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Band structure determines the motion of electrons in a solid, giving rise to exotic phenomena when properly engineered. Drawing an analogy between electrons and photons, artificially designed optical lattices indicate the possibility of a similar band modulation effect in graphene systems. Yet due to the fermionic nature of electrons, modulated electronic systems promise far richer categories of behaviors than those found in optical lattices. Here, we uncovered a strong modulation of electronic states in bilayer graphene subject to periodic potentials. We observed for the first time the hybridization of electron and hole sub-bands, resulting in local band gaps at both primary and secondary charge neutrality points. Such hybridization leads to the formation of flat bands, enabling the study of correlated effects in graphene systems. This work may also offer a viable platform to form and continuously tune Majorana zero modes, which is important to the realization of topological quantum computation.
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We consider ground state of electron-hole graphene bilayer composed of two independently doped graphene layers when a condensate of spatially separated electron-hole pairs is formed. In the weak coupling regime the pairing affects only conduction band of electron-doped layer and valence band of hole-doped layer, thus the ground state is similar to ordinary BCS condensate. At strong coupling, an ultrarelativistic character of electron dynamics reveals and the bands which are remote from Fermi surfaces (valence band of electron-doped layer and conduction band of hole-doped layer) are also affected by the pairing. The analysis of instability of unpaired state shows that s-wave pairing with band-diagonal condensate structure, described by two gaps, is preferable. A relative phase of the gaps is fixed, however at weak coupling this fixation diminishes allowing gapped and soliton-like excitations. The coupled self-consistent gap equations for these two gaps are solved at zero temperature in the constant-gap approximation and in the approximation of separable potential. It is shown that, if characteristic width of the pairing region is of the order of magnitude of chemical potential, then the value of the gap in the spectrum is not much different from the BCS estimation. However, if the pairing region is wider, then the gap value can be much larger and depends exponentially on its energy width.
We consider the pairing of electrons and holes due to their Coulomb attraction in two parallel, independently gated graphene layers, separated by a barrier. At weak coupling, there exist the BCS-like pair-condensed state. Despite the fact that electrons and holes behave like massless Dirac fermions, the problem of BCS-like electron-hole pairing in graphene bilayer turns out to be rather similar to that in usual coupled semiconductor quantum wells. The distinctions are due to Berry phase of electronic wave functions and different screening properties. We estimate values of the gap in one-particle excitation spectrum for different interlayer distances and carrier concentrations. Influence of disorder is discussed. At large enough dielectric susceptibility of surrounding medium, the weak coupling regime holds even at arbitrarily small carrier concentrations. Localized electron-hole pairs are absent in graphene, thus the behavior of the system versus coupling strength is cardinally different from usual BCS-BEC crossover.
The superconducting pairing of electrons in doped graphene due to in-plane and out-of-plane phonons is considered. It is shown that the structure of the order parameter in the valley space substantially affects conditions of the pairing. Electron-hole pairing in graphene bilayer in the strong coupling regime is also considered. Taking into account retardation of the screened Coulomb pairing potential shows a significant competition between the electron-hole direct attraction and their repulsion due to virtual plasmons and single-particle excitations.
We present transport measurements through an electrostatically defined bilayer graphene double quantum dot in the single electron regime. With the help of a back gate, two split gates and two finger gates we are able to control the number of charge carriers on two gate-defined quantum dot independently between zero and five. The high tunability of the device meets requirements to make such a device a suitable building block for spin-qubits. In the single electron regime, we determine interdot tunnel rates on the order of 2~GHz. Both, the interdot tunnel coupling, as well as the capacitive interdot coupling increase with dot occupation, leading to the transition to a single quantum dot. Finite bias magneto-spectroscopy measurements allow to resolve the excited state spectra of the first electrons in the double quantum dot; being in agreement with spin and valley conserving interdot tunneling processes.
Using electrical transport experiments and shot noise thermometry, we investigate electron-phonon heat transfer rate in a suspended bilayer graphene. Contrary to monolayer graphene with heat flow via three-body supercollision scattering, we find that regular electron - optical phonon scattering in bilayer graphene provides the dominant scattering process at electron energies $ gtrsim 0.15$ eV. We determine the strength of these intrinsic heat flow processes of bilayer graphene and find good agreement with theoretical estimates when both zone edge and zone center optical phonons are taken into account.
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