Scanning tunneling microscope study of quantum Hall isospin ferromagnetic states in the zero Landau level in a graphene monolayer

Abstract

A number of quantum Hall isospin ferromagnetic (QHIFM) states have been predicted in the "relativistic" zero Landau level (LL) of graphene monolayer. These states, especially the states at LL filling factor  = 0 of charge-neutral graphene, have been extensively explored in experiment. To date, identification of these high-field broken-symmetry states has mostly relied on macroscopic transport techniques. Here, we study splitting of the zero LL of graphene at partial filling and demonstrate a direct approach by imaging the QHIFM states at atomic scale with a scanning tunneling microscope. At half filling of the zero LL ( = 0), the system is in a spin unpolarized state and we observe a linear magnetic-fieldscaling of valley splitting. Simultaneously, the spin degeneracy in the two valleys is also lifted by the magnetic fields. When the Fermi level lies inside the spinpolarized states (at  = 1 or -1), the spin splitting is dramatically enhanced because of the strong many-body effects. At  = 0, we direct image the wavefunctions of the QHIFM states at atomic scale and observe an interaction-driven density wave featuring a Kekulé distortion, which is responsible for the large gap at charge neutrality point in high magnetic fields.

Quantum-dot assisted spectroscopy of degeneracy-lifted Landau levels in graphene

“…So far, existing experiments sensitive to degeneracy lifting effects were provided by probes sensitive to the ground state. These include transport 23 – 25 and STM measured near the Fermi energy 26 , 27 . The nature of degeneracy lifting in excited states remains an open question: A two-fold splitting of the filled N = 0 level has been observed by STM 26 , and it is indeed clear that excited energy levels should retain the Zeeman splitting.…”

Broken Symmetries and Kohn’s Theorem in Graphene Cyclotron Resonance

“…In graphene, Coulomb interactions combine with spin and valley degrees of freedom to generate an approximate SU(4) symmetry, which when broken can give rise to novel magnetic ground states in the quantum Hall regime at high magnetic fields. These phenomena have been explored by a variety of experimental probes, including electronic transport, quantum capacitance, and scanning probe microscopy experiments [1][2][3][4][5][6][7]. However, the excited states of this system due to collective excitations between Landau levels (LLs) in the broken-symmetry regime have not been explored much to date [8,9].…”

Spectroscopic characterization of Landau-level splitting and the intermediate v=0 phase in bilayer graphene

“…For the magnetic fields B < 9 T, an obvious enhancement of both the spin splitting and orbital splitting is observed in the partially filled LL(0,1,-). Such a partial-fillingenhanced splitting, which has been observed in monolayer and trilayer graphene [25,37,43], arises from the exchange interaction, indicating strong many-body effects in the lowest LL of the BLG. It is very interesting to note that the spin splitting in the fully unoccupied LL(0,1,+) is also enhanced when the LL(0,1,-) is partially filled, as shown in Fig.…”

“…In this letter, we present scanning tunneling microscopy and spectroscopy (STM and STS) measurements of high-quality BLG on graphite substrate under ultralowtemperature (~500 mK) and high magnetic field (up to 15 T). There are two unique advantages of the STM/STS measurements: i) the atomic-scale spatial resolution [22][23][24], which allows us to visualize the quantum phases in real space and, therefore, directly identify them [25,26]; ii) the ability to probe the electronic states both near and far from the Fermi level, which enables us to investigate the splitting of the broken symmetry states at different filling, ranging from full filling to complete empty, in the BLG. Our result demonstrates that both the spin and orbital splittings of the lowest n = (0,1) LL depend sensitively on the filling state and have an enhancement at partialfilling, revealing remarkable many-body effects in the lowest LL of the BLG.…”