Hidden order and finite temperature topological phase transition in graphene samples in the presence of adatoms
László Oroszlány
Department of Physics of Complex Systems, Eötvös Loránd University
and MTA-BME Lendület Topology and Correlation Research Group
Duncan and Kekulé
Duncan, Charlie, Gene and Kekulé
Competing personalities
A colourful mess!
Individual adatoms
- adatoms distort the lattice, alter hopping around a hexagon
- adatoms introduce Kane-Mele type SOC on a plaquette
- adatoms DO NOT distort onsite of carbon atoms
- adatoms DO NOT have impurity level
Hidden order of adatoms via RKKY
V.V.Cheianov et al. Solid State Commun. 149, 1499 (2009)
"Ferro"
"Para"
\hat{H}=v\hat{\boldsymbol{p}}\cdot\boldsymbol{\sigma}\otimes\tau_{z}
V^{\mathrm{RKKY}}_{ij}=\int_{-\infty}^{\infty}\text{d}\omega\text{Tr}\left[\hat{V}_{i}\hat{G}(\omega)\hat{V}_{j}\hat{G}(-\omega)\right]
\hat{V}_{i}=\delta(\boldsymbol{r}-\boldsymbol{r}_i)\left(
\Delta_{\text{Kek}}\sigma_{0}\otimes\boldsymbol{u}_{i}\cdot\boldsymbol{\tau}+
\Delta_{\text{KM}}\sigma_{z}\otimes\tau_{0}
\right )
V^{\mathrm{RKKY}}_{ij}=-\frac{\Delta_{\text{Kek}}^{2}\boldsymbol{u}_{i}\cdot\boldsymbol{u}_{j}+\Delta_{\text{KM}}^{2}}{8\pi r_{ij}^{3}v}
\boldsymbol{u}_{i}=\left(
\begin{array}{c}
\cos\left(\frac{2\pi}{3}\nu_{i}\right) \\
\sin\left(\frac{2\pi}{3}\nu_{i}\right)
\end{array}\right),\,\nu_i\in[-1,0,1]
Large adatom \( \Rightarrow \) strong SOC
Disorder?
KPM!
Weiße et al. Rev. Mod. Phys. 78, 275 (2006)
m =\frac{\sqrt{3}}{3}|t' -t|
"Ferro"
"Para"
T
I to TI transition at finite temperature!
C. W. Groth, et al. Phys. Rev. Lett. 103, 196805 (2009)
FM vs PM \(E_{Tot}\) for higher concentrations
50 x 50 cell 10% coverage
\displaystyle E_{Tot}=\int_{-\infty}^{E_F} E\varrho(E) \mathrm{d}E
Are there such adatoms ???
What could go wrong?
Adatoms might not like to sit @ hollow
Are there such adatoms ???
What could go wrong?
Adatoms might develop magnetism instead of strong SOC
Os @ 4x4 graphene
Jun Hu, Jason Alicea, Ruqian Wu, and Marcel Franz
Phys. Rev. Lett. 109, 266801(2012)
Are there such adatoms ???
What could go wrong?
Adatoms might aggregate leading to phase separation
Promising candidates: Hg
Promising candidates: Th and dimers
Phys. Rev. X 1, 021001 (2011)
Phys. Rev. Lett. 109, 266801 (2012)
E[eV]
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