Even-denominator fractional quantum Hall physics in ZnO

Abstract

The fractional quantum Hall (FQH) e ect emerges in high-quality two-dimensional electron systems exposed to a magnetic field when the Landau-level filling factor, ν e , takes on a rational value. Although the overwhelming majority of FQH states have odd-denominator fillings, the physical properties of the rare and fragile even-denominator states are most tantalizing in view of their potential relevance for topological quantum computation. For decades, GaAs has been the preferred host for studying these even-denominator states, where they occur at ν e = 5/2 and 7/2. Here we report an anomalous series of quantized evendenominator FQH states outside the realm of III-V semiconductors in the MgZnO/ZnO 2DES electron at ν e = 3/2 and 7/2, with precursor features at 9/2; all while the 5/2 state is absent. The e ect in this material occurs concomitantly with tunability of the orbital character of electrons at the chemical potential, thereby realizing a new experimental means for investigating these exotic ground states.T he framework for the wide range of ground states observed in two-dimensional electron systems (2DES) resides in the discretized energy spectrum with a high degeneracy of the allowed states which emerges with the addition of a perpendicular magnetic field, B p . A ladder of spin-split Landau-levels (LLs) results with B p , inducing quantization of the orbital motion and lifting of the spin degeneracy. Each level is characterized by its orbital index N e = 0, 1, . . . and spin orientation (↑ or ↓). These levels can host as many charge carriers as magnetic flux quanta thread the sample and the filling factor, ν e , indicates how many levels are occupied. With increasing B p these LLs are successively depopulated and, on emptying a level completely, ν e takes on an integer value and the bulk of the 2DES becomes incompressible (see ref. 1 for an overview). The system exhibits the integer quantum Hall effect: vanishing longitudinal resistance (R xx ) and a Hall resistance (R xy ) quantized in units of h/e 2 . Further incompressible ground states may form at fractional fillings p/q when the electron number and number of flux quanta are commensurable. In contrast to FQH states at odd-denominator fillings, where the anti-symmetry constraint on the many-particle wavefunction imposed by the Pauli exclusion principle for fermions is automatically fulfilled, the development of even-denominator states 2-11 requires some mechanism which either restores the anti-symmetry of the manyparticle wavefunction or simply lifts the need to fulfil the Pauli exclusion principle. For systems where the charge carriers possess another degree of freedom, such as a layer or subband index, the anti-symmetry issue at even-denominator fillings may be solved by a two-component wavefunction. Indeed, in wide GaAs quantum wells with two subbands or in double-layer systems evendenominator states have been observed 2-7 and consensus has been reached that they are described by many-particle wavefunctions like the two-component ψ 331 -Laughlin sta...

Missing fractional quantum Hall states in ZnO

“…As mentioned above, in the experiment of [25] there is no indication of the 5 2 state, which is quite strong in the GaAs system. There could be several possible reasons for this: (i) the LL mixing may decrease or even close the gap of the incompressible ground state; (ii) a spin-mixed charge density wave state may exist between |0, ↓ and |1, ↑ , since the gap ∆ between the two levels is very small (for B = 3.75T, the gap is only ∆ = 0.05329 meV = 0.004167e 2 /ǫℓ [25]); or (iii) the screened Coulomb potential which integrates out all other LLs, changes the ground state.…”

“…The odd-denominator fractional states such as ν = 4 3 , 5 3 and 8 3 were observed here with indications of the ν = 2 5 state in the extreme quantum limit. Soon after, the evendenominator states, such as ν = 3 2 , and 7 2 were also observed [25], but surprisingly, the most prominent evendenominator state of the GaAs systems, the ν = 5 2 is conspicuously absent in the ZnO system. The system of 2DEG in ZnO is unique as compared to that in GaAs.…”

“…In the case of GaAs-based 2DEG, the LL gap is large compared to that for the Coulomb interaction (e 2 /ǫℓ, where ǫ is the dielectric constant and ℓ = /eB is the magnetic length with a magnectic field B). However, in a ZnO heterosturcutre [23][24][25] the LL gap is very small. The ratio κ between the Coulomb interaction and the LL gap is the relevant parameter in this context.…”

“…For odd denominator FQHE, for simplicity and without loss of generality, we consider only one LL and compare the collective modes with and without screening for filling factors ν = k/3, since the spin is polarized. This work focuses on the even denominator FQHE [25]. In a perpendicular magnetic field, ν = 3/2 state is not observed as is the case in GaAs system.…”

Nonlinear response of a MgZnO/ZnO heterostructure close to zero bias

“…(3), given by τ in /τ ∼ E F /τ (k B T ) 2 (E F is the Fermi energy, τ in is the inelastic relaxation time), can be significantly larger than unity, especially in high density and low mobility 2DESs [8,[13][14][15][16][17][18][19]. In such systems, nonlinear transport at small j offers a convenient way to obtain τ in and thus access the strength of electron-electron interactions in the 2DES under study.In this paper the capability of nonlinear transport to reveal information about scattering sources is exploited on a Mg x Zn 1−x O/ZnO heterostructure [11,[22][23][24][25][26][27]. We find that the correction to the differential resistivity can be well described by Eq.…”