Bulk Single crystals

All the single crystal samples are provided by our collaborator (Dr. F.C. Chou’s laboratory at National Taiwan University). Bulk single crystals are first shaped into appropriate size and shape. Conventional 4-probe measurement is used for measuring resistivity and Hall effect (see Fig. 2.3a). The resistance R = ^V_I = ρ_w^ℓ_·t, where V is the voltage drop between voltage leads, I is the applied current, ρ is resistivity, ℓ is the distance between voltage leads, w is the width of sample, and t is the sample’s thickness. In order to maximize the measured signal V and also for the convenience of sample mounting, sample size is typically about 1∼5 mm in length, 1∼3 mm in width, and the thickness is usually the thinner the better. The samples are first cut into a slab with appropriate length and width by diamond saw, and then milled to desired thickness by sand paper. Some soft samples can be easily cleaved and shaped by razor blade into appropriate dimensions. The shaped sample is thermally anchored onto sapphire substrate using thermally conductive grease (Apiezon-N), and the sapphire substrate is again thermally anchored onto sample stage by the same grease. Sapphire is chosen because of it’s excellent thermal conductivity and electrical insulation. Fine gold wires (1 or 2 mil) are thermal anchored on sapphire substrate using silver epoxy (Epotek H20E). One end of the gold wires are attached to sample and the other to the probe using silver paint (SPI Supplies) as shown in Fig. 2.3.

If care is taken in all steps, contact size smaller than 300µm, contact resistance lower than 50Ω can be achieved.

For electrical transport measurements the resistivity tensor ρ_ij can be determined through

E_i = ρ_ijJ_j, (2.1)

where E_i is the measured electric field, and J_j the input current density. Note that we define z-axis as out-of-plane direction, and xy plane as in-plane, with i, j = (x, y). By

)b* 3nn )c*

5nn

Figure 2.3: (a)A photo showing two bulk single crystals connected to superconducting magnet sample probe by wire binding techniques described in the main context. The two black thin flakes in the center of picture with shining surfaces are single crystals to be measured. The transparent square substrate beneath them is sapphire, it was chosen for it’s excellent thermal conductivity and electrical insulation. The 16 leads surrounding the sapphire are probe leads made of phosphor bronze, and they are connected to the crystals through gold wires. (b)A photo of the front part of sample probe. The sample stage can be fixed at arbitrary angle with respect to field direction, as shown in the photo.

convention, x is defined as the current direction. For isotropic systems, ρxx = ρyy and ρxy = −ρyx. In this thesis, the in-plane resistivity parallel to current is denoted by ρxx

and the Hall resistivity (resistivity in-plane and transverse to current) is denoted by ρyx. The main difficulty in identifying the surface states of Bi2Se3is that the Fermi surface often lies inside bulk conduction band. We have tried to grow single crystals by melt growth, Bridgman method and vapour transport (CVT) (table 2.1 and table 3.1) under different temperature gradients. However, Fermi surface in those samples are still in the bulk conduction band. We have tried several other attempts on tuning the Fermi surface into the bulk band-gap. One of the attempts is through doping. It has been reported that calcium doping can tune the Fermi surface into bulk band-gap without degrading the surface states [13]. The resistivity of the doped single crystals show non-metallic temperature dependence and the value at 4K is two orders of magnitude larger than the undoped Bi2Se3 [26]. Another attempt is to increase the ratio of selenium in the Bi2Se3

Topological Insulator Sample List

Chemical Formula Batch Number Growing Method

Bi2Se3 RS-210-B1 Bridgman

Bi₂Se₃ KK01017B Bridgman

Ca0.005Bi2Se3 RS-1275-B1 Melt growth

Ca_0.2Bi₂Se₃ RS-1277-B1 Melt growth

Bi2Se3 RS-210-B1-A Bridgman

Bi₂Se_3.05 RS-210-B1-B Bridgman

Bi2Se3.10 RS-210-B1-C Bridgman

Bi₂Se_3.15 RS-210-B1-D Bridgman

Bi2Se3.20 RS-210-B1-E Bridgman

Bi₂Te₂Se RS-2116-B1 Bridgman

Table 2.1: A list of the batch numbers and growing methods of the topological insulator crystals presented in this thesis.

crystals. It was suggested in some papers that the n-type doping in as-grown Bi₂Se₃ is mainly caused by selenium vacancies [43] and the carrier concentration can be varied by adding excess amount of selenium [44, 23]. Table 2.1 is a list of the batch numbers and growing methods of the topological insulator crystals presented in this thesis. Our goal is to prepare a crystal that has high mobility and in-gap Fermi level, which allows us to identify the surface states through quantum oscillations. Recently, it was reported that Bi₂Te₂Se is a chemically more stable topological insulator [45]. This compound is formed by substituting the selenium at the quintuple layer boundary (Se1 and Se1’ in Fig.1.3c) in Bi₂Se₃with tellurium atoms. Selenium atoms tend to escape Bi₂Se₃crystals, leaving behind vacancies at the boundary of quintuple layers. This problem is much less severe if the boundary atoms are tellurium, which is also less sensitive to air compared with selenium. Therefore, Bi₂Te₂Se is chemically more stable than Bi₂Se₃. Fermi surface of the as-grown Bi₂Te₂Se is in the bulk band-gap, and the RT curve shows non-metallic behavior [29, 28]. We have recently succeeded in growing such non-metallic crystals.

The transport data of all the crystals listed in table 2.1 will be given in section 3.1.

Misfit Compound Sample List

Chemical Formula Batch Number Growing Method

(SnS)(TaS2) RS-1115-B1 CVT

(SnS)(TaS₂)₂ RS-1120-B1 CVT

(PbSe)(TiSe2)2 RS-1142-B1 CVT

Table 2.2: A list of the batch numbers and growing methods of the misfit compounds presented in this thesis.