Unconventional Quantum Hall Effect Research Articles

Quantum Hall effect and Landau-level crossing of Dirac fermions in trilayer graphene

We investigate electronic transport in high mobility (\textgreater 100,000 cm$^2$/V$\cdot$s) trilayer graphene devices on hexagonal boron nitride, which enables the observation of Shubnikov-de Haas oscillations and an unconventional quantum Hall effect. The massless and massive characters of the TLG subbands lead to a set of Landau level crossings, whose magnetic field and filling factor coordinates enable the direct determination of the Slonczewski-Weiss-McClure (SWMcC) parameters used to describe the peculiar electronic structure of trilayer graphene. Moreover, at high magnetic fields, the degenerate crossing points split into manifolds indicating the existence of broken-symmetry quantum Hall states.

ELECTRONIC PROPERTIES OF GRAPHENE, FEW-LAYER GRAPHENE, AND BULK GRAPHITE UNDER VERY HIGH MAGNETIC FIELD

In the present work, we report on the magneto-transport properties of graphitic based materials (graphene, few-layer graphene, and bulk graphite) in very high magnetic field. Quantum Hall Effect (QHE) has been studied in graphitic systems in very high pulsed magnetic field (up to B = 57 T ) and at low temperature (≤ 4 K). Graphene sample shows well-defined Hall resistance plateaus at filling factors v = 2,6,10, etc. Few-layer graphene systems display clear signatures of standard and unconventional QHE. Magneto-transport studies on bulk highly oriented pyrolytic graphite show a charge density wave transition at strong enough magnetic field as well as Hall coefficient sign reversal.

UNUSUAL QUANTUM HALL EFFECTS, INDEX THEOREM AND SUPERSYMMETRY IN GRAPHENE

We exploit an index theorem and a high degree of symmetry to understand unusual quantum Hall effects of the n = 0 Landau level in graphene. The high symmetry such as the pseudospin symmetry of Fermi points in a graphene sheet cannot couple to an external magnetic field. In the absence of the magnetic field, the index theorem provides a relation between the zero-energy state of the graphene sheet and the topological deformation of the compact lattice. Under the topological deformation, the zero-energy state emerges naturally without the Zeeman splitting at the Fermi points in the graphene sheet. This results in the fact that the pseudospin is an exact symmetry. In the case of nonzero energy, the up-spin and down-spin states have the exact high symmetry of spin, forming the pseudospin singlet pairing. We describe the peculiar and unconventional quantum Hall effects of the n = 0 Landau level in graphene on the basis of the index theorem and the high degree of symmetry.

Interface states and anomalous quantum oscillations in hybrid graphene structures

One- and two-layer graphene have recently been shown to feature new physical phenomena such as unconventional quantum Hall effects and prospects of supporting a non-silicon technological platform using epitaxial graphene. While both one- and two-layer graphene have been studied extensively, continuous sheets of graphene possessing both parts have not yet been explored. Here we report a study of such graphene hybrid structures. In a bulk hybrid featuring two large-area one- and two-layer graphene and an interface between them, two sets of Landau levels and features related to the interface were found. In edge hybrids featuring a large two-layer graphene with narrow one-layer graphene edges, we observed an anomalous suppression in quantum oscillation amplitude due to the locking of one- and two-layer graphene Fermi energies and emergent chiral interface states. These findings demonstrate the importance of these hybrid structures whose unique interface states and related phenomena deserve further studies.

Graphene with structure-induced spin-orbit coupling: Spin-polarized states, spin zero modes, and quantum Hall effect

Spin splitting of the energy spectrum of single-layer graphene on Au/Ni(111) substrate has been recently reported. I show that eigenstates of spin-orbit coupled graphene are polarized in-plane and perpendicular to electron momentum $\bf k$; the magnitude of spin polarization $\bf S$ vanishes when $k \to 0$. In a perpendicular magnetic field $\bf B$, $\bf S$ is parallel to $\bf B$, and two zero modes emerge in the Landau level spectrum. Singular $\bf B$-dependence of their magnetization suggests existence of a novel magnetic instability. They also manifest themselves in a new unconventional quantum Hall effect.

Supersymmetry and unconventional quantum Hall effect in monolayer, bilayer and trilayer graphene

We present a unified description of the quantum Hall effect in monolayer, bilayer and trilayer graphene based on the supersymmetric formalism. The key property is that the Zeeman splitting is exactly as large as the Landau level separation for Dirac electrons. It follows that the zero-energy state emerges and that the nonzero-energy states make a supermultiplet made of the up-spin and down-spin states coming from different Landau levels. Analyzing Coulomb effects on the nonzero-energy states, we derive a remarkable result that the effective Coulomb potential depends on spins in each energy level.

Quantum Hall effect in graphene: Disorder effect and phase diagram

We numerically study the interplay of band structure, topological invariant and disorder effect in two-dimensional electron system of graphene in a magnetic field. Two \emph{distinct} quantum Hall effect (QHE) regimes exist in the energy band with the unconventional "half-integer" QHE appearing near the band center, consistent with the experimental observation. The latter is more robust against disorder scattering than the conventional QHE states near the band edges. The phase diagram for the unconventional QHE is obtained where the destruction of the Hall plateaus at strong disorder is through the float-up of extended levels toward band center and higher plateaus always disappear first. We further predict a new insulating phase between $\nu =\pm 2$ QHE states at the band center, which may explain the experimentally observed resistance discontinuity near zero gate voltage.

Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene

There are known two distinct types of the integer quantum Hall effect. One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems, and the other is its relativistic counterpart recently observed in graphene, where charge carriers mimic Dirac fermions characterized by Berry's phase pi, which results in a shifted positions of Hall plateaus. Here we report a third type of the integer quantum Hall effect. Charge carriers in bilayer graphene have a parabolic energy spectrum but are chiral and exhibit Berry's phase 2pi affecting their quantum dynamics. The Landau quantization of these fermions results in plateaus in Hall conductivity at standard integer positions but the last (zero-level) plateau is missing. The zero-level anomaly is accompanied by metallic conductivity in the limit of low concentrations and high magnetic fields, in stark contrast to the conventional, insulating behavior in this regime. The revealed chiral fermions have no known analogues and present an intriguing case for quantum-mechanical studies.

Unconventional Integer Quantum Hall Effect in Graphene

Monolayer graphite films, or graphene, have quasiparticle excitations that can be described by (2+1)-dimensional Dirac theory. We demonstrate that this produces an unconventional form of the quantized Hall conductivity sigma(xy) = -(2e2/h)(2n+1) with n = 0, 1, ..., which notably distinguishes graphene from other materials where the integer quantum Hall effect was observed. This unconventional quantization is caused by the quantum anomaly of the n=0 Landau level and was discovered in recent experiments on ultrathin graphite films.