Exact Quantization of the Even-Denominator Fractional Quantum Hall State atν=5/2Landau Level Filling Factor

Abstract

We report ultra-low temperature experiments on the obscure fractional quantum Hall effect (FQHE) at Landau level filling factor ν = 5/2 in a very high mobility specimen of µ = 1.7 × 10 7 cm 2 /Vs. We achieve an electron temperature as low as ∼ 4 mK, where we observe vanishing Rxx and, for the first time, a quantized Hall resistance, Rxy = h/(5/2e2 ) to within 2 ppm. Rxy at the neighboring odd-denominator states ν = 7/3 and 8/3 is also quantized. The temperature dependences of the Rxx-minima at these fractional fillings yield activation energy gaps ∆ 5/2 = 0.11 K, ∆ 7/3 = 0.10 K, and ∆ 8/3 = 0.055 K.PACS Numbers: 73.40Hm Electrons in two-dimensional systems at low temperatures and in the presence of an intense magnetic field condense into a sequence of incompressible quantum fluids with finite energy gaps for quasiparticle excitation, termed collectively the fractional quantum Hall effect (FQHE) [1]. These highly correlated electronic states occur at rational fractional filling ν = p/q of Landau levels. Their characteristic features in electronic transport experiments are vanishing resistance, R xx , and exact quantization of the concomitant Hall resistance, R xy , to h/(p/qe 2 ). Over the years, a multitude of FQHE states have been discovered -all q's being odd numbers. The only known exceptions are the states at half-filling of the second Landau level ν = 5/2 (=2+1/2) and ν = 7/2 (=3+1/2) [2-4]. Half-filled states in the lowest Landau level show no FQHE, whereas half-filled states in still higher Landau levels exhibit yet unresolved anisotropies [5]. Recent experiments in tilted magnetic field even seem to hint at a connection between the ν = 9/2 state and the state at ν = 5/2 [6].The origin of the ν = 5/2 and 7/2 states remains mysterious. Observation of odd-denominator FQHE states is intimately connected to the anti-symmetry requirement for the electronic wave function. An early, socalled hollow-core model [7] for the FQHE at ν = 5/2 and 7/2, which takes explicitly into account aspects of the modified single-particle wave functions of the second Landau level, arrived at a trial wave function. However, for a Coulomb Hamiltonian its applicability is problematic [8,9].With the advent of the composite fermion (CF) model [10] the existence of exclusively odd-denominator FQHE states is traced back to the formation of Landau levels of CFs emanating from even-denominator fillings, such as the sequence ν = p/(2p ± 1) from ν = 1/2. Evendenominator fillings themselves represent Fermi-liquid like states, resulting from the attachment of an even number of magnetic flux quanta to each electron. The obvious conflict between this theory and experiment at ν = 5/2 is resolved by invoking a CF-pairing mechanism [11][12][13][14]. In loose analogy to the formation of Cooper pairs in superconductivity such pairing creates a gapped, BCS-like ground state at ν = 5/2, called a "Pfaffian" state, which displays a FQHE. Indeed, an exact numerical diagonalization calculation by Morf [9] favors the Pfaffian state.The experimental si...

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

“…Since we are limited to standard dilution-refrigerator temperatures of T > 30mK, R xx never vanishes in our HIGFET data, in contrast to our previous ultra-low temperature measurements [2]. For this reason we cannot determine the energy gap, ∆, from activation energy measurement.…”

“…∆ quasi hovers around 150mK and there is little variation over this magnetic field range. Our previous, ultra-low temperature measurement [2] on a fixed density (2.3×10 11 cm −2 ) specimen yielded an activation energy of ∆ = 110mK. A comparison between both data indicates that the value of the ∆ quasi is a good approximation to ∆.…”

“…Results of recent ultra-low temperature experiments [2] leave no doubt that this even-denominator state is a true FQHE with vanishing resistivity and Hall plateau formation. Such an even-denominator state does not fit the normal odddenorminator rule of the FQHE and requires other or additional electron correlations.…”

Fractional quantum Hall hierarchy and the second Landau level

“…2,3 The observed filling fractions, the measured fractional charge of quasiparticles, 4-6 and recent results from interferometric experiments 7,8 all support this picture, and are backed up by a wealth of theoretical and numerical evidence. The physics of the second Landau level, however, remains far more perplexing, with the prominence of an evendenominator =5/ 2 FQH state 9,10 that cannot be explained by the standard hierarchy. Fully developed FQH plateaus have been observed at =7/ 3, 12/5, 5/2, 8/3, and 14/5, 10,11 but advances in experiments and sample quality may find additional plateaus developing where "features" have been observed, including at another intriguing even-denominator =19/ 8.…”

“…The physics of the second Landau level, however, remains far more perplexing, with the prominence of an evendenominator =5/ 2 FQH state 9,10 that cannot be explained by the standard hierarchy. Fully developed FQH plateaus have been observed at =7/ 3, 12/5, 5/2, 8/3, and 14/5, 10,11 but advances in experiments and sample quality may find additional plateaus developing where "features" have been observed, including at another intriguing even-denominator =19/ 8. 11,12 There are also sometimes observed signs of what appear to be developing FQH states at =11/ 5, 16/7, 13/5, 19/7, and 25/9, but these dematerialize as lower temperatures are attained.…”