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)