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The electronic properties of graphene are described by a Dirac Hamiltonian with a four-fold symmetry of spin and valley. This symmetry may yield novel fractional quantum Hall (FQH) states at high magnetic field depending on the relative strength of symmetry-breaking interactions. However, observing such states in transport remains challenging in graphene, as they are easily destroyed by disorder. In this work, we observe in the first two Landau levels the two-flux composite-fermion sequences of FQH states between each integer filling factor. In particular, the odd-numerator fractions appear between filling factors 1 and 2, suggesting a broken-valley symmetry, consistent with our observation of a gap at charge neutrality and zero field. Contrary to our expectations, the evolution of gaps in a parallel magnetic field suggests that states in the first Landau level are not spin-polarized even up to very large out-of-plane fields.

The quantum Hall effect is investigated in the organic conductor (TMTSF${)}_{2}$P${\mathrm{F}}_{6}$ (TMTSF is tetramethyltetraselenafulvalene) under hydrostatic pressure. Under a pressure of $p\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}9$ kbar, the sequence of the quantum Hall numbers $L\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\sigma}}_{\mathrm{xy}}/({\ensuremath{-}2e}^{2}/h)$ with increasing magnetic field is regular: $L\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\dots{},3,2,1,\dots{}$ as reported earlier. At $p\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8.5$ kbar, however, the irregular sequence $L\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\dots{},3,\ensuremath{-}2,2,1,\dots{}$ is found. The temperature--magnetic field phase diagram is investigated in detail. We discuss our findings in the framework of recent theories of the quantum Hall effect in magnetic-field-induced spin-density waves.

The study of the magnetoresistance in the organic quasi-one-dimensional conductor (TMTSF)2NO3 at a pressure (8 kbar) exceeding the critical pressure required for the stabilization of a conducting state at low temperature has revealed the existence of quantum oscillations with a frequency of 190 T in good agreement with an extended Huckel-type calculation of the band structure. Unlike other members of the (TMTSF)2X series the ambient pressure SDW ground state in (TMTSF)2NO3 can be understood in terms of an instability involving the nesting of 2D semi-metallic Fermi surfaces.

The resistivity along the conducting chains, ρ xx , and the Hall resistivity ρ xy are investigated as a function of the electric field in the magnetic-field-induced spin-density wave (FISDW) states of (TMTSF) 2 PF 6 under hydrostatic pressure. Both resistivities decrease with increasing electric field above the same well-defined threshold electric field in the order of 100 μV/cm. We interpret the nonlinearity by the depinning and sliding of the FISDW. The nonlinearity in ρ xy is much stronger than in ρ xx what we attribute to an unusually strong coupling between the FISDW and single-particle excitations

We present and analyze the normal phase temperature dependence of resistivity and nuclear spin-lattice relaxation of $(\mathrm{TMTSF}{)}_{2}{\mathrm{ClO}}_{4}$ under strong transverse magnetic fields. From a field-dependent scaling theory we show that the singular enhancement of the one-dimensional electron-electron umklapp scattering and antiferromagnetic spin correlations under field play a fundamental role in the large enhancement of magnetoresistance and nuclear relaxation of Bechgaard salts.

Measurements of the Hall effect at low electric fields in the metallic and spin-density wave (SDW) phases in (TMTSF) 2 AsF 6 shows that the scattering of single particles is strongly reduced in the SDW phase. This is attributed to a strong electron-electron scattering present in the metallic phase and absent in the SDW phase. Above the depinning threshold field for the nonlinear SDW conductivity the Hall voltage is a reliable measure of the quasiparticle current. This current is reduced above the depinning threshold because of the backflow of quasiparticles due to the interaction with the moving SDW. At 4.2 K the backflow coefficient is comparable to what is observed in CDW systems