Landau level mixing by full spin-orbit interactions

This work addresses a method for constructing supersymmetric vector coherent states (VCS) for a two-dimensional electron gas in a perpendicular magnetic field in the presence of both Rashba and Dresselhaus spin-orbit (SO) interactions, with an effective Zeeman coupling. The model Hamiltonian, decomposed into two conveniently defined operators, acts on a tensor product of two Hilbert spaces associated with corresponding chiral sectors. Supersymmetric (SUSY) VCS, related to a SUSY pair of Hamiltonians, are built. A generalized oscillator algebra is provided using quadrature operators. Mean-values of position and momentum operators and uncertainty relation in the SUSY VCS are obtained and discussed. Besides, the SUSY VCS time evolution is also given.

We theoretically investigate photoinduced phenomena induced by time-periodic driving fields in two-dimensional electron gases under perpendicular magnetic fields with Rashba spin-orbit coupling. Using perturbation theory, we provide analytical results for the Floquet-Landau energy spectrum appearing due to THz radiation. By employing the resulting photo-modulated states, we compute the dynamical evolution of the spin polarization function for an initially prepared coherent state. We find that the interplay of the magnetic field, Rashba spin-orbit interaction and THz radiation can lead to inversion of the spin polarization. The dynamics also induces fractional revivals and non-trivial beating patterns in the autocorrelation function due to interference of the photo-modulated quantum states. We also calculate the transverse photo-assisted conductivity in the linear response regime using Kubo formalism and analyze the impact of the radiation field and Rashba spin-orbit interaction. In the static limit, we find that our results reduce to well-known expressions of the conductivity in non-relativistic and quasi-relativistic (topological insulator surfaces) two-dimensional electron gas thoroughly described in the literature. We discuss the possible experimental detection of our theoretical prediction and their relevance for spin-orbit physics at high magnetic fields.

The quantum dynamics of the electron's spin and orbital angular momenta in semiconductor quantum rings is analyzed. Both Rashba and Dresselhaus spin-orbit interactions (SOIs) in their quasi-two-dimensional forms are taken into account. The narrow quantum rings are treated with models including one and two radial modes. We find that when either Rashba or Dresselhaus SOI acts alone, the different angular momentum states are coupled in blocks of two (for a single radial mode) or four (for two radial modes). We also show that the full Hilbert space splits into two disjoint subspaces, which are not coupled by either of the two SOIs, thereby decoupling accordingly the state evolution. When both SOI mechanisms are present, in principle infinitely many states are coupled, but we find by numerical computation of the quantum dynamics that for typical evolution times in practice only a few neighboring states are involved in the dynamics. Thus the exchange of angular momenta proceeds only via very few states. Furthermore, we find a trend that when initially high orbital momenta are prepared, the time evolution of spin and orbital momenta is almost unaffected by the availability of a second radial mode, in sharp contrast to the case of preparing the system in low orbital angular momentum states. The implications of our findings for the coherent control of angular momentum in quantum rings are pointed out.

We investigate the properties of persistent charge current driven by magnetic flux in a quasi-periodic mesoscopic Fibonacci ring with Rashba and Dresselhaus spin-orbit interactions. Within a tight-binding framework we work out individual state currents together with net current based on second-quantized approach. A significant enhancement of current is observed in presence of spin-orbit coupling and sometimes it becomes orders of magnitude higher compared to the spin-orbit interaction free Fibonacci ring. We also establish a scaling relation of persistent current with ring size, associated with the Fibonacci generation, from which one can directly estimate current for any arbitrary flux, even in presence of spin-orbit interaction, without doing numerical simulation. The present analysis indeed gives a unique opportunity of determining persistent current and has not been discussed so far.

Coulomb screening and weak interactions in a hot, magnetized plasma are investigated. Coulomb screening is evaluated in a relativistic thermal plasma in which electrons and positrons are in equilibrium. In addition to temperature effects, effects on weak screening from a strong external magnetic field are evaluated. In high fields, the electron transverse momentum components are quantized into Landau levels. The characteristic plasma screening length at high temperatures and at high magnetic fields is explored. In addition to changes to the screening length, changes in weak interaction rates are estimated. It is found that high fields can result in increased β-decay rates as the electron and positron spectra are dominated by Landau levels. Finally, the effects studied here are evaluated in a simple r-process model. It is found that relativistic Coulomb screening has a small effect on the final abundance distribution. While changes in weak interaction rates in strong magnetic fields can have an effect on the r-process evolution and abundance distribution, the field strength required to have a significant effect may be larger than what is currently thought to be typical of the r-process environment in collapsar jets or neutron star mergers. If r-process sites exist in fields G, effects from fields on weak decays could be significant.

Electronic structure and Landé g-factor of a quantum ring in the presence of spin-orbit coupling: Temperature and Zeeman effect

We study transport properties of a two-dimensional electron system with Rashba spin-orbit coupling in a perpendicular magnetic field. The spin-orbit coupling competes with Zeeman splitting to introduce additional degeneracies between different Landau levels at certain magnetic fields. This degeneracy, if occurring at the Fermi level, gives rise to a resonant spin Hall conductance, whose height is divergent as 1/T and whose weight is divergent as -ln(T at low temperatures. The Hall conductance is unaffected by the Rashba coupling.

Within the noncollinear local spin-density approximation, we have studied the ground state structure of a parabolically confined quantum wire submitted to an in-plane magnetic field, including both Rashba and Dresselhaus spin-orbit interactions. We have explored a wide range of linear electronic densities in the weak strong coupling regimes that appear when the ratio of spin-orbit to confining energy is small large. These results are used to obtain the conductance of the wire. In the strong coupling limit, the interplay between the applied magnetic field—irrespective of the in-plane direction, the exchange-correlation energy, and the spinorbit energy—produces anomalous plateaus in the conductance vs linear density plots that are otherwise absent, or washes out plateaus that appear when the exchange-correlation energy is not taken into account.

We have investigated the magnetoresistance of lithographically prepared single-layer graphene nanoribbons in pulsed, perpendicular magnetic fields up to 60 T and performed corresponding transport simulations using a tight-binding model and several types of disorder. In experiment, at high carrier densities we observe Shubnikov-de Haas oscillations and the quantum Hall effect, while at low densities the oscillations disappear and an initially negative magnetoresistance becomes strongly positive at high magnetic fields. The strong resistance increase at very high fields and low carrier densities is tentatively ascribed to a field-induced insulating state in the bulk graphene leads. Comparing numerical results and experiment, we demonstrate that at least edge disorder and bulk short-range impurities are important in our samples.

We present a detailed theoretical study on zero-frequency Drude weight and optical conductivity of a two-dimensional heavy-hole gas (2DHG) with k-cubic Rashba and Dresselhaus spin-orbit interactions. The presence of k-cubic spin-orbit couplings strongly modifies the Drude weight in comparison to the electron gas with k-linear spin-orbit couplings. For large hole density and strong k-cubic spin-orbit couplings, the density dependence of Drude weight deviates from the linear behavior. We establish a relation between optical conductivity and the Berry connection. Unlike two-dimensional electron gas with k-linear spin-orbit couplings, we explicitly show that the optical conductivity does not vanish even for equal strength of the two spin-orbit couplings. We attribute this fact to the non-zero Berry phase for equal strength of k-cubic spin-orbit couplings. The least photon energy needed to set in the optical transition in hole gas is one order of magnitude smaller than that of electron gas. Types of two van Hove singularities appear in the optical spectrum are also discussed.

The combined effect of a lateral square superlattice potential and the Coulomb interaction on the ground state of a two-dimensional electron gas in a perpendicular magnetic field is studied for different rational values of $\Gamma$, the inverse of the number of flux quanta per unit cell of the external potential, at filling factor $\nu =1$ in Landau level $N=0.$ When Landau level mixing and disorder effects are neglected, increasing the strength $W_{0}$ of the potential induces a transition, at a critical strength $W_{0}^{\left( c\right) },$ from a uniform and fully spin polarized state to a two-dimensional charge density wave (CDW) with a meronlike spin texture at each maximum and minimum of the CDW. The collective excitations of this vortex-CDW are similar to those of the Skyrme crystal that is expected to be the ground state near filling factor $\nu =1$. In particular, a broken U(1) symmetry in the vortex-CDW results in an extra gapless phase mode that could provide a fast channel for the relaxation of nuclear spins. The average spin polarization $% S_{z}$ changes in a continuous or discontinuous manner as $W_{0}$ is increased depending on whether $\Gamma \in \left[ 1/2,1\right] $ or $\Gamma \in \left[ 0,1/2\right] .$ The phase mode and the meronlike spin texture disappear at large value of $W_{0},$ leaving as the ground state a partially spin-polarized CDW if $\Gamma \neq 1/2$ or a spin-unpolarized CDW if $\Gamma =1/2.$

We calculate the non-linear charge currents in a two-dimensional electron system with Rashba (α) and Dresselhaus (β) linear spin-orbit interactions (SOIs) in the presence of in-plane electricEand magneticBfields. Working in a rotated system of coordinates that introducesα±βas effective couplings on perpendicular directions, we show that the currents, quadratic in the electric field, exist for all values of the chemical potentialµ, above or below the band crossing energyE0. Our formalism uses a second order correction to the particle distribution functionδf(2)derived in a semi-classical approximation that takes into account the local change in the single-particle energy under the action of the electric field. In a quantum well, whereμ>E0, for a spin-orbit energy larger than the Zeeman splitting, the non-linear currents that flow perpendicular on the direction of the magnetic field are found to be proportional withα±βwhenE⊥Band with(α±β)2/(α∓β)whenE∥B, a result independent of the presence of any additional SOIs, such as the cubic Dresselhaus or warping.

The ground state energy and the lowest excitations of a two dimensional Wigner crystal in a perpendicular magnetic field with one and two electrons per cell is investigated. In case of two electrons per lattice site, the interaction of the electrons {\em within} each cell is taken into account exactly (including exchange and correlation effects), and the interaction {\em between} the cells is in second order (dipole) van der Waals approximation. No further approximations are made, in particular Landau level mixing and {\em in}complete spin polarization are accounted for. Therefore, our calculation comprises a, roughly speaking, complementary description of the bubble phase (in the special case of one and two electrons per bubble), which was proposed by Koulakov, Fogler and Shklovskii on the basis of a Hartree Fock calculation. The phase diagram shows that in GaAs the paired phase is energetically more favorable than the single electron phase for, roughly speaking, filling factor $f$ larger than 0.3 and density parameter $r_s$ smaller than 19 effective Bohr radii (for a more precise statement see Fig.s 4 and 5). If we start within the paired phase and increase magnetic field or decrease density, the pairs first undergo some singlet- triplet transitions before they break.

High magnetic field is an important research condition which can provide great opportunities for the development of many subjects. Since 1913, there are 19 Nobel Prizes which are related to high magnetic field. Scientific research under high magnetic field involves a large amount of subjects and various scientific issues. In many research areas such as the quantum transport in semiconductors, Fermi surface measurements, the study of the upper critical field of high temperature superconductors, nuclear magnetic resonance study etc., high magnetic field is an essential condition. Therefore, the scientific research under high magnetic field is always the frontier. In this review, the cutting-edge scientific issues under high magnetic field are presented. The issues in physics include the fractional quantum Hall effect in graphene, the quantum oscillations in black phosphorus, the topological insulator Bi2Se3, the Weyl semimetal NbP, the quantum ordering in non-conventional superconductor, the magnetic field induced new superconducting phase, the magnetic field induced metamagnetism transition, the quantum effect of low dimensional materials, the spin frustration, etc. In chemistry and material science, the focuses are magnetic field induced new chemical reaction, control of reaction routes, the reaction kinetics, synthesis of single molecular magnet and chiral materials, nano-catalysis, etc. Issues related to nuclear magnetic resonance are also mentioned, including the protein structure determination, magnetic resonance imaging for medical science, the structure of melt, geosciences and environmental sciences, etc. Moreover, the present condition and achievement of the high magnetic field facility in China are shown in the following part. Three water-cooled magnets have created three world records. The water-cooled magnet WM1 with a 32 mm bore can generate a steady magnetic field of 38.5 Tesla, which has exceeded the previous record 37.5 Tesla. The water-cooled magnet WM5 with a 50 mm bore has produced a magnetic field of 35 Tesla, which is also the highest for the same type of magnets. The water-cooled magnet WM4 with a 32 mm bore has generated a magnetic field of 27.5 Tesla when inputting 10 MW power. All the magnets have corresponding experimental systems. For example, WM1 has a 3He extreme low temperature experiment dewar installed providing a temperature region from 325 mK to 70 K, which is mainly used for transport measurement. The high-homogeneity water-cooled magnet WM2 has a high field high frequency (82 to 690 GHz) electron magnetic resonance continuous wave system installed. WM5 can cooperate with a Fourier transform infrared spectroscopy (18000 to 4000 cm - 1), a vibrating sample magnetometer for magnetization measurement, and a high pressure experiment system (0–200 GPa). The service of the high magnetic field facilities in China will provide strong support for various cutting-edge research and create advantage for significant original achievement.

Anisotropic magnetoresistance (AMR) is a relativistic magnetotransport phenomenon arising from combined effects of spin-orbit coupling and broken symmetry of a ferromagnetically ordered state of the system. In this work we focus on one realization of the AMR in which spin-orbit coupling enters via specific spin-textures on the carrier Fermi surfaces and ferromagnetism via elastic scattering of carriers from polarized magnetic impurities. We report detailed heuristic examination, using model spin-orbit coupled systems, of the emergence of positive AMR (maximum resistivity for magnetization along current), negative AMR (minimum resistivity for magnetization along current), and of the crystalline AMR (resistivity depends on the absolute orientation of the magnetization and current vectors with respect to the crystal axes) components. We emphasize potential qualitative differences between pure magnetic and combined electro-magnetic impurity potentials, between short-range and long-range impurities, and between spin-1/2 and higher spin-state carriers. Conclusions based on our heuristic analysis are supported by exact solutions to the integral form of the Boltzmann transport equation in archetypical two-dimensional electron systems with Rashba and Dresselhaus spin-orbit interactions and in the three-dimensional spherical Kohn-Littinger model. We include comments on the relation of our microscopic calculations to standard phenomenology of the full angular dependence of the AMR, and on the relevance of our study to realistic, two-dimensional conduction-band carrier systems and to anisotropic transport in the valence band of diluted magnetic semiconductors.