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Register a new userOptical Hall response of bilayer graphene: the manifestation of chiral hybridised states in broken mirror symmetry lattices
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Understanding the mechanisms governing the optical activity of layered-stacked materials is crucial to the design of devices aimed at manipulating light at the nanoscale. Here, we show that both twisted and slid bilayer graphene are chiral systems that can deflect the polarization of linear polarized light. However, only twisted bilayer graphene supports circular dichroism. Our calculation scheme, which is based on the time-dependent Schrodinger equation, is particularly efficient for calculating the optical-conductivity tensor. Specifically, it allows us to show the chirality of hybridized states as the handedness-dependent bending of the trajectory of kicked Gaussian wave packets in bilayer lattices. We show that nonzero Hall conductivity is the result of the noncanceling manifestation of hybridized states in chiral lattices. We also demonstrate the continuous dependence of the conductivity tensor on the twist angle and the sliding vector.
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The flat bands in bilayer graphene(BLG) are sensitive to electric fields Ebot directed between the layers, and magnify the electron-electron interaction effects, thus making BLG an attractive platform for new two-dimensional (2D) electron physics[1-5]. Theories[6-16] have suggested the possibility of a variety of interesting broken symmetry states, some characterized by spontaneous mass gaps, when the electron-density is at the carrier neutrality point (CNP). The theoretically proposed gaps[6,7,10] in bilayer graphene are analogous[17,18] to the masses generated by broken symmetries in particle physics and give rise to large momentum-space Berry curvatures[8,19] accompanied by spontaneous quantum Hall effects[7-9]. Though recent experiments[20-23] have provided convincing evidence of strong electronic correlations near the CNP in BLG, the presence of gaps is difficult to establish because of the lack of direct spectroscopic measurements. Here we present transport measurements in ultra-clean double-gated BLG, using source-drain bias as a spectroscopic tool to resolve a gap of ~2 meV at the CNP. The gap can be closed by an electric field Ebot sim13 mV/nm but increases monotonically with a magnetic field B, with an apparent particle-hole asymmetry above the gap, thus providing the first mapping of the ground states in BLG.
The quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded and brought into focus the concept of topological order in physics. The topologically protected quantum Hall edge states are of crucial importance to the QH effect but have been measured with limited success. The QH edge states in graphene take on an even richer role as graphene is distinguished by its four-fold degenerate zero energy Landau level (zLL), where the symmetry is broken by electron interactions on top of lattice-scale potentials but has eluded spatial measurements. In this report, we map the quantum Hall broken-symmetry edge states comprising the graphene zLL at integer filling factors of $ u=0,pm 1$ across the quantum Hall edge boundary using atomic force microscopy (AFM). Measurements of the chemical potential resolve the energies of the four-fold degenerate zLL as a function of magnetic field and show the interplay of the moire superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields.
Measuring degeneracy and broken-symmetry states of a system at nanoscale requires extremely high energy and spatial resolution, which has so far eluded direct observation. Here, we realize measurement of the degeneracy and subtle broken-symmetry states of graphene at nanoscale for the first time. By using edge-free graphene quantum dots, we are able to measure valley splitting and valley-contrasting spin splitting of graphene at the single-electron level. Our experiments detect large valley splitting around atomic defects of graphene due to the coexistence of sublattice symmetry breaking and time reversal symmetry breaking. Large valley-contrasting spin splitting induced by enhanced spin-orbit coupling around the defects is also observed. These results reveal unexplored exotic electronic states in graphene at nanoscale induced by the atomic defects.
We present low temperature transport measurements on dual-gated suspended trilayer graphene in the quantum Hall (QH) regime. We observe QH plateaus at filling factors { u}=-8, -2, 2, 6, and 10, in agreement with the full-parameter tight binding calculations. In high magnetic fields, odd-integer plateaus are also resolved, indicating almost complete lifting of the 12-fold degeneracy of the lowest Landau levels (LL). Under an out-of-plane electric field E, we observe degeneracy breaking and transitions between QH plateaus. Interestingly, depending on its direction, E selectively breaks the LL degeneracies in the electron-doped or hole-doped regimes. Our results underscore the rich interaction-induced phenomena in trilayer graphene.
The dominance of Coulomb interactions over kinetic energy of electrons in narrow, non-trivial moir{e} bands of magic-angle twisted bilayer graphene (TBG) gives rise to a variety of correlated phases such as correlated insulators, superconductivity, orbital ferromagnetism, Chern insulators and nematicity. Most of these phases occur at or near an integer number of carriers per moir{e} unit cell. Experimental demonstration of ordered states at fractional moir{e} band-fillings at zero applied magnetic field $B$, is a challenging pursuit. In this letter, we report the observation of states at half-integer band-fillings of $ u = 0.5$ and $3.5$ at $Bapprox 0$ in a TBG proximitized by a layer of tungsten diselenide (WSe$_2$). The magnetotransport data enables us to deduce features in the underlying band structure consistent with a spontaneously broken translational symmetry supercell with twice the area of the original TBG moir{e} cell. A series of Lifshitz transitions due to the changes in the topology of the Fermi surface implies the evolution of van Hove singularities (VHS) of the diverging density of states at a discrete set of partial fillings of flat bands. Further, we observe reset of charge carriers at $ u = 2, 3$. In addition to magnetotransport, we employ thermoelectricity as a tool to probe the system at $B=0$. Band structure calculations for a TBG moir{e} pattern, together with a commensurate density wave potential and spin-orbit coupling (SOC) terms, allow to obtain degeneracy-lifted, zone-folded moir{e} bands with spin-valley isospin ordering anisotropy that describe the states at half-integer fillings observed experimentally. Our results suggest the emergence of a spin-charge density wave ground state in TBG in the zero $B-$ field limit.
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