Measurement of theν=1/3Fractional Quantum Hall Energy Gap in Suspended Graphene

Abstract

We report on magnetotransport measurements of multi-terminal suspended graphene devices. Fully developed integer quantum Hall states appear in magnetic fields as low as 2 T. At higher fields the formation of longitudinal resistance minima and transverse resistance plateaus are seen corresponding to fractional quantum Hall states, most strongly for ν = 1/3. By measuring the temperature dependence of these resistance minima, the energy gap for the 1/3 fractional state in graphene is determined to be at ∼20 K at 14 T.PACS numbers: 73.63.-b, 73.22.-f, 73.43.-f In the low magnetic field regime, the integer quantum Hall (IQH) effect of graphene is marked by an anomalous half-integer quantum Hall conductivity σ xy = g s (n + 1/2)e 2 /h, where n is an integer and g s = 4 is the Landau level (LL) degeneracy resulting from the degenerate spin and valley isospin degrees of freedom. This anomalous quantum Hall conductivity led to the observation of the filling factor sequence ν = ±2, ±6, ±10 [1, 2]. Subsequently, new broken-symmetry IQH states, corresponding to filling factors ν = 0, ±1, ±4 have been resolved in magnetic fields of B > 20 T, indicating the lifting of the fourfold degeneracy of the LLs [3,4]. These filling factors have been suggested to be the result of various novel correlated states mediated by electron-electron (e-e) interactions [5].In the strong quantum limit, e-e interactions in 2-dimensional electron gasses (2DEGs) can lead to the fractional quantum Hall (FQH) effect [6], many-body correlated states where the Hall conductance quantization appears at fractional filling factors. In recent investigations of transport properties in two-terminal high-mobility suspended graphene devices [7,8], a quantized conductance corresponding to the ν = 1/3 FQH state has been observed, suggesting the presence of strong e-e interactions in this system. However, due to the inherent mixing between longitudinal and transverse resistivities in this twoterminal measurement [9], quantitative characterization of the observed FQH states such as the FQH energy gap is only possible in an indirect way [10]. Although multiterminal measurements on suspended graphene samples have been reported previously [11,12], the mechanical [13] or thermal instability [14] of these samples has precluded even the observation of a fully-quantized IQH effect.Recently, the improvement of graphene mobility up to 8 m 2 /Vsec has been reported for substrate-supported graphene devices fabricated on a single-crystal hexagonal boron nitride substrates [15]. Multi-terminal transport measurements performed on such devices in magnetic fields up to 35 T reveal several FQH states whose filling factors are mostly integer multiples of 1/3. The energy gaps of these states have been measured for ν > 1, exhibiting an unusual hierarchy among these FQH states [16]. However, the characterization of FQH states with ν < 1, notably the 1/3 FQH state, could not be reliably conducted in these samples due to inhomogeneous broadening near the charge neutrality point. As str...

Broken SU(4) Symmetry and the Fractional Quantum Hall Effect in Graphene

“…However, because graphene sheets on substrates generally have stronger disorder than modulation-doped GaAs/AlGaAs 2DESs, it has until recently not been possible to observe their fractional quantum Hall effects. Recent studies of highquality graphene samples have started to clear the fog [6][7][8][9][10][11] however, and the view that has emerged is surprising. Experiments indicate that the graphene FQHE is stronger for 0 < |ν| < 1 than for 1 < |ν| < 2, and that phase transitions between distinct states at the same ν occur as a function of magnetic field strength [10,11].…”

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

“…Several classes of unpolarized FQH states have been formulated, including the so-called Halperin (mmn) states [24] and spin unpolarized composite fermion states [25][26][27][28]. In materials such as AlAs or graphene, ordinary electron spin may furthermore combine with valley degrees of freedom, which can change the sequence of the observed integer and FQH states [29][30][31][32][33][34][35][36][37][38].…”

Stable Pfaffian State in Bilayer Graphene

“…Theoretical studies of FQHE in monolayer [18] and bilayer graphene [19] were reported earlier by us. Recent experimental observations of the ν = 1 3 FQHE in monolayer graphene [20] have provided a glimpse of the role highly correlated electrons play in graphene. Given the accute interest in studying the properties of the ν = 5 2 state in conventional twodimensional electron gas (2DEG), a natural question to ask is how does this state manifests itself in graphene.…”