Missing fractional quantum Hall states in ZnO

Abstract

We have analyzed the crucial role the Coulomb interaction strength plays on the even and odd denominator fractional quantum Hall effects in a two-dimensional electron gas (2DEG) in the ZnO heterointerface. In this system, the Landau level gaps are much smaller than those in conventional GaAs systems. The Coulomb interaction is also very large compared to the Landau level gap even in very high magnetic fields. We therefore consider the influence of higher Landau levels by considering the screened Coulomb potential in the random phase approximation. Interestingly, our exact diagonalization studies of the collective modes with this screened potential successfully explain recent experiments of even and odd denominator fractional quantum Hall effects, in particular, the unexpected absence of the 5/2 state and the presence of 9/2 state in ZnO.Discovery of the odd-denominator fractional quantum Hall effects (FQHE) in GaAs heterojunctions in 1982 [1] and its subsequent explanation by Laughlin [2,3], has remained the 'gold standard' for novel quantum states of correlated electrons in a strong magnetic field. These effects also have been observed in 'Dirac materials' such as graphene [4,5,9]. and are expected to be present in other graphene-like materials [6][7][8] with novel attributes. The FQHE states in monolayer and bilayer graphene were investigated theoretically [9][10][11][12] and experimentally [13,14]. For example, in bilayer graphene the application of a bias voltage results in some Landau levels (LLs) a phase transition between incompressible FQHE and compressible phases [11,12]. The FQHE in silicene and germanene indicated that because of the strong spinorbit interaction present in these materials as compared to graphene, the electron-electron interaction and the FQHE gap are significantly modified [15]. The puckered structure of phosphorene exhibits a lower symmetry than graphene. This results in anisotropic energy spectra and other physical characteristics of phosphorene, both in momentum and real space in the two-dimensional (2D) plane [16,17]. The anisotropic band structure of phosphorene causes splitting of the magnetoroton mode into two branches with two minima. For long wavelengths, we also found a second mode with upward dispersion that is clearly separated from the magnetoroton mode and is entirely due to the anisotropic bands [18].In 1987, a discovery of the quantum Hall state at the LL filling factor ν = 5 2 , the first even-denominator state observed in a single-layer system [19] added to the mystery of the FQHE. It soon became clear that this state must be different from the FQHE in predominantly odd-denominator filling fractions [1]. Understanding this enigmatic state has remained a major challenge in all these years [20,21]. At this half-filled first excited LL, a novel state described by a pair wave function involving a Pfaffian [12,22], where the low-energy excitations obey non-Abelian exchange statistics, has been the strongest * Tapash.Chakraborty@umanitoba.ca candidate.The field of FQHE has...

Pfaffian state in an electron gas with small Landau level gaps

“…However, the ground state should be compressible in the thermodynamic limit since the energy gap in this case is very size dependent and oscillates very much in Fig. 2(a), which agrees with our previous works in the less size-dependent torus geometry [25].…”

“…Consequently, we have proposed that the screened Coulomb interaction in which all the other LLs are integrated out in the random phase approximation (RPA) replaces the bare one, so that the correlations of the electrons become very different at different filling factors. This seems to explain the extraordinary phenomenon observed in the experiment [25,27].…”

“…Consequently, we have proposed that the screened Coulomb interaction in which all the other LLs are integrated out in the random phase approximation (RPA) replaces the bare one, so that the correlations of the electrons become very different at different filling factors. This seems to explain the extraordinary phenomenon observed in the experiment [25,27].Trial wavefunctions have been proposed to describe this special even-denominator FQHE state [3,[30][31][32]. It appears that the spin polarized Pfaffian state [33,34] is the most probable candidate.…”

“…The Pfaffian states and its topological properties can be potentially observed in this new system, albeit its low mobility. Surprisingly, in ZnO the well-known ν = 5 2 FQHE was found to go missing while its spinful electron-hole conjugate ν = 7 2 FQHE survived [24,25]. Tilted-field studies [26] also unveiled some interesting results in this system [24,27].…”

“…The screened pseudopotential was also used (although a simplified version of it) in [14]. As in the torus geometry, the two-dimensional Coulomb potential V (q) = [25,42,43],…”