NMR investigation of how free composite fermions are at nu=1 / 2

Luttinger Theorem for the Strongly Correlated Fermi Liquid of Composite Fermions

While an ordinary Fermi sea is perturbatively robust to interactions, the paradigmatic composite-fermion (CF) Fermi sea arises as a nonperturbative consequence of emergent gauge fields in a system where there was no Fermi sea to begin with. A mean-field picture suggests two Fermi seas, of composite fermions made from electrons or holes in the lowest Landau level, which occupy different areas away from half filling and thus appear to represent distinct states. Using the microscopic theory of composite fermions, which satisfies particle-hole symmetry in the lowest Landau level to an excellent approximation, we show that the Fermi wave vectors at filling factors ν and 1-ν are equal when expressed in units of the inverse magnetic length, and are generally consistent with the experimental findings of Kamburov et al. [Phys. Rev. Lett. 113, 196801 (2014)]. Our calculations suggest that the area of the CF Fermi sea may slightly violate the Luttinger area rule.

Enigmatic 4/11 state: a prototype for unconventional fractional quantum Hall effect

The origin of the fractional quantum Hall effect (FQHE) at 4/11 and 5/13 has remained controversial. We make a compelling case that the FQHE is possible here for fully spin polarized composite fermions, but with an unconventional underlying physics. Thanks to a rather unusual interaction between composite fermions, the FQHE here results from the suppression of pairs with a relative angular momentum of three rather than one, confirming the exotic mechanism proposed by Wójs, Yi, and Quinn [Phys. Rev. B 69, 205322 (2004)]. We predict that the 4/11 state reported a decade ago by Pan et al. [Phys. Rev. Lett. 90, 016801 (2003)] is a conventional partially spin polarized FQHE of composite fermions, and we estimate the Zeeman energy where a phase transition into the unconventional fully spin polarized state will occur.

Phase diagram of the two-component fractional quantum Hall effect

We calculate the phase diagram of the two component fractional quantum Hall effect as a function of the spin or valley Zeeman energy and the filling factor, which reveals new phase transitions and phase boundaries spanning many fractional plateaus. This phase diagram is relevant to the fractional quantum Hall effect in graphene and in GaAs and AlAs quantum wells, when either the spin or valley degree of freedom is active.

Multi-component fractional quantum Hall states in graphene: SU(4) versus SU(2)

Because of the spin and Dirac-valley degrees of freedom, graphene allows the observation of one-, two- or four-component fractional quantum Hall effects in different parameter regions. We address the stability of various states in the SU(2) and SU(4) limits. In the SU(4) limit, we predict that new low-energy Goldstone modes determine the stability of the fractional quantum Hall states at 2/5, 3/7, etc; SU(4) skyrmions are not found to be relevant for the low-energy physics. These results are discussed in light of experiments.

Dynamic nuclear polarization in the fractional quantum Hall regime

We investigate dynamic nuclear polarization in quantum point contacts (QPCs) in the integer and fractional quantum Hall regimes. Following the application of a dc bias, fractional plateaus in the QPC shift symmetrically about half filling of the lowest Landau level, ν=1/2, suggesting an interpretation in terms of composite fermions. Polarizing and detecting at different filling factors indicates that Zeeman energy is reduced by the induced nuclear polarization. Mapping effects from integer to fractional regimes extends the composite fermion picture to include hyperfine coupling.

Nature of the spin transition in the half-filled Landau level

We report transport and nuclear spin relaxation studies of a density tunable two-dimensional electron system at filling nu=1/2 in tilted magnetic fields. The transition from partial to full spin polarization with an in-plane field leaves a clear signature in the resistance. Nuclear spin relaxation studies suggest that puddles of minority spins are responsible for an observed non-Korringa temperature dependence. This inhomogeneous spin polarization, similarly encountered in manganites where it strongly affects resistance, may help with understanding the spin dependent transport at nu=1/2.

Absorption in the fractional quantum Hall regime: trion dichroism and spin polarization

We present measurements of optical interband absorption in the fractional quantum Hall regime in a GaAs quantum well in the range 0<nu<or=1. We investigate the mechanism of singlet trion absorption, and show that its circular dichroism can be used as a probe of the spin polarization of the ground state of the two-dimensional electron system (2DES). We find that at nu<or=1/3 the 2DES is fully spin polarized. Increasing the filling factor results in a gradual depolarization, with a sharp minimum in the dichroism near nu=2/3. We find that in the range 0.5<or=nu<0.85 the 2DES remains partially polarized for the broad range of magnetic fields from 2.75 to 11 T. This is consistent with the presence of a mixture of polarized and depolarized regions.

Spin transition in the half-filled Landau level

The transition from partial to complete spin polarization of two-dimensional electrons at half filling of the lowest Landau level has been studied using resistively detected nuclear magnetic resonance (RDNMR). The nuclear spin-lattice relaxation time is observed to be density independent in the partially polarized phase but to increase sharply at the transition to full polarization. At low temperatures the RDNMR signal exhibits a strong maximum near the critical density.

Composite-fermion spin excitations as nu approaches 1/2: interactions in the Fermi sea

Measurements of low-lying spin excitations by inelastic light scattering unveil a delicate balance between spin reversal and Fermi energies in the Fermi sea of composite fermions that emerges in the limit of nu --> 1/2. The interplays between these two fundamental quasiparticle interactions are uncovered in lowest spin-flip excitations in which the spin orientation and Landau level index of composite fermions change simultaneously. A collapse of the spin-flip excitation gap as nu --> 1/2 is linked to vanishing quasiparticle energy level spacings and loss of full spin polarization.

Direct measurement of the g factor of composite fermions

The activation gap Delta of the fractional quantum Hall states at constant fillings nu=2/3 and 2/5 has been measured as a function of the perpendicular magnetic field B. A linear dependence of Delta on B is observed while approaching the spin-polarization transition. This feature allows a direct measurement of the g factor of composite fermions which appears to be heavily renormalized by interactions and strongly sensitive to the electronic filling factor.

Anomalous-filling-factor-dependent nuclear-spin polarization in a 2D electron system

Spin-related electronic phase transitions in the fractional quantum Hall regime are accompanied by a large change in resistance. Combined with their sensitivity to spin orientation of nuclei residing in the same plane as the 2D electrons, they offer a convenient electrical probe to carry out nuclear magnetometry. Despite conditions which should allow both electronic and nuclear-spin subsystems to approach thermodynamic equilibrium, we uncover for the nuclei a remarkable and strongly electronic filling-factor-dependent deviation from the anticipated thermal nuclear-spin polarization.