Hall plateaus at magic angles in bismuth beyond the quantum limit (original) (raw)
Related papers
Reviews of Modern Physics, 2010
We present a review of experimental and theoretical studies of the anomalous Hall effect (AHE), focusing on recent developments that have provided a more complete framework for understanding this subtle phenomenon and have, in many instances, replaced controversy by clarity. Synergy between experimental and theoretical work, both playing a crucial role, has been at the heart of these advances. On the theoretical front, the adoption of Berry-phase concepts has established a link between the AHE and the topological nature of the Hall currents which originate from spin-orbit coupling. On the experimental front, new experimental studies of the AHE in transition metals, transition-metal oxides, spinels, pyrochlores, and metallic dilute magnetic semiconductors, have more clearly established systematic trends. These two developments in concert with first-principles electronic structure calculations, strongly favor the dominance of an intrinsic Berry-phase-related AHE mechanism in metallic ferromagnets with moderate conductivity. The intrinsic AHE can be expressed in terms of Berry-phase curvatures and it is therefore an intrinsic quantum mechanical property of a perfect cyrstal. An extrinsic mechanisms, skew scattering from disorder, tends to dominate the AHE in highly conductive ferromagnets. We review the full modern semiclassical treatment of the AHE which incorporates an anomalous contribution to wavepacket group velocity due to momentum-space Berry curvatures and correctly combines the roles of intrinsic and extrinsic (skew scattering and side-jump) scattering-related mechanisms. In addition, we review more rigorous quantum-mechanical treatments based on the Kubo and Keldysh formalisms, taking into account multiband effects, and demonstrate the equivalence of all three linear response theories in the metallic regime. Building on results from recent experiment and theory, we propose a tentative global view of the AHE which summarizes the roles played by intrinsic and extrinsic contributions in the disorder-strength vs. temperature plane. Finally we discuss outstanding issues and avenues for future investigation.
Signatures of Electron Fractionalization in Ultraquantum Bismuth
Science, 2007
In elemental bismuth (contrary to most metals), due to the long Fermi wavelength of itinerant electrons, the quantum limit can be attained with a moderate magnetic field. Beyond this limit, electrons travel in quantized orbits whose circumference (shrinking with increasing magnetic field) becomes shorter than their Fermi wavelength. We present a study of transport coefficients of a single crystal of bismuth up to 33 T, i.e. deep in this ultraquantum limit. The Nernst coefficient presents three unexpected maxima which are concomitant with quasi-plateaus in the Hall coefficient. The results suggest that this bulk element may host an exotic quantum fluid reminiscent of the one associated with the fractional quantum Hall effect and raise the issue of electron fractionalization in a three dimensional metal.
Intrinsic mechanism of anomalous Hall effect in a twodimensional magnetic system with impurities
physica status solidi (c), 2006
We report some new results on the Anomalous Hall effect induced by the Berry phase in momentum space. Our main calculations are performed within the model of a two-dimensional electron gas with the spin-orbit interaction of Rashba type, taking into account the scattering from impurities. We demonstrate that such an "intrinsic" mechanism can really dominate but there is a competition between the geometric Berry-phaseinduced term σ II xy in the Hall conductivity and the impurity-induced term σ I xy , related to the contribution of the states in the vicinity of the Fermi surface. We also show that the contribution to the Hall conductivity from the electron states close to the Fermi surface has the intrinsic property as well, and it does not vanish in the clean limit. The main effect of the impurity-related contribution is a possible change of sign of the off-diagonal conductivity. The resulting magnitude and sign of the Hall conductivity strongly depend on the electron density in the system.
Experimental evidence for a two-dimensional quantized Hall insulator
Nature, 1998
The general theoretical de®nition of an insulator is a material in which the conductivity vanishes at the absolute zero of temperature. In classical insulators, such as materials with a band gap, vanishing conductivities lead to diverging resistivities. But other insulators can show more complex behaviour, particularly in the presence of a high magnetic ®eld, where different components of the resistivity tensor can display different behaviours: the magnetoresistance diverges as the temperature approaches absolute zero, but the transverse (Hall) resistance remains ®nite. Such a system is known as a Hall insulator 1 . Here we report experimental evidence for a quantized 2 Hall insulator in a two-dimensional electron systemÐcon®ned in a semiconductor quantum well. The Hall resistance is quantized in the quantum unit of resistance h/e 2 , where h is Planck's constant and e the electronic charge. At low ®elds, the sample reverts to being a normal Hall insulator.
Journal of Physics: Condensed Matter, 2020
When an electron is free or in the ground state of an atom, its g-factor is 2, as first shown by Dirac. But when an electron or hole is in a conduction band of a crystal, it can be very different from 2, depending upon the crystalline anisotropy and the direction of the applied magnetic induction B. In fact, it can even be 0! To demonstrate this quantitatively, the Dirac equation is extended for a relativistic electron or hole in an orthorhombically-anisotropic conduction band with effective masses mj for j = 1, 2, 3 with geometric mean mg = (m1m2m3) 1/3. Its covariance is established with general proper and improper Lorentz transformations. The appropriate Foldy-Wouthuysen transformations are extended to evaluate the non-relativistic Hamiltonian to O(mc 2) −4 , where mc 2 is the particle's Einstein rest energy. The results can have extremely important consequences for magnetic measurements of many classes of clean anisotropic semiconductors, metals, and superconductors. For B||êµ, the Zeeman gµ factor is 2m √ mµ/m 3/2 g + O(mc 2) −2. While propagating in a two-dimensional (2D) conduction band with m3 ≫ m1, m2, g || << 2, consistent with recent measurements of the temperature T dependence of the parallel upper critical induction B c2,|| (T) in superconducting monolayer NbSe2 and in twisted bilayer graphene. While a particle is in its conduction band of an atomically thin one-dimensional metallic chain alongêµ, g << 2 for all B = ∇ × A directions and vanishingly small for B||êµ. The quantum spin Hall Hamiltonian for 2D metals with m1 = m2 = m || is K[E × (p − qA)] ⊥ σ ⊥ + O(mc 2) −4 , where E and p − qA are the planar electric field and gauge-invariant momentum, q = ∓|e| is the particle's charge, σ ⊥ is the Pauli matrix normal to the layer, K = ±µB/(2m || c 2), and µB is the Bohr magneton.
Hall effect in heavy fermion metals
Advances in Physics, 2012
The heavy fermion systems present a unique platform in which strong electronic correlations give rise to a host of novel, and often competing, electronic and magnetic ground states. Amongst a number of potential experimental tools at our disposal, measurements of the Hall effect have emerged as a particularly important one in discerning the nature and evolution of the Fermi surfaces of these enigmatic metals. In this article, we present a comprehensive review of Hall effect measurements in the heavy-fermion materials, and examine the success it has had in contributing to our current understanding of strongly correlated matter. Particular emphasis is placed on its utility in the investigation of quantum critical phenomena which are thought to drive many of the exotic electronic ground states in these systems. This is achieved by the description of measurements of the Hall effect across the putative zero-temperature instability in the archetypal heavy-fermion metal YbRh 2 Si 2. Using the CeM In 5 (with M = Co, Ir) family of systems as a paradigm, the influence of (antiferro-)magnetic fluctuations on the Hall effect is also illustrated. This is compared to prior Hall effect measurements in the cuprates and other strongly correlated systems to emphasize on the generality of the unusual magnetotransport in materials with non-Fermi liquid behavior.
Quantum Hall Ferromagnetism in the Presence of Tunable Disorder
Physical Review Letters, 2011
In this Letter, we report our recent experimental results on the energy gap of the ¼ 1 quantum Hall state (Á ¼1 ) in a quantum antidot array sample, where the effective disorder potential can be tuned continuously. Á ¼1 is nearly constant at small effective disorders, and collapses at a critical disorder. Moreover, in the weak disorder regime, Á ¼1 shows a B total 1=2 dependence in tilted magnetic field measurements, while in the strong disorder regime, Á ¼1 is linear in B total , where B total is the total magnetic field at ¼ 1. We discuss our results within several models involving the quantum Hall ferromagnetic ground state and its interplay with sample disorder.
Anomalous Hall effect in ferromagnetic disordered metals
Annalen der Physik, 2006
The anomalous Hall effect in disordered band ferromagnets is considered in the framework of quantum transport theory. A microscopic model of electrons in a random potential of identical impurities including spin-orbit coupling is used. The Hall conductivity is calculated from the Kubo formula for both, the skew scattering and the side-jump mechanisms. The recently discussed Berry phase induced Hall current is also evaluated within the model. The effect of strong impurity scattering is analyzed and it is found to affect the ratio of the non-diagonal (Hall) and diagonal components of the conductivity as well as the relative importance of different mechanisms. I.
A new transport regime in the quantum Hall effect
Solid State Communications, 1998
Our evolving understanding of the dramatic features of charge-transport in the quantum Hall (QH) regime has its roots in the more general problem of the metal-insulator transition. Conversely, the set of conductivity transitions observed in the QH regime provides a fertile experimental ground for studying many aspects of the metal-insulator transition. While earlier works tend to concentrate on transitions between adjacent QH liquid states, more recent works focus on the transition from the last QH state to the high-magnetic-field insulator. Here we report on measurements that identified a novel transport regime which is distinct from both, the fully developed QH liquid, and the critical scaling regime believed to exist asymptotically close to the transition at very low temperatures (T 's).
Itinerant Electron Ferromagnetism in the Quantum Hall Regime
Physical Review B, 1998
We report on a study of the temperature and Zeeman-coupling-strength dependence of the one-particle Green's function of a two-dimensional (2D) electron gas at Landau level filling factor nu=1\nu =1nu=1 where the ground state is a strong ferromagnet. Our work places emphasis on the role played by the itinerancy of the electrons, which carry the spin magnetization and on analogies between this system and conventional itinerant electron ferromagnets. We discuss the application to this system of the self-consistent Hartree-Fock approximation, which is analogous to the band theory description of metallic ferromagnetism and fails badly at finite temperatures because it does not account for spin-wave excitations. We go beyond this level by evaluating the one-particle Green's function using a self-energy, which accounts for quasiparticle spin-wave interactions. We report results for the temperature dependence of the spin magnetization, the nuclear spin relaxation rate, and 2D-2D tunneling conductances. Our calculations predict a sharp peak in the tunneling conductance at large bias voltages with strength proportional to temperature. We compare with experiment, where available, and with predictions based on numerical exact diagonalization and other theoretical approaches.