Spin Orbitronics and Topological Properties of Nanostructures

The following section is included:

• Preface
• Contents

The work provides an overview on some recent advances in the area of quantum thermodynamics and quantum heat engines. A particular emphasis is put on the possibility of constructing finite time quantum cycles and adiabatic shortcuts. We discuss in details the particular quantum heat engines operating with a multiferroic working substance.

Proximity induced spin-orbit coupling effects in graphene on transition-metal dichalcogenides (TMD) have potential to bring graphene spintronics to the next level. Here we discuss electronic structure of graphene on monolayer MoS₂, MoSe₂, WS₂ and WSe₂. The Dirac electrons of graphene lie within the semiconducting gap and exhibit a giant global proximity spin-orbit coupling, without compromising the semimetallic character. We found that graphene on MoS₂, MoSe₂, and WS₂ has a topologically trivial band structure, while graphene on WSe₂ exhibits inverted bands. Within the inverted regime the graphene zigzag nanoribbon hosts protected helical edge states demonstrating the quantum spin Hall effect, which opens a new route to access topological states of matter in graphene-based systems. Additionally the use of graphene/TMD vertical heterostructures serve as a promising platform for optospintronics, in particular for optical spin injection into graphene.

Bethe Ansatz (BA) is known as a genious mathematical guess which admits an exact solution to some non-trivial many-body problems (integrable systems) which include the eigenproblem of the Heisenberg Hamiltonian for the ring of N spins 1/2 with isotropic nearest-neighbour interaction (the XXX model) as the seminal example. Algebraic Bethe Ansatz (ABA) of Faddeev and Tachtajan is a formalism which reproduces this guess in an elegant algebraic form, in terms of monodromy, Lax operators and transfer matrix. Both approaches, the original BA (known nowadays as the coordinate BA) and ABA, imply a need to solve the system of BA equations for spectral Bethe parameters - the system of r highly nonlinear algebraic equations, with r being the number of spin deviations from the ferromagnetic saturation state | 0 〉. Then, each regular solution (λ₁, ..., λ_r) yields the corresponding exact eigenstate of the system in a form B(λ₁)...B(λ_r) | 0 〉, where B(λ) is the creation operator for an excitation characterized by the spectral parameter λ. The aim of our report is to point out another way for determination of exact eigenstates within ABA formalism, namely - by application of the set of N commuting observables T^(l) (constants of motion) from the transfer matrix T(λ). Knowledge of spectra of these constants of motion allows us to determine exact eigenstates of the Heisenberg Hamiltonian, along the standard quantum-mechanical prescription of Dirac. It is worth to mention that the numerical problem of solving non-linear BA equations is replaced by elementary algebraic manipulations with matrices of finite dimension, and the results are given in the form of density matrices - the one-dimensional projectors onto exact eigenstates. Bethe parameters can be then recovered from already known eigenstates by famous Baxter TQ equation.

A two-dimensional electron plasma in high-electron mobility heterostructures couples to terahertz (THz) radiation which allows to study fundamental properties of this electron system and construct plasma - based devices. The present paper reviews some of recent experimental results obtained on high-electron- mobility heterostructures based on GaAs, CdTe and GaN. Magnetospectroscopy experiments involved measurements of photocurrent, photovoltage and transmission with monochromatic excitation, and photovoltage or transmission with a Fourier spectrometer. Plasmon dispersion relations were determined in each type of samples and showed to follow theoretically predicted dependences. However, a correct interpretation of data required taking into account sample - dependent factors which were related either to the geometry of the sample (this was mainly the case of GaAs-based heterostructures) or to peculiar material properties (mainly in the case of CdTe- and GaN-related heterostructures). The paper gives an elementary description of notions and phenomena related to magnetoplasmon excitations in a two-dimensional plasma as well as a detailed description of procedures of data analysis leading from experimental results to plasmon dispersion relations. This text can be also considered as a tutorial on magnetoplasmon spectroscopy for beginners.

In these lecture notes we study the disordered two-dimensional electron gas in the presence of Rashba spin-orbit coupling, by using the Keldysh non-equilibrium Green function technique. We describe the effects of the spin-orbit coupling in terms of a SU(2) gauge field and derive a generalized Boltzmann equation for the charge and spin distribution functions. We then apply the formalism to discuss the spin Hall and the inverse spin galvanic (Edelstein) effects. Successively we show how to include, within the generalized Boltzmann equation, the side jump, the skew scattering and the spin current swapping processes originating from the extrinsic spin-orbit coupling due to impurity scattering.

A characteristic feature of topological systems is the presence of robust gapless edge states. In this work the effect of time-dependent perturbations on the edge states is considered. Specifically we consider perturbations that can be understood as changes of the parameters of the Hamiltonian. These changes may be sudden or carried out at a fixed rate. In general, the edge modes decay in the thermodynamic limit, but for finite systems a revival time is found that scales with the system size. The dynamics of fermionic edge modes and Majorana modes are compared. The effect of periodic perturbations is also referred allowing the appearance of edge modes out of a topologically trivial phase.

We report experimental measurements of melting behavior of liquids adsorbed in carbon and silica nanopores. Phase transition of H₂O, D₂O and C₆H₅NO₂ confinement in pores of different inner diameter in the range of 2.2-7.5nm has been characterized by Dielectric Spectroscopy and Differential Scanning Calorimetry methods. The measurements presented in this paper have been made in a wide temperature range from 150K to 300K.We find that the melting point inside pores strongly depend on pores size and fluid-wall interaction. We show that melting temperatures Tmp of confinement system decrease relative to the bulk for weaker fluid-wall than fluid-fluid interaction (silica glasses) and increase in the case of stronger fluid-wall interaction (carbon pores).

Experimental results of the magneto-transport measurements (longitudinal magneto-transport measurements (longitudinal magneto-resistance R_xx and the Hall resistance R_xy) over a wide interval of temperatures for several samples of Hg_1−xCd_xTe (x ≈ 0.13 − 0.15) grown by MBE. An amazing temperature stability of the SdH-oscillation period and amplitude is observe in the entire temperature interval of measurements up to 50 K. Moreover, the quantum Hall effect (QHE) behaviour of the Hall resistance was shown in the same temperature interval. These peculiarities of the R_xx and R_xy for strained thin layers are interpreted using quantum Hall conductivity on topologically protected surface states. The adventures of the HgCdTe alloys as the 3D topological Dirac semimetal analysed.

Spin-orbit coupling for itinerant particles is usually represented in solid state and condensed matter physics as a symmetry-determined sum of products of operators describing the Cartesian components of particle spin and momentum. By general rules of quantum mechanics, this coupling causes a spin-dependent term in the particle velocity operator, the so-called anomalous velocity contribution. Here we present and discuss general concept of this anomalous velocity and analyze two examples of its critical effects in condensed matter physics. As a first example we consider collapse of spin-orbit coupled self-attractive Bose-Einstein condensates. We show that the collapse can be inhibited if the anomalous velocity is taken into account. Second, we analyze short-term spin dynamics of Bose-Einstein condensate in a random one-dimensional potential. Here the anomalous velocity strongly influences the spin evolution by producing random mixed spin states and, therefore, leads to a novel spin relaxation mechanism.

This article discusses the construction of a theory which is capable to explain so-called non-Fermi liquid behavior of strongly correlated Fermi systems. We show that such explanation can be done within the framework of a so-called fermion condensation approach. In this approach, as a result of fermion condensation quantum phase transition, ordinary Landau quasiparticles do not decay, but reborn, gaining new properties, as Phoenix from the ashes. The physical reason for that is altering of Fermi surface topology. To be more specific, in contrast to standard Landau paradigm stating that the quasiparticle effective mass does not depend on external stimuli like magnetic field and/or temperature, the effective mass of new quasiparticles strongly depends on them. Our extensive analysis of experimental data gathered on strongly correlated Fermi systems of quite different microscopic nature, shows that the multitude of their non-Fermi liquid properties are due to FC occurrence in them.

Magnetic electric effects in ferromagnetic metals are discussed from the viewpoint of effective spin electromagnetic field that couples to conduction electron spin. The effective field in the adiabatic limit is the spin Berry’s phase in space and time, and it leads to spin motive force (voltage generated by magnetization dynamics) and topological Hall effect due to spin chirality. Its gauge coupling to spin current describes the spin transfer effect, where magnetization structure is driven by an applied spin current. The idea of effective gauge field can be extended to include spin relaxation and Rashba spin-orbit interaction. Voltage generation by the inverse Edelstein effect in junctions is interpreted as due to the electric component of Rashba-induced spin gauge field. The spin gauge field arising from the Rashba interaction turns out to coincides with toroidal moment, and causes asymmetric light propagation (directional dichroism) as a result of the Doppler shift. Rashba conductor without magnetization is shown to be natural metamaterial exhibiting negative refraction.

The Jack polynomials $J_{\lambda }^{\alpha }$ are a remarkable family of symmetric polynomials. They generalize many families of symmetric polynomials including: Schur polynomials, monomial symmetric polynomials, and elementary symmetric polynomials. The original development of Jack polynomials focused on the case of the real parameter α > 0. This assures that the corresponding $J_{\lambda }^{\alpha }$ has no pole and is well defied. However for a specific values of α < 0, Jack polynomials have no pole as well and reveal interesting properties, useful in physics of fractional quantum Hall effect. This solid state phenomenon involves essentially two-dimensional electrons in extremely low temperatures and strong magnetic field. Aim of this paper is to introduce the Jack polynomials in the context of fractional quantum Hall effect. We give a brief description of classical version of Hall effect and discuss both the integer and fractional quantum Hall effect. Then we introduce the basics of the theory of symmetric functions; in particular we define, describe, and construct the Jack polynomials. This knowledge is later applied and illustrated with numerical generation of the coefficients of “Jack states” (quantum Hall states related to the Jack polynomials). As an illustration we examine overlaps of the Jack state wave functions and the Coulomb ground states for different system sizes.

We describe recent research on Zitterbewegung (ZB, trembling motion) of electrons in semiconductors. A brief history of the subject is presented. Zitterbewegung of charge carriers in monolayer and bilayer graphene is elaborated in some detail. Effects of an external magnetic field on ZB are described using monolayer graphene as an example. Nature of electron ZB in crystalline solids is explained. It is proposed to trigger the coherent trembling motion of many electrons by exciting them from the valence to the conduction band by laser pulses and detecting the resulting ZB by nonlinear optical effects. Simulations of the trembling motion in vacuum and in semiconductors are reviewed. A recent experimental observation of the trembling motion in semiconducting material InGaAs is mentioned.