Title Page

Abstract

Contents

1. Introduction 16

1.1. Topological insulator 16

1.1.1. Weak localization and weak antilocalization 17

1.1.2. Aharonov-Bohm oscillation in topological insulator 19

1.2. Superconductivity 21

1.2.1. Josephson junction 21

1.2.2. RCSJ model of Josephson junction 22

1.2.3. Escaping mechanism of the phase particle 23

1.2.4. Andreev Bound States 26

1.2.5. Superconducting quantum interference devices 28

1.3. Topological superconductivity 30

1.3.1. Brief introduction to the Majorana Bound states 30

1.3.2. Fractional Josephson effect 34

2. Fabrication and measurement 35

2.1. Device fabrication 35

2.1.1. Nanowire/nanoribbon transfer to substrate 35

2.1.2. Electron beam lithography 36

2.2. Low temperature measurement 39

2.2.1. Cryostat and ³He refrigerator 39

2.2.2. Cryogen-free dilution refrigerator 40

3. Part I: Zero bias conductance peak in InAs nanowire coupled to superconducting electrodes 42

3.1. Introduction 43

3.2. Fabrication and measurement 44

3.3. Results and discussion 45

3.3.1. Conduction type of InAs nanowire 45

3.3.2. General electrical transport characteristics of InAs nanowire 45

3.3.3. Bias voltage and temperature dependence of ZBCP 47

3.3.4. Magnetic field dependence of ZBCP 48

3.4. Conclusion 50

4. Part II: Superconducting quantum interference devices made of Sbdoped Bi2Se₃ topological insulator nanoribbons 51

4.1. Introduction 52

4.2. Fabrication and measurement 54

4.3. Result and discussion 56

4.3.1. General electrical transport characteristics of Bi2Se₃ nanoribbon 56

4.3.2. Magnetic field modulation at T＝2.4 K 57

4.3.3. Current bias dependence at T＝2.4 K 59

4.3.4. Magnetic field modulation at T＝0.3 K 59

4.3.5. Current bias dependence at T＝0.3 K 60

4.3.6. Voltage modulation at higher magnetic field 61

4.4. Conclusion 63

5. Part III: Anomalous temperature dependence of Shapiro steps in Josephson junction of topological nanoribbon 64

5.1. Introduction 65

5.2. Fabrication and measurement 65

5.3. Result and discussion 67

5.3.1. Characteristic of Bi2Se₃ nanoribbon 67

5.3.2. Basic properties of Josephson junction 68

5.3.3. Frequency dependence of AC Josephson effect 70

5.3.4. Temperature dependence of AC Josephson effect 72

5.3.5. Step-width ratio △I1,max/△I2,max[이미지참조] 74

5.3.6. Magnetic field dependence 75

5.4. Conclusion 76

6. References 77

Curriculum Vitae 88

Table 4-1. Physical parameters of the SQUIDs: w (t) is the width (thickness) of TI NR. L1 and L2 are the channel length of each Josephson junction. LS and WS are the length and width of the SQUID, respectively. Tbase is the base temperature for IC measurement.[이미지참조] 55

Figure 1-1. (a) Topologically protected surface state by band inversion of the edge mode. In edge state dispersion, the up (blue) and down (green) spins propagate in opposite directions. (b) Dirac cone of the 3D TI with topological... 17

Figure 1-2. Schematics of time reversed paths for two electron waves in a diffusive system (a) in absence of spinorbitcoupling and (b) in presence of spin-orbit coupling. (c) Magnetoconductance curves for WL (red) and WAL (blue). 18

Figure 1-3. (a) A schematic of electron path for AB effect. Interfering trajectories cause h/e oscillation. (b) magnetoconductance curve which shows the maximum value at Φ＝nΦ0.[이미지참조] 19

Figure 1-4. Schematic of 1D subbands in TI NR (a) Gap opening by spin Berry phase π. The gap size of the 1 Dsubb and is △1DD＝hvF/Lpp. (b) Gapless 1D mode[이미지참조] 20

Figure 1-5. Schematic of a Josephson junction, SL and SR are the left and right superconductors with |𝛹L|e-iφL and |𝛹R|e-iφR, respectively.[이미지참조] 21

Figure 1-6. (a) Equivalent circuit for the Josephson junction in the RCSJ model. (b) Washboard potential as a function of phase difference varying the bias current. 23

Figure 1-7. Representative I-V curves for a Josephson junction in the case of (a) overdamped junction and (b) underdamped junction. 23

Figure 1-8. (a) Schematic diagram of the tilted-washboard potential. Phase particles can escape the potential well via the three different types of processes. (b) Temperature dependence of the escaping rate. 25

Figure 1-9. (a) Schematic of an N-S interface. The superconducting electrodes have a gap (2△BCS) in their density of state (DOS). In N regime, a right moving electron (filled) is back reflected as a hole (open) with opposite spin. At... 27

Figure 1-10. Andreev Bound State energy-phase spectrums with varying the transparency: τ＝0.1 (black), 0.5 (red), 0.8 (blue), 0.98 (green), 1 (magenta). The ground (excited) state E-(E+) is plotted as dashed (solid) line. 27

Figure 1-11. (a) A Schematic of DC SQUID under the external magnetic flux penetrating the loop. (b) Plot of current vs. voltage characteristic of a SQUID (Left). Upper and lower curves correspond to (n+1/2)Φ0 and nΦ0 with the...[이미지참조] 29

Figure 1-12. Schematic of Kitaev model (a) The fermion operator Cj is consist of two Majorana fermion operator on the same site. (b) In the limit of -|△|＝t and μ＝0, two neighboring operators, γ, are coupled leaving two unpaired... 32

Figure 1-13. (a) A Schematic of a topological Josephson junction with MFs. (b) Energy-phase relation of MBS with odd (blue) and even (red) parity. 33

Figure 2-1. (a) An optical microscope image of as-grown Sb-doped Bi2Se₃ topological insulator nanoribbons (b) Optical microscope with XYZ micro-positioner and edge of the tungsten tip with a nanoribbon. 35

Figure 2-2. Standard electron beam lithography system consisting of FE-SEM (Tescan-MIRA3) and Elphy quantum(RAITH) 37

Figure 2-3. Schematic of e-beam lithography process. (a) Transferring nanowire/nanoribbon onto the silicon substrate (b) PMMA coating (c) E-beam expose (d) Ar+ milling (e) Metal evaporation (f) Lift-off 38

Figure 2-4. Cryogen-Free 4 K cryostat with magnet (Seongwoo Instruments Inc.) 39

Figure 2-5. (a) Cryogen Free Measurement System (CFMS, Cryogenic) (b) Sample holder and He-3 insert (300 mK) 39

Figure 2-6. Cryogen-free dilution refrigerator system (CFDR, BlueFors Cryogenics) 40

Figure 2-7. (a) Schematic circuit diagram (b) Real PCB boards of 3 stage RC-π filter (c) Coldfinger with multiple-stage filtering system 41

Figure 3-1. SEM image of the InAs NW device (D1) with the typical measurement configuration. The current bias I is applied between two PbIn electrodes (+I and -I) through the InAs NW, and the voltage V is monitored between the... 44

Figure 3-2. Differential conductance G of sample D2 with the back-gate voltage Vg at T＝10 K. Vg was applied to the Si substrate, and the source-drain bias voltage was VSD＝1 mV[이미지참조] 45

Figure 3-3. (a) R vs. T plot obtained from sample D1. The superconducting transition temperature was TC＝7.3 K. The red solid line represents the fitting result (see text). (b) Normalized conductance (G) as a function of V at T＝2.4...[이미지참조] 46

Figure 3-4. (a) Lock-in voltage (Vac) dependence of the ZBCP at T＝2.4 K. From top to bottom, Vac＝3.9 μV (black), 11 μV (red), 22 μV (blue), 130 μV (green), and 310 μV (magenta). The curves are offset for clarity. (b) Temperature...[이미지참조] 48

Figure 3-5. (a) G vs. V curve with varying magnetic field at T＝2.4 K. From top to bottom, B＝0 mT (black), 14 mT (red), 25 mT (blue), 29 mT (green), and 34 mT (magenta). The curves are offset for clarity. (b) Zero-bias conductance... 49

Figure 4-1. (a) SEM image of the Sb-doped Bi2Se₃ NR. Inset: Tilted-SEM image of the NR. Scale bar is 500 nm. (b) Energy-dispersive X-ray spectroscopy (EDX) for the Sb-doped Bi2Se₃ NR. The atomic percentage is obtained 36.3... 55

Figure 4-2. (a) MC, △σ＝σ(B)-σ(0), curves at various magnetic field orientations, as a function of perpendicular magnetic field component, Bsinθ (sample D1). The solid line is the best fit to the Eq. (1). (b) MR curve under the... 57

Figure 4-3. (a) Current-voltage (I-V) curves for different magnetic fluxes through the TI-NR SQUID loop at T＝2.4 K (sample Sq2). Inset: Schematic of TI-NR SQUID. (b) Color plot of dV/dI as a function of bias current and magnetic... 58

Figure 4-4. (a) Voltage modulation as a function of Φ/ΦS under a dc current bias of Idc＝0.2 μA (black), 0.4 μA (red), 0.6 μA (blue), 0.8 μA (green) and 1.0 μA (magenta), respectively. (b) Squid sensitivity as a function of Idc. Error bars...[이미지참조] 59

Figure 4-5. (a) I-V curves of device Sq4 at various magnetic fluxes at T＝0.3 K. (b) Color plot of dV/dI as a function of Idc, B, and Φ/ΦS. The white line is calculation results using Eq. (2) considering IC asymmetry.[이미지참조] 60

Figure 4-6. (a) Output voltage as a function of Φ/ΦS with Idc＝2.8 μA (black), 4.9 μA (red), 7.0 μA (blue), 7.7 μA (green) and 8.4 μA (magenta), respectively. (b) SQUID sensitivity as a function of Idc.[이미지참조] 61

Figure 4-7. (a) Voltage modulation of Sq2 as a function of B field at T＝2.4 K. Inset: FFT analysis of V(B) modulation. (b) Magnetic field dependence of IC of Sq2. Solid line is a fitting result using Eq. (4.3) (see text). 62

Figure 5-1. (a) SEM image of the TI NR junction used for δG(Baxial) measurement. The external magnetic field was aligned along the NR axis. (b) The conductance difference δG(Baxial) curve obtained from long junction, after...[이미지참조] 67

Figure 5-2. (a) SEM image of the Sb-doped Bi2Se₃ NR Josephson junction contacted with PbIn superconducting electrodes. A current bias was applied from +I to -I and the voltage difference was measured between +V and -V.... 68

Figure 5-3. (a) I-V characteristics of TI NR Josephson junction measured at T＝0.01 and 7.2 K, respectively. The excess current, which is the zero-voltage crossing point extrapolated lined of the I-V curve from the high-bias region,... 69

Figure 5-4. The microwave frequency fmw dependent color plots as a function of dc voltage and microwave power for (a) fmw＝1.58 GHz (b) 2.32 GHz (c) 2.6 GHz at T＝10 mK. (d-f) Current step sizes △In (n＝0, 1, 2, 3, and 4) of...[이미지참조] 71

Figure 5-5. Temperature dependent color plots for (a) 0.8 K, (b) 1.0 K, (c) 1.2 K, and (d) 1.5 K, the microwave frequency is fixed at 1.58 GHz. Bottom, current step size line plots as a function of rf power for each temperature... 72

Figure 5-6. Temperature dependent color plots for (a) 0.8 K, (b) 1.0 K, (c) 1.2 K, and (d) 1.5 K, the microwave frequency is fixed at 2.32 GHz. Bottom, current step size line plots as a function of rf power for each temperature... 73

Figure 5-7. Temperature dependent color plots for (a) 0.6 K, (b) 1.0 K, (c) 1.2 K, and (d) 1.5 K, the microwave frequency is fixed at 2.6 GHz. Bottom, current step size line plots as a function of rf power for each temperature... 73

Figure 5-8. (a) Step-width ratio △I1,max/△I2,max as a function of temperature for different microwave frequency. (b) △I1,max/△I2,max based on the axial magnetic field with fixed fmw＝2.32 GHz at T＝20 mK. Inset: Axial magnetic field...[이미지참조] 74

Figure 5-9. Axial magnetic field dependent color plots for (a) 0.01 T, (b) 0.03 T, (c) 0.05 T, and (d) 0.07 T at T＝20 mK. The microwave frequency was 2.32 GHz. Bottom, line plots of the current step size for n＝0, 1, 2, 3, and 4... 75