Yuan Li — Page 30 | Search arXiv

arXiv2006

Spin relaxation of two-dimensional electrons with a hierarchy of spin-orbit couplings

The density matrix formalism is applied to calculate the spin-relaxation time for two-dimensional systems with a hierarchy of spin-orbit couplings, such as Rashba-type, Dresselhaus-type and so on. It is found that the spin-relaxation time can be infinite if those coupling strengths $α$, $β$, $γ_1$ and $γ_2$ satisfy either condition (i) $α=β, γ_1=0$ or (ii) $α=-β, γ_2=0$, which correspond to the vanishing Yang-Mills "magnetic" field. The effect caused by the application of an external magnetic field is also discussed. It is found that the longitudinal and in-plane spin components can possess infinite life time when the spin components, the Larmor precession frequency and the external magnetic field satisfy certain relations.

cond-mat.mes-hall↗

arXiv2006

Balanced Symmetric Functions over $GF(p)$

Under mild conditions on $n,p$, we give a lower bound on the number of $n$-variable balanced symmetric polynomials over finite fields $GF(p)$, where $p$ is a prime number. The existence of nonlinear balanced symmetric polynomials is an immediate corollary of this bound. Furthermore, we conjecture that $X(2^t,2^{t+1}l-1)$ are the only nonlinear balanced elementary symmetric polynomials over GF(2), where $X(d,n)=\sum_{i_1<i_2<...<i_d}x_{i_1} x_{i_2}... x_{i_d}$, and we prove various results in support of this conjecture.

math.CO↗

arXiv2005

Electron transport of a quantum wire containing a finite-size impurity under THz electromagnetic field illumination

We theoretically investigate the electron transport properties for a semiconductor quantum wire containing a single finite-size attractive impurity under an external terahertz electromagnetic field illumination in the ballistic limit. Within the effective mass free-electron approximation, the scattering matrix for the system has been formulated by means of a time-dependent mode matching method. Some interesting properties of the electron transmission for the system have been shown through a few groups of numerical examples. It is found that in the case of the comparative stronger field amplitude and the frequency resonant with the two lowest lateral energy levels in the impurity region, the field-induced intersubband transition dominates the process as if without the impurity. And there is a step-arising on the transmission as a function of the incident electron energy. However, in the case of lower field amplitude and the non-resonant frequencies both multiple symmetry Breit-type resonance peaks and asymmetry Fano-type dip lines appear in the electron transmission dependence on the incident energy due to the presence of the impurity and the external field. Therefore, within certain energy range the transmission as a function of the field frequency and/or field amplitude shows a rich structure. Moreover, the transmission dependence on the strength and size of the impurity is also discussed. It is suggested that these results mostly arise from the interplay effects between the impurity in a quantum wire and the applied field.

cond-mat.mes-hall↗