Dynamics Of Spin,Valley Polarization And Bogoliubov Quasiparticle In Semiconductors,Cold Atoms,Transition Metal Dichalcogenides And Superconductors

Spintronics mainly aims to actively manipulate the spin(or pseudospin)degree of freedom in solid-state materials,in which the understanding on the spin and charge dy-namics and their interplay are quite essential.Focusing on this theme,this dissertation is divided into three parts according to the concerning physical system.In part I,we study the spin dynamics in semiconductor and ultracold atoms,including the spin relaxation and spin diffusion.In part II,we investigate the dynamics of the valley polarization due to exciton in monolayer and bilayer transition metal dichalcogenides,including the valley depolarization dynamics and valley Hall effect of exciton.In part III,we focus on the spin and charge dynamics of the Bogoliubov quasiparticles and condensate in the s-wave and(s + p)-wave superconductors.In part I,from Chapter 1 to 4,we focus on the spin dynamics in ultracold atoms and semiconductor.In Chapter 1,the background of the semiconductor spintronics and its application in the spin dynamics of ultracold atoms are reviewed.We first review the spin generation,spin detection,spin relaxation and spin diffusion in semiconductors,in which the spin Hall effect,the main spin relaxation mechanisms including the Dyakonov-Perel',Elliott-Yafet and Bir-Aronov-Pikus mechanisms,and the understanding on the spin diffusion in the literature including the drift-diffusion model and inhomogeneous picture are introduced.Then we briefly introduce the background of ultracold atoms and the recently-realized spin-orbit-coupled ultracold atoms and its experimental progress.In Chapter 2,we find in ultracold spin-orbit-coupled 40K gas,when the Zeeman energy is much larger than the spin-orbit-coupling energy,the D'yakonov-Perel' spin relaxation is anomalous.Transverse and longitudinal configurations with spin polarization perpen-dicular and parallel to the effective Zeeman field are considered,respectively.We find that with small spin polarization,the transverse spin relaxation is divided into four rather than two regimes:the normal weak scattering regime,the anomalous D'yakonov-Perel'-like regime,the anomalous Elliott-Yafet-like regime and the normal strong scattering regime.With large spin polarization,we reveal that the Hartree-Fock self-energy,acting as an effective magnetic field,can extremely-efficiently suppress the transverse spin relaxation in the weak scattering limit.In In As(110)quantum wells with the magnetic field in the Voigt configuration much stronger than the spin-orbit-coupled field,the influence of the Hartree-Fock self-energy on the anomalous D'yakonov-Perel' spin relaxation is further revealed.For the transverse configuration,it is found that the spin relaxation is very sensi-tive to the Hartree-Fock effective magnetic field.Even an extremely small spin polarization(P =0.1%)can significantly influence the behavior of the spin relaxation.Moreover,we find that the transverse spin relaxation can be enhanced rather than suppressed by the Hartree-Fock field with moderate spin polarization.These features are very different from the conventional situation.With the understanding on the anomalous D'yakonov-Perel' spin relaxation,anoma-lous features for the spin diffusion are expected in the similar configuration.In Chapter 3,we investigate the steady-state spin diffusion in ultracold spin-orbit-coupled 40K gas.It is found that the behaviors of the steady-state spin diffusion are determined by three char-acteristic lengths:the mean free path,the Zeeman oscillation length and the spin-orbit coupling oscillation length.It is analytically revealed and numerically confirmed that by tuning the scattering strength,the system can be divided into five regimes,in which the behaviors of the spacial evolution of the steady-state spin polarization are very rich,show-ing different dependencies on the scattering strength,Zeeman field and spin-orbit coupling strength.The rich behaviors of the spin diffusions in different regimes are hard to be un-derstood in the framework of the simple drift-diffusion model or the direct inhomogeneous broadening picture in the literature.However,almost all these rich behaviors can be well understood by means of our modified drift-diffusion model and/or modified inhomogeneous broadening picture.Specifically,several anomalous features of the spin diffusion are re-vealed,which are in contrast to those obtained from both the simple drift-diffusion model and the direct inhomogeneous broadening picture.Apart from the study on the D'yakonov-Perel' spin relaxation mechanism,the Elliott-Yafet mechanism in intrinsic Germanium is also investigated.In Chapter 4,we investigate the hot-electron effect in the spin relaxation of electrically injected electrons in intrin-sic Germanium,in which comparison with the recent transport experiment in the spin-injection configuration[Phys.Rev.Lett.111,257204(2013)]is performed.Reasonable agreement is obtained.We reveal that the spin relaxation is significantly enhanced at low temperature in the presence of weak electric field,originating from the obvious center-of-mass drift effect due to the weak electron-phonon interaction.This can explain the discrepancy between the experimental observation and the previous theoretical calcula-tion[Phys.Rev.B 86,085202(2012)],which deviates from the experimental results by about two orders of magnitude at low temperature.In part ?,from Chapter 5 to 8,we focus on the valley dynamics due to the electron-hole exchange interaction in mono-and bilayer transition metal dichalcogenides MX2(M=Mo,W;X=S,Se),including valley depolarization dynamics and valley Hall effect of exciton.In Chapter 5,we review the recent experimental and theoretical progresses in the valley dynamics in the newly emerging mono-and bilayer MX2.In monolayer MX2,the valley dynamics of the free carrier,exciton and trion are introduced,respectively,in which the recent rich experiments on the creation of the valley polarization and its depo-larization are reviewed.In bilayer MX2,the new features on the exciton dynamics in the experiments are emphasized.The transition metal dichalcogenide heterostructure and its charge-transfer dynamics are also introduced.In Chapter 6,the electron-hole exchange interaction in monolayer MoS2 is derived,due to which the valley depolarization is investigated.We find that both the long-and short-range exchange interactions can cause the inter-and intra-valley bright exciton tran-sitions.With the intra-valley bright exciton transition channel nearly forbidden due to the large energy splitting of the valence bands,the inter-valley channel due to the exchange interaction can cause the valley depolarization efficiently by the Maialle-Silva-Sham mech-anism[Phys.Rev.B 47,15776(1993)].With only the long-range exchange interaction,the calculations show good agreement with the recent valley polarization experiments,including the time-resolved valley polarization measurement,the pump-probe experiment and the steady-state photoluminescence polarization measurement.Furthermore,inspired by recent photoluminescence experiment by Zhu et al.[PNAS 111,11606(2014)],in Chapter 7,we investigate the optical excitation spectra and the photoluminescence depolarization dynamics in bilayer WS2.A different understanding of the optical excitation spectra is proposed.By considering there exist both the intra-layer and charge-transfer excitons in the bilayer WS2,with inter-layer hopping of the hole,there exists excimer state from the superposition of them.Accordingly,the four optical excitations observed in the experiment are calculated to be the A charge-transfer exciton,A'excimer,B' excimer and B intra-layer exciton states,respectively.These states are different from the ones speculated in the experiment:indirect exciton for the ? valley,trion,A exciton and B exciton excitations.We further derive the electron-hole exchange interaction in the bilayer WS2,due to which the photoluminescence depolarization dy-namics is studied.Anomalously,we find that there is always a residual photoluminescence polarization that is exactly half of the initial one,lasting for infinitely long time,which is robust against the initial energy broadening and strength of the momentum scattering.This large steady-state photoluminescence polarization indicates that the photolumines-cence relaxation time is extremely long,and hence can be the cause of the anomalously large photoluminescence polarization,nearly 100%observed in the experiment by Zhu et al.in the bilayer WS2.It can be further seen that in monolayer and bilayer MX2,above electron-hole ex-change interaction is very strong,which can modify the exciton energy spectra efficiently.Thus,in Chapter 8,we reveal the influence of this modification on the valley depolariza-tion dynamics in mono-and bilayer MoS2.With this modification,we can consider the valley Hall effect of exciton due to the exchange interaction.For the valley depolarization dynamics,in the monolayer MoS2,it is found that in the strong scattering regime,the motional narrowing picture in the conventional strong scattering regime is no longer valid,and a novel valley depolarization channel is opened.For the valley Hall effect of exciton,in both the mono-and bilayer MoS2,with the drift of the equilibrium state by applied uni-axial strain,the exchange interaction leads to the valley/photoluminescence Hall current.Specifically,the disorder strength dependence of the valley Hall conductivity is revealed.In the strong scattering regime,the valley Hall conductivity decreases with the increase of the disorder strength;whereas in the weak scattering regime,it saturates to a constant,which can be much larger than the one in Fermi system due to the absence of the Pauli blocking.In part III,from Chapter 9 to 14,we study the spin and charge dynamics of the quasi-particle and condensate in the superconducting semiconductor quantum wells in the weak and strong spin-orbit coupling limit,respectively.In Chapter 9,we introduce the quasiclas-sical kinetic equations including Gor'kov equation,Eilenberger equation,Usadel equation and Ginzburg-Landau equation in the superconducting metal.All these equations can be constructed from the non-equilibrium Green function method.Then we introduce the triplet superconductivity and its possible realization in different material system,including 3He superfluid and nonconventional superconductor Sr2RuO4,the conventional supercon-ductor with interface spin-orbit coupling,the non-centrosymmetric superconductor,and the interface between conventional superconductor and ferromagnet.In Chapter 10,we first introduce the concept of the charge and spin imbalances in the conventional supercon-ductor and their dynamics revealed in the experimental and theoretical studies,including their generation and relaxation.We then review the theoretical and experimental studies on the linear and non-linear optical response in the conventional superconductor,with the emphasis on the response to the THz field,in which the phonon energy is around the superconducting gap.In the nonlinear optical response,the concepts of Nambu-Goldstone mode,Higgs mode and Leggett mode in the superconductor are introduced and their possible dynamics in the optical excitation processes are reviewed.In Chapter 11,in the weak spin-orbit coupling limit,we first investigate the quasipar-ticle spin relaxation with superconducting-velocity-tunable state in GaAs(100)quantum wells in proximity to s-wave superconductor.We show the quasiparticle state in GaAs(100)quantum wells can be tuned by the superconducting velocity.In the driven quasi-particle state,we address that the quasiparticle Fermi surface is composed by two arcs,referred to as Fermi arcs,which are contributed by the electron-and hole-like branches.When the Fermi arc emerges,the D'yakonov-Perel' spin relaxation is anomalous when the order parameter tends to zero,because the branch-mixing scattering is forbidden.When the condensation process associated with the annihilation of the quasi-electron and quasi-hole is slow,this indicates that the electron-and hole-like Fermi arcs are independent.The open structure of the Fermi arc leads to the nonzero angular-average of the effective magnetic field due to the spin-orbit coupling,which acts as an effective Zeeman field.This Zeeman field leads to the spin oscillations even in the strong scattering regime.Moreover,in the strong scattering regime,we find that the open structure of the Fermi arc also leads to the insensitiveness of the spin relaxation to the momentum scattering,in contrast to the conventional motional narrowing situation.In Chapter 12,we then investigate the quasiparticle and condensate dynamics in re-sponse to the THz optical pulses in the weak spin-orbit-coupled s-wave superconducting semiconductor quantum wells by using the gauge-invariant optical Bloch equations in the quasiparticle approximation.Specifically,in the Bloch equations,not only can the micro-scopic description for the quasiparticle dynamics be realized,but also the dynamics of the condensate is included,with the superfluid velocity and the effective chemical potential naturally incorporated.We reveal that the superfluid velocity itself can contribute to the pump of quasiparticles(pump effect),with its rate of change acting as the drive field to drive the quasiparticles(drive effect).We find that the oscillations of the Higgs mode with twice the frequency of the optical field are contributed dominantly by the drive ef-fect rather than the pump effect as long as the driven superconducting momentum is less than the Fermi momentum.This is in contrast to the conclusion from the Liouville or Bloch equations in the literature,in which the drive effect on the anomalous correlation is overlooked with only the pump effect considered.Furthermore,in the gauge-invariant optical Bloch equations,the charge neutrality condition is consistently considered based on the two-component model for the charge,in which the charge imbalance of quasiparticles can cause the fluctuation of the effective chemical potential for the condensate.It is pre-dicted that during the optical process,the quasiparticle charge imbalance can be induced by both the pump and drive effects,leading to the fluctuation of the chemical potential.This fluctuation of the chemical potential is further demonstrated to directly lead to a relaxation channel for the charge imbalance even with the elastic scattering due to impu-rities.This is very different from the previous understanding that in the isotropic s-wave superconductivity,the elastic scattering cannot cause any charge-imbalance relaxation.In the strong spin-orbit coupling limit,to start,in Chapter 13,we first show that the gapped triplet superconductivity,i.e.,a triplet superconductor with triplet order pa-rameter,can be realized in strong spin-orbit-coupled(100)quantum wells in proximity to s-wave superconductor.It is revealed that with the singlet order parameter induced from the superconducting proximity effect,in quantum wells,not only can the triplet pairings arise due to the spin-orbit coupling,but also the triplet order parameter can be induced due to the repulsive electron-electron Coulomb interaction.Specifically,we derive the effective Bogoliubov-de Gennes equation,in which the self-energies due to the effective electron-electron interaction contribute to the singlet and triplet order parameters.For the triplet order parameter,it is the p-wave(px±ipy)one with the d-vector parallel to the effective magnetic field due to the spin-orbit coupling.The numerical calculation in InSb(100)quantum wells shows that with proper electron density,the singlet and triplet order parameters can be even comparable,which can be experimentally distinguished.Finally,we introduce that the predicted(s+p)-wave superconducting quantum wells can be the platform for the helical topological superconductor.Based on the understanding on the equilibrium state in above(s+p)-wave supercon-ducting InSb quantum wells,in Chapter 14,we further investigate the quasiparticle and condensate dynamics in response to the THz optical pulses by using the gauge-invariant optical Bloch equations.Both the dynamics of triplet and singlet superconductivity are studied.Specifically,for the triplet superconductivity,we predict that with the vector po-tential parallel to the quantum wells,the optical field can cause the total spin polarization of Cooper pairs,oscillating with the frequency of the optical field.The direction of the total Cooper-pair spin polarization is shown to be parallel to the vector potential.For the singlet superconductivity,we show that due to the large spin-orbit coupling in InSb(100)quantum wells,there exist two Fermi surfaces including the inner and outer ones.In this specific configuration,the superconducting momentum can be tuned to be larger than the inner Fermi momentum but smaller than the outer one.We find that in this regime,the dynamics of the Higgs mode and charge imbalance shows different features in comparison with the conventional s-wave case.Finally,we summarize in Chapter 15.