Absence of edge reconstruction for quantum Hall edge channels in graphene devices

AI: The main results of the paper are: - Quantum Hall (QH) edge states in graphene are confined to a few magnetic lengths at the crystal edges. - The QH edge states are defined by boundary conditions of vanishing electronic wavefunctions at the crystal edges, resulting in ideal one-dimensional chiral channels. - The QH edge states in graphene do not undergo electrostatic reconstruction. - There is a uniform charge carrier density at the edges of graphene. - The absence of electrostatic reconstruction of QH edge states has implications for electron and heat transport experiments in graphene-based systems and other 2D crystalline materials. - The use of CITS (constant impedance topography spectroscopy) to locate the edge of graphene. - The observation of inhomogeneous bright spots in the topographic map near the edge, indicating lifting of the graphene sheet. - The presence of a hump in the height profile near the edge, indicating lifting of the edge of the graphene sheet. - The disappearance of Landau level peaks when approaching the edge and the opening of a gap at the edge in tunneling conductance spectroscopy. - The dispersion of Landau level peaks toward higher energy near the edge. - The measurement of an effective Fermi velocity and carrier density as a function of distance from the edge, showing an increase in Fermi velocity and a decrease in carrier density near the edge. - Quantum Hall edge states are observed in graphene by tunneling spectroscopy. The tunneling conductance reveals a series of peaks corresponding to Landau levels, which are stable far from the edge but suppressed as the edge is approached. - The suppression of Landau level peaks near the edge is attributed to sharply-confined quantum Hall edge states. The spectral weight of the Landau levels spreads to higher energies due to an abrupt edge state dispersion. - The suppression of Landau level peaks and the emergence of a V-shaped tunneling density of states near the edge are consistent with theoretical simulations of charge-neutral graphene with an armchair edge. - The Kekul\'{e}-bond order, a broken-symmetry state, is observed at 20 nm from the edge, indicating its robustness even in the proximity of the edge. - The authors investigated the charge carrier accumulation at the graphene edges and its effect on transport properties. - They performed tunneling experiments and measured the energy shift of the Landau level spectrum due to charge inhomogeneity on the edge. They found that the charge accumulation was not large enough to depin the chemical potential from the zeroth Landau level. - The authors enhanced the sensitivity of the spectroscopy by performing measurements at filling factor $\nu=2$, where a small variation in charge density would result in a substantial shift of the Landau levels in the tunneling spectra. - They observed that the Landau level peaks stayed at the same energy over the scan and vanished at about 20 nm from the edge, indicating the absence of charge accumulation. - They performed systematic gate-tuned tunneling spectroscopy maps at various locations near the edge and measured a variation in charge density within 20 nm of the edge. - The small spatial scale of this charge accumulation could not explain recent scanning probe experiments that showed indirect responses within hundreds of nanometers from the edge. - The results suggest that the charge accumulation on the edge is not significant enough to invalidate the existence of the quantum Hall topological insulator phase in charge-neutral graphene. - The authors discussed the implications of their findings for edge reconstruction, inter-edge state interactions, and QH interferometry in graphene systems.