Experimental evidence for a spin-polarized ground state in the ν=5/2 fractional quantum Hall effect

Abstract

We study the ν = 5/2 even-denominator fractional quantum Hall effect (FQHE) over a wide range of magnetic field in a heterojunction insulated gate field-effect transistor (HIGFET). The electron density can be tuned from n = 0 to 7.6 × 10 11 cm −2 with a peak mobility µ = 5.5 × 10 6 cm 2 /Vs. The ν = 5/2 state shows a strong minimum in diagonal resistance and a developing Hall plateau at magnetic fields (B) as high as 12.6T. The strength of the energy gap varies smoothly with B-field. We interpret these observations as strong evidence for a spin-polarized ground state at ν = 5/2. Eisenstein et al.[4] tested the spin-polarization of the ν = 5/2 state by tilted magnetic field experiments [5] in a traditional, fixed-density sample. While the orbital motion of the electrons and hence their correlation energy (E c ) is subject only to the perpendicular component of the magnetic (B) field, the Zeeman energy (E z ) depends on the total B-field. Varying angle and B-field, the specimen can be kept in the ν = 5/2 state while the Zeeman energy is raised. Such a procedure should leave a spinpolarized state intact, but should be detrimental to a spin-unpolarized state, once the Zeeman energy cost surmounts the gain in correlation energy. In the experiment the strength of the ν = 5/2 state decreased quickly upon tilting and the state disappeared totally at θ ∼ 50 • . This was taken as evidence of a spin-singlet state at ν = 5/2.In recent years, with the advent of the composite fermion (CF) model [6,7], there has been a renewed interest in the ν = 5/2 state [8][9][10][11][12][13][14][15][16][17][18][19]. Moore and Read (MR) proposed a ground state of p-wave paired CF's [8]. Unlike the HR state, the MR state is spin-polarized. It is now being argued that the earlier disappearance of the ν = 5/2 state under tilt may be the result of the compression of the wave function due to the in-plane component of the B-field. This reduction of the z-extend of the wave function affects electron correlation and is the cause for the gap collapse, rather than the suspected increase in Zeeman energy. Indeed, recently two tilted field experiments [20,21] showed that the added in-plane magnetic field not only destroys the FQHE at ν = 5/2 but also induces an electronic transport anisotropy. Theoretical modeling [22] suggests that this is due to a phase transition from the MR pairing state to an anisotropic state and unrelated to any spin-effect. Hence, the spinpolarization of the ν = 5/2 FQHE remains unresolved and there is presently little experimental input into the debate over the nature of the even-denominator FQHE state.Here we pursue the spin-polarization of the ν = 5/2 state in analogy to the tilted field experiments by investigating the competition between E c and E z . Rather than tuning their ratio in a fixed density specimen by tilt, we keep the B-field perpendicular to the 2DES and employ a variable density specimen. Since for a fixed filling factor, such as ν = 5/2, E c ∝ n 1/2 , whereas E z ∝ n, increasing electron density modifies the...

Observation of an anomalous density-dependent energy gap of the ν=5/2 fractional quantum Hall state in the low-density regime

“…A contrasting behavior of precipitous collapse of ∆ 5/2 with an increasing density 15 has only been observed with the polulation of the second electrical subband 11,15,72 . The absence of any beating in the Shubnikov-de Haas oscillations and a lack of reduction of the mobility with an increasing density show that in our sample we do not populate the second electric subband 4,82 . We note that a linear extrapolation of our lowest density data from Fig.4 shows that ∆ 5/2 vanishes near the extrapolated value of n 4.5 × 10 10 cm −2 , a value which is in a reasonable agreement with other data measured at low densities 16,25 .…”

“…This trend is captured in Fig.4. Such a suppression of ∆ 5/2 with a decreasing density is expected 64,65,70 and it has experimentally been observed in the regime in which only the lowest electrical subband is populated 4,10,[14][15][16]25 . A contrasting behavior of precipitous collapse of ∆ 5/2 with an increasing density 15 has only been observed with the polulation of the second electrical subband 11,15,72 .…”

“…In a disorder-free environment the energy gap at a given filling factor is expected to scale with the Coulomb energy E C and, therefore with √ n. As seen in Fig.4, the measured dependence of ∆ on n is clearly not captured by such a simple √ n functional dependence. However, in addition to the Coulomb term proportional to √ n one also has to consider the disorder broadening of the energy levels 64 , a parameter with an unknown density dependence 4,10,[14][15][16]25 .…”

Fractional quantum Hall effect of two-dimensional electrons in high-mobility Si/SiGe field-effect transistors

“…3, we display the evolution of R xx vs. B from B = 5 T to 17 T, showing that the minima at ν = 10/7, 6/5, and 4/5 have weak temperature dependence while the adjacent maxima rise with decreasing temperature. In order to quantitatively analyze the temperature dependence, we employ the method used in previous studies to assign a characteristic strength to a FQH state [24,25]. We define the strength (S) of the state as the ratio of the resistance minimum to the average of the adjacent maxima, as depicted in Fig.…”

Spin and Charge Ordering in the Quantum Hall Regime

“…In later years, the vanishing 5 ⁄2 state was attributed rather to the emergence of an anisotropic stripe phase [108,109,122,151,152]. Pan et al approached the spin polarization of the 5 ⁄2 state in a different way [153]. They determined the energy gap at = 5 ⁄2 over a wide density range and compared its evolution with the behavior of the FQHS at = 8 ⁄5, a state known to be unpolarized at low electron densities.…”