. 4(a)). The angle-resolved photoemission spectroscopy (ARPES) band map of sample 4 shows a single Dirac cone with the Dirac point located at ev below the Fermi level, which indicates a clear TI surface state of sample 4 (see Fig. 4(b)). The Hall structure of this sample for the transport measurement is much narrower than the Hall structures of samples 1 3. The width of the Hall structure is 40 µm and the distance between two adjacent Hall bars is 400 µm (see the inset of Fig. 4(c)). The 3D carrier density calculated by low field Hall resistance is cm 3 Figure 3 In plane magnetoresistance of samples 2 and 3 (these two samples are from the same 200 nm thick Bi 2 Se 3 film). (a) The magnetic field is perpendicular to the current and crystal axis [1 10] of sample 2 at 1.8 K. (b) The field is parallel to the current and crystal axis [1 10] of sample 2. (c) The magnetic field is perpendicular to the current direction and crystal axis [110] of sample 3. (d) The magnetic field is parallel to the current direction and crystal axis [110] of sample 3

5 Nano Res. 2012, 5(10): (2D density: cm 2 ) and the mobility is 1230 cm 2 /Vs at 1.8 K. When the in-plane field is perpendicular to the measuring current, the MR is positive (Fig. 4(c)). This observation is consistent with that found in samples 1 3. The positive MR weakens with increasing temperature. For example, the change in resistance from zero to 80 koe at 100 K is almost five times smaller than that at 1.8 K (Fig. 4(c)). When the in-plane field is along the measuring current, the MR is positive below 35 koe and negative above 35 koe (Fig. 4(d)) at 1.8 K. With increasing temperature, the positive MR, while weakened, is extended to higher magnetic field. At 200 K, positive MR is observed up to 80 koe before the appearance of negative MR behavior (Fig. 4(d)). It is interesting that when the bias current is parallel to the field direction, negative MR is eventually observed at a sufficiently high and temperature dependent magnetic field. This behavior is qualitatively consistent with that observed in the 200 QL samples presented above. We now develop an empirical interpretation of our principal observation: namely, we find an anisotropic MR for in-plane magnetic field, independent of the crystal axes but dependent on the relative direction Figure 4 Results from sample 4 (45 nm thick Bi 2 Se 3 ). (a) A typical scanning tunneling microscope (STM) image of sample 4. (b) Angle-resolved photoemission spectroscopy (ARPES) data for the surface state of sample 4. (c) In plane magnetoresistance at different temperatures when the field is perpendicular to the current. The inset is an optical image of the Hall bar measurement structure. The width of the Hall strip is 40 µm and the distance between two adjacent Hall bars is 400 µm. (d) In plane magnetoresistance at different temperatures when the field is parallel to the current

6 744 Nano Res. 2012, 5(10): of the field and the current. Before seeking an explanation related to the TI surface state, we first rule out simpler explanations by contrasting our observations with the anisotropic MR occasionally found in conventional narrow band gap semiconductors that have a strong spin orbit coupling. Such semiconductors are well-known to have spin-momentum locking in the bulk Rashba states but do not possess a symmetrydriven Dirac cone surface state. The surface states of a topological insulator can be seen as a Rashba model with vanishing kinetic energy or with an infinite mass and very large Rashba coefficient, large enough to split one of the two bands completely away from the Fermi energy. For conventional semiconductors with the Rashba splitting, the two Fermi surfaces always have opposite chiralities (spin-momentum locking) due to the time-reversal symmetry. Therefore, the responses of two Fermi surfaces to in-plane Zeeman fields are always opposite. As a result, the effects of the in-plane magnetic fields on two Fermi surfaces will be largely cancelled. While for the surface states, there is always only one surface. This is the major difference between conventional semiconductors and the topological surface states. We are aware of one such detailed study [39] that examined the MR in InSb thin films with magnetic field and current in the relative configurations identical to those presented here. Importantly, these measurements showed no qualitative anisotropy for an in-plane field parallel and perpendicular to the current density: While either positive or negative in-plane MR was observed with a complex dependence on film thickness and temperature, qualitatively identical MR was always seen in both in-plane field-current configurations. This suggests that the observed anisotropy in our samples is unlikely to have either a classical (skipping orbits) or quantum (weak localization) explanation based upon Lorentz force considerations alone. In a transport measurement configuration, the collective spin polarization of the TI surface state is aligned by the current [20]. When the field is perpendicular to the current, it is parallel to the spin polarization direction. Conversely, when the field is along the current, it is perpendicular to the spin polarization of surface current. However, this simple argument does not account for the anisotropic MR in the present observation explicitly, because the Zeeman coupling of an in-plane field in an ideal Dirac cone of the surface states does not produce any MR effect. The hexagonal warping effect or snowflake Fermi surface for the surface states [40] may provide a possible mechanism to produce an anisotropic negative MR, which depends on the relative direction between the current and the magnetic field. The Lorentz force deflects the surface electrons, leading to a positive MR from the classical galvanomagnetic effect (Figs. 2(a), 2(b), 3(a), 3(c), and 4(c)). The effect from the angle between the spin polarization of surface current and magnetic field direction appears to overcome the positive MR effect resulting in negative MR behavior in addition to the MR dip induced by possible weakanti localization. In some samples with suitable experimental configurations, as in our 200 QL samples, negative MR behavior is observed at very low field parallel to the bias current, while in other samples such as the 45 QL sample, positive MR is observed at low field but switches over to negative MR at a sufficiently high field. The mobility of the 200 QL samples (2490 cm 2 /Vs and cm 2 /Vs) is more than twice of the 45 QL sample at 1230 cm 2 /Vs. 4. Conclusions Our interpretation of the anisotropic MR in terms of spin-momentum locked surface currents is very speculative although it is consistent with our previous findings showing that current flow strongly suppresses the superconductivity in mesoscopic electrodes in superconductor-ti film systems [24]. A thorough understanding of the results presented here may require the treatment of the collective effect of the surface and bulk states, higher-order corrections for the surface states and also orbital effects. Additional insights will also require measurements of the angular dependence of the MR, as well as measurements in electrically-gated samples wherein the fermi level can be varied. Finally, it would be useful to compare the behavior observed here to that in other thin film materials with strong spin-orbit coupling, such as InAs and Bi.

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