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Register a new userThermal Transport Signatures of Broken-Symmetry Phases in Graphene
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In the half-filled zero-energy Landau level of bilayer graphene, competing phases with spontaneously broken symmetries and an intriguing quantum critical behavior have been predicted. Here we investigate signatures of these broken-symmetry phases in thermal transport measurements. To this end we calculate the spectrum of spin and valley waves in the $ u=0$ quantum Hall state of bilayer graphene. The presence of Goldstone modes enables heat transport even at low temperatures, which can serve as compelling evidence for spontaneous symmetry breaking. By varying external electric and magnetic fields it is possible to determine the nature of the symmetry breaking and temperature-dependent measurements may yield additional information about gapped modes.
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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.
We show that strained or deformed honeycomb lattices are promising platforms to realize fractional topological quantum states in the absence of any magnetic field. The strained induced pseudo magnetic fields are oppositely oriented in the two valleys [1-3] and can be as large as 60-300 Tesla as reported in recent experiments [4,5]. For strained graphene at neutrality, a spin or a valley polarized state is predicted depending on the value of the onsite Coulomb interaction. At fractional filling, the unscreened Coulomb interaction leads to a valley polarized Fractional Quantum Hall liquid which spontaneously breaks time reversal symmetry. Motivated by artificial graphene systems [5-8], we consider tuning the short range part of interactions, and demonstrate that exotic valley symmetric states, including a valley Fractional Topological Insulator and a spin triplet superconductor, can be stabilized by such interaction engineering.
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.
We study a relativistic quantum cavity system realized by etching out from a graphene sheet by quantum transport measurements and theoretical calculations. The conductance of the graphene cavity has been measured as a function of the back gate voltage (or the Fermi energy) and the magnetic field applied perpendicular to the graphene sheet, and characteristic conductance contour patterns are observed in the measurements. In particular, two types of high conductance contour lines, i.e., straight and parabolic-like high conductance contour lines, are found in the measurements. The theoretical calculations are performed within the framework of tight-binding approach and Greens function formalism. Similar characteristic high conductance contour features as in the experiments are found in the calculations. The wave functions calculated at points selected along a straight conductance contour line are found to be dominated by a chain of scars of high probability distributions arranged as a necklace following the shape of cavity and the current density distributions calculated at these point are dominated by an overall vortex in the cavity. These characteristics are found to be insensitive to increasing magnetic field. However, the wave function probability distributions and the current density distributions calculated at points selected along a parabolic-like contour line show a clear dependence on increasing magnetic field, and the current density distributions at these points are characterized by the complex formation of several localized vortices in the cavity. Our work brings a new insight into quantum chaos in relativistic particle systems and would greatly stimulate experimental and theoretical efforts towards this still emerging field.
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.
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