Topological phases 2

Presentation Title

Author· 28. November 2017

Institute· University

Overview TEX

1. Topological phases 2. 1D p-wave superconductor

Topological Phases

3 ^Author· Presentation Title QAHE

k E

k

E QSHE

k E

k E

Conducting edge channels ←→ Non-trivial bandstructure

Topological Phases TEX

QAHE

k E

k

E QSHE

k E

k E

Conducting edge channels ←→ Non-trivial bandstructure QAHE bulk Hamiltonian bH(k) = g(k) · σ

g(kx, ky) = (sin kx,sin ky,cos kx + cos ky − M)^|

Topological Phases

3 ^Author· Presentation Title QAHE

k E

k

E QSHE

k E

k E

Conducting edge channels ←→ Non-trivial bandstructure QAHE bulk Hamiltonian bH(k) = g(k) · σ

g(kx, ky) = (sin kx,sin ky,cos kx + cos ky − M)^|

M= 1 non-trivial

M= 3 trivial

1D p-wave superconductor TEX

Lattice H =

n−1

X

i=1

htc_i^†c_i+1+ ∆c_ic_i+1+ H.c.i

− µ Xn

i=1

c_i^†c_i

… …

1D p-wave superconductor

4 ^Author· Presentation Title

Lattice H =

n−1

X

i=1

htc_i^†c_i+1+ ∆c_ic_i+1+ H.c.i

− µ Xn

i=1

c_i^†c_i

… …

Majorana operators

γ_j =c_j+ c_j^† 2 γ_j⁰=c_j− cj^†

2ı

1D p-wave superconductor TEX

Lattice H =

n−1

X

i=1

htc_i^†c_i+1+ ∆c_ic_i+1+ H.c.i

− µ Xn

i=1

c_i^†c_i

… …

Majorana operators

γ_j =c_j+ c_j^† 2 γ_j⁰=c_j− cj^†

2ı

t=0.2 t=0.8

Bulk H(k) = (2t cos k − µ)τb ^z− 2∆ sin k τ^y c^†_k =

c_k^†, c_−k