一维周期性驱动拓扑绝缘体与拓扑超导体
发布时间：2018-07-16 13:50
【摘要】：拓扑绝缘体是介于普通绝缘体与低维金属之间的一种新物态。与普通绝缘体一样,它的费米面存在于带隙中,但由于其拓扑非平庸能带结构,在表面或边界上会形成稳定的无能隙边缘激发。这些无能隙边缘激发连接价带顶和导带底,受系统对称性的保护,在自旋电子学和拓扑量子计算领域有着广泛的应用前景。然而,在自然的参数条件下,具有拓扑性质的静态系统是非常有限的,需要我们人为的改变材料的结构和性质。Floquet拓扑绝缘体是最近研究的热点之一。通过Floquet定理,可以将静态时拓扑平庸的材料诱导成拓扑绝缘体。实验上,可以通过将微波或光照射到静态材料中来实现。同时,由于Floquet系统的特殊性,一般来说,Floquet拓扑绝缘体比相应的静态系统具有更丰富的相图。本论文从理论和数值上对三种一维周期性驱动拓扑绝缘体和拓扑超导体模型进行了研究。首先,我们研究了一维周期脉冲超晶格模型的拓扑相变。这一模型基于一维双色光超晶格模型,其中超晶格势以周期脉冲的形式出现。这一系统处在超晶格动量与超晶格势相位所构成的二维参数空间中,具有二维空间的拓扑性质。研究表明这样的系统拥有非平庸的拓扑能带结构。在开边界下,它有着丰富的边缘态,包括准能量±π/T附近能隙中的反常边缘态和相向而行的手性反常边缘态。因而其拓扑性质不能用陈数完全刻画。这些丰富的边缘态与拓扑相变临界点附近,体态所形成的的多Dirac锥结构有紧密的联系。与对应静态系统的另一个不同点是,通过调节周期驱动的强度或者周期,就可以实现拓扑相变。其次,我们研究了一维周期性驱动拓扑超导链在快速淬火和缓慢淬火下的动力学行为。选取初态为拓扑非平庸态,这时系统有局域在的两端的Majorana零模或π模。我们让驱动周期突然发生变化或缓慢变化,使得系统穿过相变临界点从而发生相变。研究表明,当快速淬火到拓扑非平庸相与平庸相或弱拓扑相的相变临界点时,Majorana残存几率随时间周期性变化,对应Majorana模在链的两端来回振荡。然而,当快速淬火到与另一个具有不同的Majorana边缘模数目的非平庸相的相变临界点时,没有观察到这种现象。当快速淬火到弱拓扑相时,Majorana残存几率随时间周期性变化,但是变化周期与系统长度无关。此时,对应Majorana模在链的同一端来回振荡。以上行为依赖于淬火路径,反映了不同拓扑相变下,Majorana模变化的不同。当变化到新的拓扑相时,如果之前的零(或π)边缘模依然存在并保持为原来的能量,则对应的Majorana边缘模在这种淬火下是稳定的,否则它将退相干。特别的,如果新的拓扑相中边缘模能量不再为零(或π),则Majorana残存几率随时间周期性振荡。通过分析这种路径依赖的淬火动力学行为,可反馈得到系统拓扑相变的信息。最后,我们研究了电子-电子相互作用对周期性驱动拓扑超导体的影响。相互作用主要带来两个效应：一种是抑制Majorana边缘模,使系统发生拓扑相变；另一种是引起混沌效应。混沌效应与拓扑是系统两种相对立的性质。其中,前者很容易受扰动的影响,而后者则对扰动不敏感。在驱动频率与系统带宽以及相互作用强度在同一量级时,基于高频与低频展开的解析方法不再适用。我们用精确对角化方法,根据系统的准能谱与淬火动力学行为,研究了相互作用对其拓扑性质的影响。而混沌效应则通过准能谱的能隙统计性质加以分析。结果表明,对于V较小的情形,y引起的弱混沌效应可以与拓扑性质共存。而强相互作用在引起系统强混沌效应的同时,也破坏系统的拓扑性质,使其相变到拓扑平庸态。
[Abstract]:A topological insulator is a new state between an ordinary insulator and a low dimensional metal. Like an ordinary insulator, its Fermi surface exists in a band gap, but due to its topological non mediocre energy band structure, a stable inactive edge excitation is formed on the surface or boundary. These non gap edges excite the top of the valence band and the bottom of the guide band. The protection of system symmetry has a wide range of applications in the field of spintronics and topological quantum computing. However, under the natural parameter conditions, the static system with topological properties is very limited. It is one of the hotspots of recent research that we need to change the structure and properties of the material artificially..Floquet is one of the hot topics in the field of Flo. The quet theorem can induce the static and topologically mediocre material into a topological insulator. In the experiment, it can be realized by irradiation of microwave or light into the static material. At the same time, because of the particularity of the Floquet system, the Floquet topology insulator generally has a richer phase diagram than the corresponding static system. Three one-dimensional periodic driven topological insulators and topological superconductors are studied. First, we study the topological phase transition of one dimensional periodic pulse superlattice model. This model is based on one dimensional double color optical superlattice model, in which the superlattice potential is in the form of periodic pulses. This system is in superlattice momentum and superlattice. The topological properties of two dimensional space in the potential phase constitute a two-dimensional space. The study shows that such a system has a non mediocre topological band structure. Under the open boundary, it has a rich edge state, including the anomalous marginal state in the energy gap near the quasi energy + /T and the chiral anomalous edge states which are opposite to the opposite direction. The mass can not be completely portrayed by Chen Shu. These rich marginal states are closely related to the multi Dirac cone structure formed by the body state near the critical point of the topological phase transition. Another difference between the corresponding static system and the corresponding static system is that the topological phase transition can be realized by adjusting the intensity or cycle driven by the periodic. Secondly, we study the one-dimensional period. The dynamic behavior of the topological superconducting chain under rapid quenching and slow quenching is selected as the topological non mediocre state. At this time, the system has the Majorana zero mode or the pion mode at the two ends of the local area. We make the driving cycle change suddenly or slowly, making the system pass through the phase transition point and then change. When the phase transition critical point is quenched to a topological non ordinary phase or a mediocre phase or a weak topology, the Majorana residual probability varies with time, and the corresponding Majorana mode oscillates back and forth between the two ends of the chain. However, it is not observed when the phase transition critical point of a non mediocre phase with a different Majorana edge modulus is rapidly quenched. When fast quenching to weak topological phase, the residual probability of Majorana changes with time periodically, but the change period is independent of the length of the system. At this time, the corresponding Majorana mode oscillates back and forth at the same end of the chain. The above behavior depends on the quenching path, which reflects the variation of the Majorana mode under different topological phase transitions. In phase, if the former zero (or PI) edge die still exists and remains the original energy, the corresponding Majorana edge mode is stable under this quenching, otherwise it will be decohered. In particular, if the energy of the edge mode in the new topology phase is no longer zero (or PI), the residual probability of the Majorana is oscillating with time. The dynamic behavior of the path dependent quenching can feed back the information of the topological phase transition of the system. Finally, we study the effect of the electron electron interaction on the periodic driven topological superconductors. The interaction mainly brings two effects: one is to suppress the Majorana edge mode and make the system topological phase transition; the other causes the chaos effect. The chaotic effect and topology are two relative properties of the system. Among them, the former is easily affected by the disturbance and the latter is insensitive to the disturbance. The analytical method based on the high frequency and low frequency expansion is not applicable when the driving frequency is the same in the same order of magnitude as the system bandwidth and the interaction intensity. The influence of the interaction on its topological properties is studied. The chaotic effect is analyzed by the statistical properties of the energy gap of the quasi energy spectrum. The results show that the weak chaotic effect caused by y can coexist with the topological properties for the smaller V, and the strong interaction is the same as the strong chaotic effect of the system. It also destroys the topological properties of the system and transforms it into topological banality.
【学位授予单位】：南京大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O469
本文编号：2126591
[Abstract]:A topological insulator is a new state between an ordinary insulator and a low dimensional metal. Like an ordinary insulator, its Fermi surface exists in a band gap, but due to its topological non mediocre energy band structure, a stable inactive edge excitation is formed on the surface or boundary. These non gap edges excite the top of the valence band and the bottom of the guide band. The protection of system symmetry has a wide range of applications in the field of spintronics and topological quantum computing. However, under the natural parameter conditions, the static system with topological properties is very limited. It is one of the hotspots of recent research that we need to change the structure and properties of the material artificially..Floquet is one of the hot topics in the field of Flo. The quet theorem can induce the static and topologically mediocre material into a topological insulator. In the experiment, it can be realized by irradiation of microwave or light into the static material. At the same time, because of the particularity of the Floquet system, the Floquet topology insulator generally has a richer phase diagram than the corresponding static system. Three one-dimensional periodic driven topological insulators and topological superconductors are studied. First, we study the topological phase transition of one dimensional periodic pulse superlattice model. This model is based on one dimensional double color optical superlattice model, in which the superlattice potential is in the form of periodic pulses. This system is in superlattice momentum and superlattice. The topological properties of two dimensional space in the potential phase constitute a two-dimensional space. The study shows that such a system has a non mediocre topological band structure. Under the open boundary, it has a rich edge state, including the anomalous marginal state in the energy gap near the quasi energy + /T and the chiral anomalous edge states which are opposite to the opposite direction. The mass can not be completely portrayed by Chen Shu. These rich marginal states are closely related to the multi Dirac cone structure formed by the body state near the critical point of the topological phase transition. Another difference between the corresponding static system and the corresponding static system is that the topological phase transition can be realized by adjusting the intensity or cycle driven by the periodic. Secondly, we study the one-dimensional period. The dynamic behavior of the topological superconducting chain under rapid quenching and slow quenching is selected as the topological non mediocre state. At this time, the system has the Majorana zero mode or the pion mode at the two ends of the local area. We make the driving cycle change suddenly or slowly, making the system pass through the phase transition point and then change. When the phase transition critical point is quenched to a topological non ordinary phase or a mediocre phase or a weak topology, the Majorana residual probability varies with time, and the corresponding Majorana mode oscillates back and forth between the two ends of the chain. However, it is not observed when the phase transition critical point of a non mediocre phase with a different Majorana edge modulus is rapidly quenched. When fast quenching to weak topological phase, the residual probability of Majorana changes with time periodically, but the change period is independent of the length of the system. At this time, the corresponding Majorana mode oscillates back and forth at the same end of the chain. The above behavior depends on the quenching path, which reflects the variation of the Majorana mode under different topological phase transitions. In phase, if the former zero (or PI) edge die still exists and remains the original energy, the corresponding Majorana edge mode is stable under this quenching, otherwise it will be decohered. In particular, if the energy of the edge mode in the new topology phase is no longer zero (or PI), the residual probability of the Majorana is oscillating with time. The dynamic behavior of the path dependent quenching can feed back the information of the topological phase transition of the system. Finally, we study the effect of the electron electron interaction on the periodic driven topological superconductors. The interaction mainly brings two effects: one is to suppress the Majorana edge mode and make the system topological phase transition; the other causes the chaos effect. The chaotic effect and topology are two relative properties of the system. Among them, the former is easily affected by the disturbance and the latter is insensitive to the disturbance. The analytical method based on the high frequency and low frequency expansion is not applicable when the driving frequency is the same in the same order of magnitude as the system bandwidth and the interaction intensity. The influence of the interaction on its topological properties is studied. The chaotic effect is analyzed by the statistical properties of the energy gap of the quasi energy spectrum. The results show that the weak chaotic effect caused by y can coexist with the topological properties for the smaller V, and the strong interaction is the same as the strong chaotic effect of the system. It also destroys the topological properties of the system and transforms it into topological banality.
【学位授予单位】：南京大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O469
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