Quantum transport in topological semimetals under magnetic fields

Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity may not be a compelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.     

磁场中拓扑物态的量子输运

拓扑物态包括拓扑绝缘体、拓扑半金属以及拓扑超导体.拓扑物态奇异的能带结构以及受拓扑保护的新奇表面态,使其具有了独特的输运性质.拓扑半金属作为物质的一种三维拓扑态具有无能隙的准粒子激发,根据导带和价带的接触类型分为外尔半金属、狄拉克半金属和节线半金属.本文以拓扑半金属为主回顾了在磁场下拓扑物态中量子输运的最新工作,在不同...     

Quantum transport in topological semimetals under magnetic fields (II)

Research about two-dimensional (2D) materials is growing exponentially across various scientific and engineering disciplines due to the wealth of unusual physical phenomena that occur when charge transport is confined to a plane. The applications of 2D materials are highly affected by the electrical properties of these materials, including current distribution, surface potential, dielectric response, conductivity, permittivity, and piezoelectric response. Hence, it is very crucial to characterize these properties at the nanoscale. The Atomic Force Microscopy (AFM)-based techniques are powerful tools that can simultaneously characterize morphology and electrical properties of 2D materials with high spatial resolution, thus being more and more extensively used in this research field. Here, the principles of these AFM techniques are reviewed in detail. After that, their representative applications are further demonstrated in the local characterization of various 2D materials’ electrical properties.

     

CDW patterns of two-dimensional electrons in strong magnetic fields

The phase diagram of a two-dimensional electron system in a strong magnetic field is studied in the Hartree-Fock approximation. Special attention is paid to the consequences of the electron-hole symmetry in the system. When the ground Landau level is half-filled, the high-temperature gaseous phase undergoes a second-order transition to a square CDW with a period dependent on temperature. This transition preserves the electron-hole symmetry in the sense that the square CDW is self-dual in contrast to a triangular CDW where the dual CDW has a honeycomb pattern. If the density is slightly less than the half-filled case, the gaseous phase first undergoes a first-order transition to a triangular CDW, followed by another first-order transition to a square CDW. We discuss the role of quantum effects which are responsible for this unusual phase diagram.     

Ground-state energy of two-dimensional interacting electrons in strong magnetic fields

Summary The ground-state energy of two-dimensional interacting electrons in a strong magnetic field in the angular-momentum representation is studied using a modified Lanczos diagnonalization method. In the presence of a positive background density the ground-state energy increases with the total angular momentum, while a cusp-type behaviour appears. The problem of the electron-impurities interaction is formulated as well. The results are discussed in connection with the observed fractional quantum Hall states. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction. The author of this paper has agreed to not receive the proofs for correction.     

Quantum transport in diffusive microstructures in high magnetic fields

We have studied magnetotransport in diffusive submicron wires (n⁺-GaAs) at high magnetic fields where ω_cτ>1. The system allowed us to follow a transition from orthodox mesoscopic behaviour to the regime of edge state transport.We found that for ω_cτ>1 the universal conductance fluctuations (UCF) can no longer be scaled in terms of only one parameter, the phase coherence length. This breakdown of universal scaling is seen as a large increase of the Lee-Stone correlation field while the magnitude of UCF is unchanged in strong disagreement with the theoretical prediction.A qualitatively new magnetoresistance oscillatory effect has been observed at intermediate temperatures (10K<T<50K) when the quantum transport along the edges coexists with classical (diffusive and dissipative) conduction in the bulk. The effect arises due to Landau quantization but entirely disappears at low temperatures. The latter distinguishes it from the other quantum transport phenomena and indicates the importance of dissipation in resistance measurement.     

Effect of localization on the hall conductivity in the two-dimensional system in strong magnetic fields

Some exact properties of the Hall conductivity in the two-dimensional electron system in strong magnetic fields are investigated in the presence of immobile carriers. It is shown that σ_xy should be exactly the integral multiple of — $\text{e}{}^{\mathrm{<mtext>2</mtext>}}\text{h}$ when the Fermi energy lies in the localized regime.     

Quantum transport equation for electric and magnetic fields

A quantum Boltzmann equation is derived which is valid for electron transport in electric and magnetic fields including all many-body effects. A solution in both d.c. and a.c. electric fields is given for electrons in simple metals. The solution for transport in large magnetic fields is also given including a theory of the Shubnikov-deHaas oscillations which includes inelastic phonon scattering rigorously.     

Zero-differential resistance state of two-dimensional electron systems in strong magnetic fields

We report the observation of a zero-differential resistance state (ZDRS) in response to a direct current above a threshold value I>I th applied to a two-dimensional system of electrons at low temperatures in a strong magnetic field. Entry into the ZDRS, which is not observable above several Kelvins, is accompanied by a sharp dip in the differential resistance. Additional analysis reveals an instability of the electrons for I>I th and an inhomogeneous, nonstationary pattern of the electric current. We suggest that the dominant mechanism leading to the new electron state is a redistribution of electrons in energy space induced by the direct current.     

Quantum well laser operation at low temperature in strong magnetic fields

Experimental results on quantum well laser operation in magnetic fields B < 12 T are reported. For B perpendicular (B_⊥) to the quantum well a sh?ft toward higher photon energy of ~ 0.5 meV/T is observed, with the laser threshold current decreasing significantly. In parallel magnetic fields (B∥) no significant effect is measured, thus confirming the built-in two-dimensional character of the electron gas.     

Plasmon-assisted sound amplification in semi-conductors under strong magnetic fields

We derive an expression for the contribution from plasma effects to the sound amplification in piezo-electric semiconductors subjected to a strong d.c. magnetic field applied parallel to the drift field. It is shown that this contribution largely differs from that in the absence of a magnetic field both in the strength of the effect and in angular distribution of the emitted phonons.     

Quantum transitions and magnetization of the magnetic V15 cluster in strong magnetic fields

The process of rearrangement of the magnetic structure of the low-spin cluster V₁₅ in superhigh magnetic fields is investigated. At low temperatures, this process is shown to manifest itself as three quantum jumps, each of which is a transition causing the spin of the complex to increase by two unities. The nature of these quantum jumps is discussed. The magnetization curve and the magnetic susceptibility are calculated.     

Bipartite entanglement of a two-qubit system with anisotropic couplings under nonuniform magnetic fields

This paper investigates bipartite entanglement of a two-qubit system with anisotropic couplings under an inhomogeneous magnetic field. This work is mainly to investigate the characteristics of a Heisenberg XYZ chain and obtains some meaningful results. By the concept of negativity, it finds that the inhomogeneity of magnetic field may induce entanglement and the critical magnetic field is independent of J_z. The inhomogeneous magnetic field can increase the value of critical magnetic field B_c. It also finds that the magnetic field not only suppresses the entanglement but also can induce it to revival for some time.     

Quantum dynamics in strong fluctuating fields

A large number of multifaceted quantum transport processes in molecular systems and physical nanosystems, such as e.g. nonadiabatic electron transfer in proteins, can be treated in terms of quantum relaxation processes which couple to one or several fluctuating environments. A thermal equilibrium environment can conveniently be modelled by a thermal bath of harmonic oscillators. An archetype situation provides a two-state dissipative quantum dynamics, commonly known under the label of a spin-boson dynamics. An interesting and nontrivial physical situation emerges, however, when the quantum dynamics evolves far away from thermal equilibrium. This occurs, for example, when a charge transferring medium possesses nonequilibrium degrees of freedom, or when a strong time-dependent control field is applied externally. Accordingly, certain parameters of underlying quantum subsystem acquire stochastic character. This may occur, for example, for the tunnelling coupling between the donor and acceptor states of the transferring electron, or for the corresponding energy difference between electronic states which assume via the coupling to the fluctuating environment an explicit stochastic or deterministic time-dependence. Here, we review the general theoretical framework which is based on the method of projector operators, yielding the quantum master equations for systems that are exposed to strong external fields. This allows one to investigate on a common basis, the influence of nonequilibrium fluctuations and periodic electrical fields on those already mentioned dynamics and related quantum transport processes. Most importantly, such strong fluctuating fields induce a whole variety of nonlinear and nonequilibrium phenomena. A characteristic feature of such dynamics is the absence of thermal (quantum) detailed balance.

Quantum dynamics in strong fluctuating fields

All authors

Igor Goychuk &; Peter Hänggi

https://doi.org/10.1080/00018730500429701

Published online:

19 February 2007

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The two-dimensional D complex in intense AC and strong magnetic fields

The combined effect of intense time dependent far infrared field (FIR) and a strong static magnetic field on interacting electrons in a two-dimensional complex is studied. The two-electron problem is cast in the language of the Center of Mass (CM) and relative particles, which in turn is mapped into a problem of coupled nonlinear harmonic oscillators. The time evolution of the CM and its coupling to the internal degrees of freedom via the coulomb interaction and the Pauli exclusion principle is investigated.