Anomalous Hall effect in the phonon thermal conductivity of paramagnetic dielectrics

A theory of the phonon Hall effect during heat transfer in a paramagnetic dielectric discovered by Strohm et al. [Phys. Rev. 95, 155901 (2005)] is developed. The heat flux emerging in the direction perpendicular to the magnetic field and to the temperature gradient is associated with the interaction of magnetic ions with the oscillating crystal field. In crystals with an arbitrary phonon spectrum, this interaction induces elliptic polarization of phonons. On the other hand, for any type of scattering, the temperature gradient forms part of the phonon density matrix, which is nondiagonal in modes. The combined action of these factors leads to the anomalous Hall effect.     

Anomalous Hall effect for the phonon heat conductivity in paramagnetic dielectrics

The theory of the anomalous Hall effect for the heat transfer in a parmagnetic dielectric, discovered by Strohm, Rikken, and Wyder [Phys. Rev. Lett. 95, 155901 (2005)]10.1103/PhysRevLett.95.155901, is developed. The appearance of the phonon heat flux normal to both the temperature gradient and the magnetic field is connected with the interaction of magnetic ions with the crystal field oscillations. In crystals with an arbitrary phonon spectrum this interaction creates the elliptical polarization of phonons. The kinetics related to phonon scattering induced by the spin-phonon interaction determines an origin of the off-diagonal phonon density matrix. The combination of both factors is decisive for the phenomenon under consideration.     

Hall conductivity for two-dimensional magnetic systems

A Kubo inspired formalism is proposed to compute the longitudinal and transverse dynamical conductivities of an electron in a plane (or a gas of electrons at zero temperature) coupled to the potential vector of an external local magnetic field, with the additional coupling of the spin degree of freedom of the electron to the local magnetic field (Pauli Hamiltonian). As an example, the homogeneous magnetic field Ha]] conductivity is rederived. The case of the vortex at the origin is worked out in detail. This system happens to display a transverse Ha]] conductivity (P breaking effect) which is subleading in volume compared to the homogeneous field case, but diverging at small frequencies like 1/ω². A perturbative analysis is proposed for the conductivity in the random magnetic impurity problem (Poissonian vortices in the plane). At first order in perturbation theory, the Ha]] conductivity displays oscillations close to the classical straight line conductivity of the mean magnetic field.     

Optical Hall conductivity of systems with gapped spectral nodes

We calculate the optical Hall conductivity within the Kubo formalism for systems with gapped spectral nodes, where the latter have a power-law dispersion with exponent n. The optical conductivity is proportional to n and there is a characteristic logarithmic singularity as the frequency approaches the gap energy. The optical Hall conductivity is almost unaffected by thermal fluctuations and disorder for n = 1, whereas disorder has a stronger effect on transport properties if n = 2.     

Anomalous thermal conductivity of polyacetylene

Measurements of the specific heat and of the thermal conductivity of pure and iodine doped polyacetylene from liquid helium to room temperature are reported. The thermal conductivity rises linearly from 3 to 50 K and with about the third power of the temperature from 50 to 300 K. The kink at 50 K corresponds to a very unusual minimum of the phonon mean free path, probably caused by resonant scattering of fast thermal phonons (which travel along the chains) on low frequency interchain modes. These results suggest that the polymer chains are oriented parallel to the well-known fibers in polyacetylene.     

Universal conductance and conductivity at critical points in integer quantum Hall systems

The sample averaged longitudinal two-terminal conductance and the respective Kubo conductivity are calculated at quantum critical points in the integer quantum Hall regime. In the limit of large system size, both transport quantities are found to be the same within numerical uncertainty in the lowest Landau band, and , respectively. In the second-lowest Landau band, a critical conductance is obtained which indeed supports the notion of universality. However, these numbers are significantly at variance with the hitherto commonly believed value . We argue that this difference is due to the multifractal structure of critical wave functions, a property that should generically show up in the conductance at quantum critical points.     

Anomalous emission of electrons from MIM systems

In this paper the emission of electrons from thin-film systems of the structure metal-dielectric-metal (Al-Al₂O₃-Au) is studied experimentally in the voltage region below the work potential of the top electrode. The temperature and voltage dependences of the angular distribution, energy distributionsN(E) andN (Einx) and energy-angular distribution of emitted both anomalous and normal electrons were obtained.This paper is based on the RNDr thesis of the first author.     

Anomalous hydrodynamics of fractional quantum Hall states

We propose a comprehensive framework for quantum hydrodynamics of the fractional quantum Hall (FQH) states. We suggest that the electronic fluid in the FQH regime can be phenomenologically described by the quantized hydrodynamics of vortices in an incompressible rotating liquid. We demonstrate that such hydrodynamics captures all major features of FQH states, including the subtle effect of the Lorentz shear stress. We present a consistent quantization of the hydrodynamics of an incompressible fluid, providing a powerful framework to study the FQH effect and superfluids. We obtain the quantum hydrodynamics of the vortex flow by quantizing the Kirchhoff equations for vortex dynamics.     

量子反常霍尔效应研究进展

在没有外加磁场的作用下就能表现出量子化霍尔电导的量子反常霍尔效应已经成为霍尔家族中的重要一员,其物理起源是体能带反转结构和铁磁性相互作用.量子反常霍尔效应最重要的表现是在边缘态处具有无耗散运动的手性电流,这种性质拥有可以改变未来量子电子学的潜力,极大推动器件小型化、低损耗、高速率发展.近年来,基于理论指导,人们在实验上已多次观察到量子反常霍尔效应.在本文中,从实验层面上重点回顾了量子反常霍尔效应在铬(Cr)、钒(V)掺杂的(Bi, Sb)₂Te₃体系的研究进展,以及目前量子反常霍尔效应在其它体系中的研究现状,深入理解量子反常霍尔效应的起源和机理,最后对量子反常霍尔效应进行总结和展望.     

Analysis of the Anomalous Brillet and Hall Experimental Result

The persistent, second-order, anomalous signal found in the Brillet and Hall experiment is derived by applying 4D differential geometry in the rotating earth frame. By incorporating the off diagonal time-space components of the rotating frame metric directly into the analysis, rather than arbitrarily transforming them away, one finds a signal dependence on the surface speed of the earth due to rotation about its axis. This leads to a Brillet-Hall signal prediction in remarkably close agreement with experiment. No signal is predicted from the speed of the earth in solar or galactic orbit, as the associated metric for gravitational orbit has no off diagonal component. To corroborate this result, a repetition by other experimentalists of the Brillet-Hall experiment, in which the test apparatus turns with respect to the earth surface, is urged.     

Hall conductivity of a spin-triplet superconductor

We calculate the Hall conductivity for a spin-triplet superconductor, using a generalized pairing symmetry dependent on an arbitrary phase phi. A promising candidate for such an order parameter is Sr2RuO4, whose superconducting order parameter symmetry is still subject to investigation. The value of this phase can be determined through Kerr rotation and dc Hall conductivity measurements. Our calculations impose significant constraints on phi.     

Topological investigation of the fractionally quantized Hall conductivity

Using the fiber bundle concept developed in geometry and topology, the fractionally quantized Hall conductivity is discussed in the relevant many-particle configuration space. Electronmagnetic field and electron-electron interactions under FQHE conditions are treated as functional connections over the torus, the torus being the underlying two-dimensional manifold. Relations to the (2 + 1)-dimensional Chern-Simons theory are indicated. The conductivity being a topological invariant is given as e²/h times a linking number which is the quotient of the winding numbers of the self-consistent field and the magnetic field, respectively. Odd denominators are explained by the two spin structures which have been considered for the FQHE correlated electron system.     

Detecting the Anomalous Quantum Hall phase under magnetic field

Detecting the charming topological phase has been an ongoing topic. In this work, we take the square lattice as an example and try to detect the anomalous quantum Hall (AQH) phase under magnetic field. We analyze the topological energy levels of the system, the quantum Hall effect and quantum valley Hall effect, and the number of scattered electrons after a laser pulse, from which the unambiguous signals to characterize the AQH phases can be obtained. Meanwhile the corresponding valley polarizations of electrons are investigated. Our study opens new perspectives for the applications of valleytronics in the future.     

Anomalous Hall effect in the mixed state of high-temperature superconductors

The Hall effect in the mixed state of high-T_c superconductors (HTSC) is of an anomalous nature: near the transition there is a range of temperatures and of magnetic fields where the sign of the Hall effect is opposite to that in the normal state. The universality of the phenomenon in question is indicative of its connection with some general properties of the mixed state of type-II superconductors, namely, with peculiarities of motion of magnetic flux vortex lines (vortices) in these superconductors. This work puts forward a model accounting for a number of vortex motion specific features and providing a possibility to obtain the characteristics of the anomalous Hall effect.

The work is based on the phenomenologically generalized results of Bardeen-Stephen and Nozieres-Vinen, supplemented with an allowance for a new mechanism of vortex “friction” associated with Andreev electron reflection on the interface between the normal core and the superconducting periphery of a vortex. Within the framework of the model suggested, magnetic field (and temperature) dependences of the longitudinal and Hall resistances of a mixed state superconductor have been calculated at temperatures nearing T_c. At certain quite realistic parameters which define the forces acting on the vortices, there is a range of magnetic fields and temperatures where the sign of the Hall effect is opposite to that in the normal state. The lower limit of this range is the irreversibility line and the upper critical field.