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Register a new userProbing quantum criticality using nonlinear Hall effect in a metallic Dirac system
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Interaction driven symmetry breaking in a metallic (doped) Dirac system can manifest in the spontaneous gap generation at the nodal point buried below the Fermi level. Across this transition linear conductivity remains finite making its direct observation difficult in linear transport. We propose the nonlinear Hall effect as a direct probe of this transition when inversion symmetry is broken. Specifically, for a two-dimensional Dirac material with a tilted low-energy dispersion, we first predict a transformation of the characteristic inter-band resonance peak into a non-Lorentzian form in the collisionless regime. Furthermore, we show that inversion-symmetry breaking quantum phase transition is controlled by an exotic tilt-dependent line of critical points. As this line is approached from the ordered side, the nonlinear Hall conductivity is suppressed owing to the scattering between the strongly coupled incoherent fermionic and bosonic excitations. Our results should motivate further studies of nonlinear responses in strongly interacting Dirac materials.
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An antiphased magnetoplasma (MP) mode in a two-dimensional electron gas (2DEG) has been studied by means of inelastic light scattering (ILS) spectroscopy. Unlike the cophased MP mode it is purely quantum excitation which has no classic plasma analogue. It is found that zero momentum degeneracy for the antiphased and cophased modes predicted by the first-order perturbation approach in terms of the {it e-e} interaction is lifted. The zero momentum energy gap is determined by a negative correlation shift of the antiphased mode. This shift, observed experimentally and calculated theoretically within the second-order perturbation approach, is proportional to the effective Rydberg constant in a semiconductor material.
The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative consequences. We provide compelling theoretical evidence that the localization of a single quasiparticle of the fractional quantum Hall state at filling factor $ u=n/(2n+1)$ has a striking {it quantitative} correspondence to the localization of a single electron in the $(n+1)$th Landau level. By analogy to the dramatic experimental manifestations of Anderson localization in integer quantum Hall effect, this leads to predictions in the fractional quantum Hall regime regarding the existence of extended states at a critical energy, and the nature of the divergence of the localization length as this energy is approached. Within a mean field approximation these results can be extended to situations where a finite density of quasiparticles is present.
We report experimental observation of the Planar Hall effect (PHE) in a type-II Dirac semimetal PtTe$_2$. This unusual Hall effect is not expected in nonmagnetc materials such as PtTe$_2$, and has been observed previously mostly in magnetic semiconductors or metals. Remarkably, the PHE in PtTe$_2$ can be observed up to temperatures near room temperature which indicates the robustness of the effect. This is in contrast to the chiral anomaly induced negative longitudnal magnetoresistance (LMR), which can be observed only in the low temperature regime and is sensitive to extrinsic effects, such as current jetting and chemical inhomogeneities in crystals of high mobility. Planar Hall effect on the other hand is a purely intrinsic effect generated by the Berry curvature in Weyl semimetals. Additionally, the PHE is observed for PtTe$_2$ even though the Dirac node is $approx 0.8$~eV away from the Fermi level. Thus our results strongly indicate that PHE can be used as a crucial transport diagnostic for topological character even for band structures with Dirac nodes slightly away from the Fermi energy.
The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to super-fluidity, and from the periodic table to coherent propagation of light. The dichotomy originates from the symmetry of the quantum mechanical wave function to the interchange of two identical particles. In systems that are confined to two spatial dimensions particles that are neither fermions nor bosons, coined anyons, may exist. The fractional quantum Hall effect offers an experimental system where this possibility is realized. In this paper we present the concept of anyons, we explain why the observation of the fractional quantum Hall effect almost forces the notion of anyons upon us, and we review several possible ways for a direct observation of the physics of anyons. Furthermore, we devote a large part of the paper to non-abelian anyons, motivating their existence from the point of view of trial wave functions, giving a simple exposition of their relation to conformal field theories, and reviewing several proposals for their direct observation.
We discuss the development of a sensitive electrometer that utilizes a two-dimensional electron gas (2DEG) in the quantum Hall regime. As a demonstration, we measure the evolution of the Landau levels in a second, nearby 2DEG as the applied perpendicular magnetic field is changed, and extract an effective mass for electrons in GaAs that agrees within experimental error with previous measurements.
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