1. One-dimensional topological edge states of bismuth bilayers
Author: Iiya K. Drozdov, A. Alexandradinata, Sangjun Jeon, Stevan Nadj-Perge, Huiwen Ji, R. J. Cava, B. Andrei Bernevig and Ali Yazdani
Present: Yuqin Sophia Duan

2. Background Quantum Spin Hall Effect Bi bilayer vs. graphene
Top View
Quantum Spin Hall Effect
Bi bilayer vs. graphene
Strong spin-orbit coupling
Side View

3. motivation
Conductance: only showed by semiconducting heterostructures in the topological phase
Experiments on Bi suffered from an irregular structure of their edges

4. Experiment Single Bi crystal growth using the Bridgeman method
STM Measurement
Atomic structure of Bi-bilayer in (111) plane

5. experiment Simulation:
Hybridization calculation of edges based on Liu-Allen model & ab initio1
Type-A edge has less bonds with the substrate;
Type-B has direct hoppings to the substrate

6. Stm measurement

7. conductivity
dI/dV spectra were acquired using a lock-in amplifier at f = 757 Hz.
Type A show clear signature of 1D edge state, next we will look at its connection to the bulk electronic state of Bi bilayer.

8. Conclusion: Propagating 1D edge state is similar to the prediction for free-standing Bi bi-layer.
To determine whether the 1D edge states have the predicted topological properties of free-standing Bi bilayer, they further examine the scattering properties.
STM maps obtained along a line perpendicular to the edge & along the edge

9. Scattering properties
The topological nature of the two edge modes, reflected in their spin properties allow scattering only between the states of similar spin
Spatial 1D Fourier transform of the conductance map along the type A atomic step edge
Wavefactors q = kf – k1

10. Dispersion and spin texture
Spin expectation values for the top branch are plotted as a function of momentum.
Employ Liu-Allen tight-binding model, but with a self-consistent Hartree term

11. Summary
Strong suppression of the backscattering wavevector q*
Experimentally characterized properties of q1 scattering channel
Model calculation for a Bi bilayer
Type A zigzag edges behave in a manner similar to free-standing Bi-bilayer quantum spin Hall system