Competition of trivial and topological phases in graphene based hybrid systems
Zoltán Tajkov
PhD Student
CMD2020GEFES, 2 September 2020
Graphene is ...
A. K. Geim, I. V. Grigorieva Nature 499, 419 (2013)
Graphene is ...
... a good template!
A. K. Geim, I. V. Grigorieva Nature 499, 419 (2013)
Graphene is ...
... a good template!
A. K. Geim, I. V. Grigorieva Nature 499, 419 (2013)
How can we induce topological phase into graphene?
Graphene is ...
... a good template!
A. K. Geim, I. V. Grigorieva Nature 499, 419 (2013)
How can we induce topological phase into graphene?
SOC!!
BiTeX: giant SOC
Ishizaka et al. Nature Materials 10, 521 (2011)
BiTeX monolayer
Fülöp et al. 2D Mater. 5, 031013 (2018)
BiTeX/graphene heterostructures
Geometry
Z. Tajkov et al. Nanoscale 11, 12704 (2019)
BiTeX/graphene heterostructures
DFT results for tellurium faced arrangements
Z. Tajkov et al. Nanoscale 11, 12704 (2019)
Z. Tajkov et al. Nanoscale 11, 12704 (2019)
Tiny, trivial gap
What can we do about it?
Mechanical distortions
in graphene
Weiss et al. Advanced Materials, 24 5782(2012)
Pressure→I, inplane strain →TI !?!
Z. Tajkov et al. Appl. Sci. 9, 4330 (2019)
BiTeBr
BiTeCl
BiTeI
pressure
strain
What did we learn from DFT?
The most important parameters
Kekulé
Kane-Mele
Strain promotes SOC \( \rightarrow \) TI
\begin{array}{c}
\hat{H}=v\left(
{\boldsymbol{k}}\cdot\boldsymbol{\sigma}\otimes\tau_{0}
-\boldsymbol{A}\cdot\boldsymbol{\sigma}\otimes\tau_{z}
\right)\\
+\Delta\sigma_0\otimes\tau_x
+m\sigma_z\otimes\tau_0
\end{array}
\boldsymbol{A}=\underbrace{\frac{\beta}{2a_{0}}\varepsilon\left(1+\rho\right)}\left(\begin{array}{r}
\cos2\vartheta\\
-\sin2\vartheta
\end{array}\right)
|\xi|=\sqrt{\Delta^2-m^2}
\xi/v
Strain can close the gap at \(\boldsymbol{k}=\boldsymbol{0}\) if
Minimal model
Z. Tajkov et al. Phys. Rev. B 101, 235146 (2020)
\Psi_\boldsymbol{k}=\left(-\left| A, \boldsymbol{k}+ \boldsymbol{G} \right. \rangle \left|B,\boldsymbol{k}-G\right.\rangle \left|B,\boldsymbol{k}+G\right.\rangle \left|A,\boldsymbol{k}+G\right.\rangle \right)
Strain kills Kekulé but KM gap is resilient!
\Delta=0; m=0.2
\Delta=0.2; m=0
\Delta = 0.2; m=0.1
\Delta = 0.1; m=0.2
The Team
László Oroszlány
János Koltai
József Cserti
Thank You!
László Oroszlány
János Koltai
József Cserti
Z. Tajkov et al. Nanoscale 11, 12704 (2019)
Z. Tajkov et al. Appl. Sci. 9, 4330 (2019)
Z. Tajkov et al. Phys. Rev. B 101, 235146 (2020)
Competition of trivial and topological phases in graphene based hybrid systems
By novidad21
Competition of trivial and topological phases in graphene based hybrid systems
Talk was given on 2020.08 at the cmd2020gefes
