stacking one layer on another monolayer of graphene in a 'magic angle' changes the properties of the bilayer significantly. Which phenomenon will be responsible for the superconductivity. I already encountered lesser conductivity of ordinary bilayer as compared to that of a monolayer graphene.
The coupling between the layers of a twisted bilayer of graphene close to a magic angle [1] gives rise to flat bands close to the chemical potential at half filling, resulting in a strongly-correlated metallic state of electrons at small dopings [2]. To my knowledge, the pairing mechanism of the superconductivity observed in such twisted bilayer of graphene [3] is not known at this stage, however it is strongly suspected that phonons (i.e. the quantised lattice vibrations) are not the relevant bosonic excitations [3]. I note in passing that while the BCS theory is not applicable to the superconducting state of twisted bilayers of graphene at magic angles [4], the value of the transition temperature Tc of a BCS superconductor exponentially increases for increasing density of electronic states at the chemical potential, D(0) (Tc scales like exp(-1/V D(0)), where V stands for the effective interaction potential). This is consistent with a relatively large Tc observed [3] in twisted bilayers of graphene close to a magic angle (recall the above-mentioned flat bands).
[1] R Bistritzer, and AH MacDonald, PNAS 108, 12233 (2011). Article Moire bands in twisted double-layer graphene
[2] Y Cao et al., 556, 80 (2018). Article Correlated Insulator Behaviour at Half-Filling in Magic Angl...
[3] Y Cao et al., Nature 556, 43 (2018). Article Magic-angle graphene superlattices: a new platform for uncon...
[4] The superconducting 'dome' observed in [3] hints at strong fluctuations of the phase of the superconducting order parameter in a twisted bilayer of graphene at a magic angle. See:
VJ Emery, and SA Kivelson, Nature 374, 434 (1995). Article Importance of phase fluctuations in superconductors with sma...
Relatively higher observed Tc may indicate unconventionality of such superconductivity. In fact, superconducting correlation can be induced even in a single layer graphene. Twisted bilayer graphene may provide certain quantum fluctuations to form the Cooper pairs. It shall be nice to learn more about it.
I am really curious about how did you stack two layests of graphene? I was in march meeting and Prof. Bernevig gave a talk about stacking layers of tilted graphene. Actually it was not bilayer, it was tri layer which twisted with the same angle!
Dear Bahar Jafari Zadeh ,
The CVD grown Graphene on Cu substrate is firstly spin coated with PMMA (POLYMER: POLY METHYL META ACRYLATE), then Cu is etched away in aquous solution of Ferric chloride. Now the graphene coated with PMMA, is placed in a insulating substrate (like SiO2 or Si ) and PMMA is etched away using acetone. Again same process is repeated for stacking another layer on it.
Mukesh Pandey
Thank you so much for the description, I was wondering if you tell me for stacking, should the layers overlap their honeycomb structure or, they should have the same tilted angle (for example the next layer is tilted and then put it on the first one.
Dear Bahar Jafari Zadeh ,
I must say, it is a good question. In general Graphite consists of graphene layers with ABAB..... stacking or Bernal stacking. If you go from top to bottom approach for example mechanical exfoliation of graphite, bernal stacked FLG (few layer Graphene) can be obtained. On the other hand, if you want to deposite a single layer on top of the other in order to get FLG again, then it is hard to get ABAB.. stacking rather it may yield twisted graphene layers with some angle. This process can lead to generate van hove singularities in the crystal lattice which then tend to show new and exciting phases of matter under consideration.
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