Integer Quantum Hall Effect in Trilayer Graphene

Kumar, Amit; Escoffier, Walter; Poumirol, Jean-Marie; Faugeras, C.; Arovas, Daniel P.; Fogler, M. M.; Guinea, F.; Roche, Stephan; Goiran, M.; Raquet, Bertrand

doi:10.1103/physrevlett.107.126806

Cited by 108 publications

(104 citation statements)

References 40 publications

(42 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Measured in semiconductor 2D electron gases more than 30 years ago 26 and in the yearly days of graphene, in both monolayer 5,27 and bilayer samples 28 (very recently also in trilayer graphene 29 ), the static quantum Hall effect is an hallmark elementary of excitations in electronic systems. 30 Its dynamical analogue-the ac quantum Hall effectcan provide additional information about charge carriers, such as the opening of gaps in the spectrum.…”

Section: Equation Of Motion Methods For the Calculation Of The Magmentioning

confidence: 99%

Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids

et al. 2011

View full text Add to dashboard Cite

We show that by enclosing graphene in an optical cavity, giant Faraday rotations in the infrared regime are generated and measurable Faraday rotation angles in the visible range become possible. Explicit expressions for the Hall steps of the Faraday rotation angle are given for relevant regimes. In the context of this problem we develop an equation of motion (EOM) method for the calculation of the magneto-optical properties of metals and semiconductors. It is shown that properly regularized EOM solutions are fully equivalent to the Kubo formula.

show abstract

Section: Equation Of Motion Methods For the Calculation Of The Magmentioning

confidence: 99%

Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids

et al. 2011

View full text Add to dashboard Cite

show abstract

“…The order at which the degeneracy is broken reflects the underlying competing symmetries. Prior works have reported resolution of several symmetry-broken QH states [38][39][40] , albeit only in single-gated samples where the interlayer potential U⊥ and charge density n are not independently controlled. In this Letter, by using transport measurements on high mobility dual-gated r-TLG devices, we explore symmetry-broken LLs via careful control of U⊥, B and n. All integer plateaus of the zeroth LL in the hole-doped regime are resolved in high B.…”

mentioning

confidence: 99%

Multicomponent Quantum Hall Ferromagnetism and Landau Level Crossing in Rhombohedral Trilayer Graphene

et al. 2015

Self Cite

View full text Add to dashboard Cite

Using transport measurements, we investigate multicomponent quantum Hall (QH) ferromagnetism in dual-gated rhombohedral trilayer graphene (r-TLG), in which the real spin, orbital pseudospin and layer pseudospins of the lowest Landau level form spontaneous ordering. We observe intermediate quantum Hall plateaus, indicating a complete lifting of the degeneracy of the zeroth Landau level (LL) in the hole-doped regime. In charge neutral r-TLG, the orbital degeneracy is broken first, and the layer degeneracy is broken last and only the in presence of an interlayer potential U⊥. In the phase space of U⊥ and filling factor ν, we observe an intriguing "hexagon" pattern, which is accounted for by a model based on crossings between symmetry-broken LLs.Keywords: quantum Hall ferromagnetism, graphene, trilayer, rhombohedral stacking, Landau level crossing * Emails: kenosis101@gmail.com, yafisb@gmail.com; lau@physics.ucr.edu In the quantum Hall (QH) regime, when the energies of two or more Landau levels (LLs) are brought to alignment, the spinor language is often used to describe the different degrees of freedom, such as layer and orbital pseudospins, due to their close analogy to the spins in a twodimensional ferromagnet. When these LLs are less than completely full, competition between these degrees of freedom leads to formation of electronic states with spontaneous ordering of pseudospins, much like the spontaneous real spin alignment in a ferromagnet. For this reason, these symmetry-broken QH states are called QH ferromagnets, with real or pseudo-spin orderings that maybe easy-plane, i.e. akin to a XY Heisenberg magnet, or easy-axis, i.e. akin to an Ising ferromagnet. These QH ferromagnetic states provide a rich platform for investigation of the competition among different symmetries, as well as providing insight into the itinerant magnetism in standard magnets.The recent emergence of two-dimensional (2D) graphene provides new playground for multicomponent QH ferromagnetic states and the associated phase transitions 1-6 7-19 20-28 . With the advent of high mobility samples that may be either suspended 29,30 or supported on BN substrates 31,32 , and advanced device geometry such as dual-gates or split top gates [33][34][35] , few-layer graphene provides QH systems with unusual symmetries and unprecedented tunability.In particular, rhombohedral trilayer graphene is such a QH system with very flat bands near the charge neutrality point. Its LL energies are given bywhere N is an integer denoting the LL index, e the electron charge, v F~1 0 6 m/s the Fermi velocity of single layer graphene, γ 1~0 .3 eV the interlayer hopping energy, and h Planck's constant. The degeneracy between the N=0, 1 and 2 LLs, together with the spin and valley degrees of freedom, yield the 12-fold degeneracy of the lowest LL, and give rise to plateaus at filling factors ν=±6, ±10, ±14… Interactions and/or single particle effects lift this 12-fold degeneracy, leading to incompressible QH ferromagnetic states at intermediate fillings 36,37 , with ex...

show abstract

“…22 Using magnetic fields up to 60 T, there has been evidence of the integer quantum Hall effect in trilayer graphene. 23 The Hall resistivity plateaus have been reproduced by using a self-consistent Hartree calculation on ABC-stacked graphene. 23 It has been suggested that the differences in the quantum Hall effect between ABC and ABA stacking might be used to identify the stacking order of high-quality trilayer samples.…”

mentioning

confidence: 99%

Ferromagnetism in ABC-stacked trilayer graphene

2013

View full text Add to dashboard Cite

In this article we study the ferromagnetic behavior of ABC-stacked trilayer graphene. This is done using a nearest-neighbor tight-binding model, in the presence of long-range Coulomb interactions. For a given electronelectron interaction g and doping level n, we determine whether the total energy is minimized for a paramagnetic or ferromagnetic configuration of our variational parameters. The g versus n phase diagram is first calculated for the unscreened case. We then include the effects of screening using a simplified expression for the fermion bubble diagram. We show that ferromagnetism in ABC-stacked trilayer graphene is more robust than in monolayer, in bilayer, and in ABA-stacked trilayer graphene. Although the screening reduces the ferromagnetic regime in ABC-stacked trilayer graphene, the critical doping level remains one order of magnitude larger than in unscreened bilayer graphene.

show abstract

Integer Quantum Hall Effect in Trilayer Graphene

Cited by 108 publications

References 40 publications

Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids

Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids

Multicomponent Quantum Hall Ferromagnetism and Landau Level Crossing in Rhombohedral Trilayer Graphene

Ferromagnetism in ABC-stacked trilayer graphene

Contact Info

Product

Resources

About