纳米结构中的交流响应隧穿
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摘要
随着纳米微刻技术和材料生长技术的发展,制造各种介观结构已经成为可能,对介观系统的研究与日俱增。应用电场来控制和操纵介观结构中的输运问题,为交流响应的隧穿这个课题提供了一个广阔的研究领域。本论文主要研究了当交变电场作用在介观系统上,对电子输运的影响和调控。应用非平衡态Green函数方法,研究了几种介观系统的输运行为,对影响输运的条件(交变电场的频率、强度、温度等)作了定性分析,进行了较系统的理论研究,并得到了一些有意义的结果。主要做了以下几项工作:
(1)研究了单个金属电极与量子点耦合系统的自旋流的交流响应问题,在具体处理问题时我们只考虑量子点中一个自旋简并能级,为简单起见忽略了量子点内的库仑斥力。在引线中引入一个交变驱动电压,量子点内引入一个泵浦旋转磁场,研究在外部交变频率的驱动下,是否会使系统的自旋流产生新的现象。基于非平衡态Green函数方法得到了时间平均自旋流和它的微分表达式。我们发现:由于量子点中的旋转磁场产生的自旋翻转机制,导致引线中的自旋向上和自旋向下的电子的化学势不同引起非平衡自旋分布。对于一个给定的旋转频率,自旋流将随着驱动频率的增加而快速的增长并且出现一些小的台阶。当驱动频率进一步增加,自旋流将会显著的增大且达到一个稳定值。光子辅助隧穿过程引起了一些有趣的特征。自旋流图像中出现的台阶与光子的吸收和发射过程紧密相关。在低温的情况下,这种量子相干特性比较显著。同时,详细讨论了门电压和温度对自旋流的影响。
(2)研究了在ac场作用下,通过带有侧向耦合量子点的量子线中的光辅助隧穿问题。研究发现电-光子相互作用和量子相干在ac场频率变化下能够产生光子辅助次带反共振。因此,光子的相干吸收和发射可以在主反共振峰附近的次峰的相位测量中探测。讨论了零温和有限温下的电导和传输相位方面的信息。与无ac场的作用的情况相比较,由于传输电子受到ac场的作用,在能级ε=εd +nω处将产生一系列光子次带谷,相对于吸收( n > 0)和发射( n < 0)光子达到共振能级发生反共振,同时伴随着由于量子相干和光子辅助隧穿引起的相移的突变。Fano共振谷的高度受ac场的强度和频率的调制,谷的位置只与ac场的频率有关。有限温的情况下,Fano共振的振幅随着温度的升高减小,当温度高到某一特定的值时( K BT = 0.4接近隧穿耦合强度Γ= 0.49),在反共振峰能级附近第一个光子次带尖谷结构会演化为一个明显的共振峰结构,随着温度进一步升高这个峰的大小会增大。同时,随着温度的升高尖谷结构将很快的被抹平,意味着升高温度破坏了相位相干效应。而且,可以通过改变ac场的强度Δ和频率ω的大小,来调控电导的相移。
(3)研究了铁磁-量子点-超导系统的自旋相关的Andreev反射隧穿问题,考虑了量子点内的自旋翻转散射相互作用,并且在量子点上加入了外部ac场。研究表明时间平均Andreev反射电导G A随外加ac场,量子点内的自旋翻转散射强度R ,两隧穿耦合强度间的比率以及铁磁引线的自旋极化度P的变化呈现了新颖的隧穿谱结构。在外加ac场的作用下,Andreev反射电导随量子点能级εd变化曲线在能量ε=εd±R + nω0处呈现了一系列光子次带峰,伴随着电子吸收( n > 0)或发射( n < 0)光子达到共振能级隧穿进入量子点的过程。研究结果发现Andreev反射电导行为是自旋翻转散射和量子点与左右引线间的隧穿耦合引起的两劈裂能级的展宽以及外加ac场引起的光子辅助隧穿间的竞争产生的。此外,Andreev反射电导G A-偏压V特性展现为:当Γf 0≥ΓS0时,Andreev反射电导谱为单峰共振,当Γf 0 <ΓS0时,Andreev反射电导谱总是形成共振双峰结构。
With the progress of nanofabrication and material growth technologies, it has been possible to fabricate a variety of mesoscopic structures, resulting in extensive investigation of mesoscopic systems. Applying electric field to control and manipulate the transport of mesoscopic structures provides a wide research field for the alternating response of tunneling. In this thesis, we investigate the influence and manipulation on transport of mesoscopic systems under an ac field. Using the nonequilibrium Green function method, we study transport properties of several kinds of mesoscopic systems and make a qualitative analysis of transport conditions (frequency and amplitude of the ac field, temperature, etc.), obtaining some meaningful results. Main results are summarized as follows:
(1) We investigate alternating response of the spin current in a quantum dot system coupled to a normal metal electrode. For simplicity, we have neglected the intradot electron-electron Coulomb interaction, and only consider a single level in the quantum dot. An alternating driving voltage and a pumping rotating magnetic field are applied to investigate whether some new phenomenon of spin current can be generated as the driving frequency of the ac field changes. The nonequilibrium Green function technique is used to obtain the general formulas of the time-averaged spin current and its differential. It is found that the spin-flip mechanism induced by pumping rotating magnetic field in the QD leads to the difference of two spin chemical potentials creating a nonequilibrium spin population. For a given rotating frequency, the spin current increases rapidly and shows a series of steps with increasing driving frequency. As the driving frequency is further increasing, the spin current can be significantly enhanced and approaches a stable value. The photon-assisted processes bring about interesting features of spin current. The steps of the spin current are closely related to the photon absorbing and emitting process. These quantum interference features are remarkable at low temperatures. The influence of the gate voltage and temperature on the spin current is examined in detail.
(2) We investigate photon-assisted transport through a perfect quantum wire with a side-coupled quantum dot in the presence of an ac field. We find that the electron-photon interaction together with the quantum interference of electron wave function can lead to photon-assisted sideband anti-resonance as the ac field frequency varies, which is then useful for tuning coherence and phases of electrons. Consequently, the coherent absorption and emission of photons can be detected via phase measurement at the sidebands of the main anti-resonance. Zero and limited temperature dependence of the conductance and transmission phase are discussed. Compared to the situation of without the ac field, the ac field leads to a series of photonic sideband valleys atε=εd + nω, that is, an electron absorbs ( n > 0) or emits ( n < 0) photons to become resonant energy level where anti-resonances occur, accompanied with a sudden change in the phase shift due to the quantum interference and the photon-assisted tunneling. The amount of the phase shift varies with the ac field amplitude, despite that the anti-resonance location does not. The conductance amplitude decreases with increasing temperatures and the width of the anti-resonance becomes larger for sufficient low temperatures. The dip structure at the first photonic sideband will develop into a noticeable peak around the anti-resonance level when the temperature increases to 0.4 comparable to the magnitude ofΓ(Γ= 0.49), and this peak is then enhanced with further increasing temperatures. Meanwhile, the dip structures are rapidly smeared out with increasing temperatures, suggesting that phase coherence is destroyed with increasing temperatures. Furthermore, we can manipulate the phase shift of the conductance by changing the frequencyωand magnitudeΔof the ac field.
(3) We investigate Andreev reflection (AR) tunneling through a ferromagnet-quantum dot-superconductor (F-QD-S) system in the presence of an external ac field. The intradot spin-flip scattering in the QD is involved. It is shown that the time-averaged AR conductance displays interesting behaviors depending on the external ac field, the intradot spin-flip scattering R , the ratio of the two tunneling coupling strengths and the spin polarization P of the F-lead, respectively. In the presence of the ac field, the AR conductance versus the QD energy level exhibits a series of photonic sideband peaksε=εd±R + nω0, that is, the electron absorbs ( n > 0) or emits ( n < 0) photons to become resonant tunneling through the QD. And the observed behaviors of the AR conductance are a consequence of the competition between the intradot spin-flip scattering and the tunneling coupling strength of the two leads together with the external ac field. In addition, the AR conductance-bias voltage characteristic shows that whenΓf 0≥ΓS0, the AR conductance displays a single-peak resonance and whenΓf 0 <ΓS0, the AR conductance always develops into the double-peak indicating a novel structure.
(1)研究了单个金属电极与量子点耦合系统的自旋流的交流响应问题,在具体处理问题时我们只考虑量子点中一个自旋简并能级,为简单起见忽略了量子点内的库仑斥力。在引线中引入一个交变驱动电压,量子点内引入一个泵浦旋转磁场,研究在外部交变频率的驱动下,是否会使系统的自旋流产生新的现象。基于非平衡态Green函数方法得到了时间平均自旋流和它的微分表达式。我们发现:由于量子点中的旋转磁场产生的自旋翻转机制,导致引线中的自旋向上和自旋向下的电子的化学势不同引起非平衡自旋分布。对于一个给定的旋转频率,自旋流将随着驱动频率的增加而快速的增长并且出现一些小的台阶。当驱动频率进一步增加,自旋流将会显著的增大且达到一个稳定值。光子辅助隧穿过程引起了一些有趣的特征。自旋流图像中出现的台阶与光子的吸收和发射过程紧密相关。在低温的情况下,这种量子相干特性比较显著。同时,详细讨论了门电压和温度对自旋流的影响。
(2)研究了在ac场作用下,通过带有侧向耦合量子点的量子线中的光辅助隧穿问题。研究发现电-光子相互作用和量子相干在ac场频率变化下能够产生光子辅助次带反共振。因此,光子的相干吸收和发射可以在主反共振峰附近的次峰的相位测量中探测。讨论了零温和有限温下的电导和传输相位方面的信息。与无ac场的作用的情况相比较,由于传输电子受到ac场的作用,在能级ε=εd +nω处将产生一系列光子次带谷,相对于吸收( n > 0)和发射( n < 0)光子达到共振能级发生反共振,同时伴随着由于量子相干和光子辅助隧穿引起的相移的突变。Fano共振谷的高度受ac场的强度和频率的调制,谷的位置只与ac场的频率有关。有限温的情况下,Fano共振的振幅随着温度的升高减小,当温度高到某一特定的值时( K BT = 0.4接近隧穿耦合强度Γ= 0.49),在反共振峰能级附近第一个光子次带尖谷结构会演化为一个明显的共振峰结构,随着温度进一步升高这个峰的大小会增大。同时,随着温度的升高尖谷结构将很快的被抹平,意味着升高温度破坏了相位相干效应。而且,可以通过改变ac场的强度Δ和频率ω的大小,来调控电导的相移。
(3)研究了铁磁-量子点-超导系统的自旋相关的Andreev反射隧穿问题,考虑了量子点内的自旋翻转散射相互作用,并且在量子点上加入了外部ac场。研究表明时间平均Andreev反射电导G A随外加ac场,量子点内的自旋翻转散射强度R ,两隧穿耦合强度间的比率以及铁磁引线的自旋极化度P的变化呈现了新颖的隧穿谱结构。在外加ac场的作用下,Andreev反射电导随量子点能级εd变化曲线在能量ε=εd±R + nω0处呈现了一系列光子次带峰,伴随着电子吸收( n > 0)或发射( n < 0)光子达到共振能级隧穿进入量子点的过程。研究结果发现Andreev反射电导行为是自旋翻转散射和量子点与左右引线间的隧穿耦合引起的两劈裂能级的展宽以及外加ac场引起的光子辅助隧穿间的竞争产生的。此外,Andreev反射电导G A-偏压V特性展现为:当Γf 0≥ΓS0时,Andreev反射电导谱为单峰共振,当Γf 0 <ΓS0时,Andreev反射电导谱总是形成共振双峰结构。
With the progress of nanofabrication and material growth technologies, it has been possible to fabricate a variety of mesoscopic structures, resulting in extensive investigation of mesoscopic systems. Applying electric field to control and manipulate the transport of mesoscopic structures provides a wide research field for the alternating response of tunneling. In this thesis, we investigate the influence and manipulation on transport of mesoscopic systems under an ac field. Using the nonequilibrium Green function method, we study transport properties of several kinds of mesoscopic systems and make a qualitative analysis of transport conditions (frequency and amplitude of the ac field, temperature, etc.), obtaining some meaningful results. Main results are summarized as follows:
(1) We investigate alternating response of the spin current in a quantum dot system coupled to a normal metal electrode. For simplicity, we have neglected the intradot electron-electron Coulomb interaction, and only consider a single level in the quantum dot. An alternating driving voltage and a pumping rotating magnetic field are applied to investigate whether some new phenomenon of spin current can be generated as the driving frequency of the ac field changes. The nonequilibrium Green function technique is used to obtain the general formulas of the time-averaged spin current and its differential. It is found that the spin-flip mechanism induced by pumping rotating magnetic field in the QD leads to the difference of two spin chemical potentials creating a nonequilibrium spin population. For a given rotating frequency, the spin current increases rapidly and shows a series of steps with increasing driving frequency. As the driving frequency is further increasing, the spin current can be significantly enhanced and approaches a stable value. The photon-assisted processes bring about interesting features of spin current. The steps of the spin current are closely related to the photon absorbing and emitting process. These quantum interference features are remarkable at low temperatures. The influence of the gate voltage and temperature on the spin current is examined in detail.
(2) We investigate photon-assisted transport through a perfect quantum wire with a side-coupled quantum dot in the presence of an ac field. We find that the electron-photon interaction together with the quantum interference of electron wave function can lead to photon-assisted sideband anti-resonance as the ac field frequency varies, which is then useful for tuning coherence and phases of electrons. Consequently, the coherent absorption and emission of photons can be detected via phase measurement at the sidebands of the main anti-resonance. Zero and limited temperature dependence of the conductance and transmission phase are discussed. Compared to the situation of without the ac field, the ac field leads to a series of photonic sideband valleys atε=εd + nω, that is, an electron absorbs ( n > 0) or emits ( n < 0) photons to become resonant energy level where anti-resonances occur, accompanied with a sudden change in the phase shift due to the quantum interference and the photon-assisted tunneling. The amount of the phase shift varies with the ac field amplitude, despite that the anti-resonance location does not. The conductance amplitude decreases with increasing temperatures and the width of the anti-resonance becomes larger for sufficient low temperatures. The dip structure at the first photonic sideband will develop into a noticeable peak around the anti-resonance level when the temperature increases to 0.4 comparable to the magnitude ofΓ(Γ= 0.49), and this peak is then enhanced with further increasing temperatures. Meanwhile, the dip structures are rapidly smeared out with increasing temperatures, suggesting that phase coherence is destroyed with increasing temperatures. Furthermore, we can manipulate the phase shift of the conductance by changing the frequencyωand magnitudeΔof the ac field.
(3) We investigate Andreev reflection (AR) tunneling through a ferromagnet-quantum dot-superconductor (F-QD-S) system in the presence of an external ac field. The intradot spin-flip scattering in the QD is involved. It is shown that the time-averaged AR conductance displays interesting behaviors depending on the external ac field, the intradot spin-flip scattering R , the ratio of the two tunneling coupling strengths and the spin polarization P of the F-lead, respectively. In the presence of the ac field, the AR conductance versus the QD energy level exhibits a series of photonic sideband peaksε=εd±R + nω0, that is, the electron absorbs ( n > 0) or emits ( n < 0) photons to become resonant tunneling through the QD. And the observed behaviors of the AR conductance are a consequence of the competition between the intradot spin-flip scattering and the tunneling coupling strength of the two leads together with the external ac field. In addition, the AR conductance-bias voltage characteristic shows that whenΓf 0≥ΓS0, the AR conductance displays a single-peak resonance and whenΓf 0 <ΓS0, the AR conductance always develops into the double-peak indicating a novel structure.
引文
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