一維周期性驅(qū)動(dòng)拓?fù)浣^緣體與拓?fù)涑瑢?dǎo)體
發(fā)布時(shí)間：2018-07-16 13:50
【摘要】：拓?fù)浣^緣體是介于普通絕緣體與低維金屬之間的一種新物態(tài)。與普通絕緣體一樣,它的費(fèi)米面存在于帶隙中,但由于其拓?fù)浞瞧接鼓軒ЫY(jié)構(gòu),在表面或邊界上會(huì)形成穩(wěn)定的無能隙邊緣激發(fā)。這些無能隙邊緣激發(fā)連接價(jià)帶頂和導(dǎo)帶底,受系統(tǒng)對(duì)稱性的保護(hù),在自旋電子學(xué)和拓?fù)淞孔佑?jì)算領(lǐng)域有著廣泛的應(yīng)用前景。然而,在自然的參數(shù)條件下,具有拓?fù)湫再|(zhì)的靜態(tài)系統(tǒng)是非常有限的,需要我們?nèi)藶榈母淖儾牧系慕Y(jié)構(gòu)和性質(zhì)。Floquet拓?fù)浣^緣體是最近研究的熱點(diǎn)之一。通過Floquet定理,可以將靜態(tài)時(shí)拓?fù)淦接沟牟牧险T導(dǎo)成拓?fù)浣^緣體。實(shí)驗(yàn)上,可以通過將微波或光照射到靜態(tài)材料中來實(shí)現(xiàn)。同時(shí),由于Floquet系統(tǒng)的特殊性,一般來說,Floquet拓?fù)浣^緣體比相應(yīng)的靜態(tài)系統(tǒng)具有更豐富的相圖。本論文從理論和數(shù)值上對(duì)三種一維周期性驅(qū)動(dòng)拓?fù)浣^緣體和拓?fù)涑瑢?dǎo)體模型進(jìn)行了研究。首先,我們研究了一維周期脈沖超晶格模型的拓?fù)湎嘧�。這一模型基于一維雙色光超晶格模型,其中超晶格勢(shì)以周期脈沖的形式出現(xiàn)。這一系統(tǒng)處在超晶格動(dòng)量與超晶格勢(shì)相位所構(gòu)成的二維參數(shù)空間中,具有二維空間的拓?fù)湫再|(zhì)。研究表明這樣的系統(tǒng)擁有非平庸的拓?fù)淠軒ЫY(jié)構(gòu)。在開邊界下,它有著豐富的邊緣態(tài),包括準(zhǔn)能量±π/T附近能隙中的反常邊緣態(tài)和相向而行的手性反常邊緣態(tài)。因而其拓?fù)湫再|(zhì)不能用陳數(shù)完全刻畫。這些豐富的邊緣態(tài)與拓?fù)湎嘧兣R界點(diǎn)附近,體態(tài)所形成的的多Dirac錐結(jié)構(gòu)有緊密的聯(lián)系。與對(duì)應(yīng)靜態(tài)系統(tǒng)的另一個(gè)不同點(diǎn)是,通過調(diào)節(jié)周期驅(qū)動(dòng)的強(qiáng)度或者周期,就可以實(shí)現(xiàn)拓?fù)湎嘧儭Ｆ浯?我們研究了一維周期性驅(qū)動(dòng)拓?fù)涑瑢?dǎo)鏈在快速淬火和緩慢淬火下的動(dòng)力學(xué)行為。選取初態(tài)為拓?fù)浞瞧接箲B(tài),這時(shí)系統(tǒng)有局域在的兩端的Majorana零�；颚心！Ｎ覀冏岒�(qū)動(dòng)周期突然發(fā)生變化或緩慢變化,使得系統(tǒng)穿過相變臨界點(diǎn)從而發(fā)生相變。研究表明,當(dāng)快速淬火到拓?fù)浞瞧接瓜嗯c平庸相或弱拓?fù)湎嗟南嘧兣R界點(diǎn)時(shí),Majorana殘存幾率隨時(shí)間周期性變化,對(duì)應(yīng)Majorana模在鏈的兩端來回振蕩。然而,當(dāng)快速淬火到與另一個(gè)具有不同的Majorana邊緣模數(shù)目的非平庸相的相變臨界點(diǎn)時(shí),沒有觀察到這種現(xiàn)象。當(dāng)快速淬火到弱拓?fù)湎鄷r(shí),Majorana殘存幾率隨時(shí)間周期性變化,但是變化周期與系統(tǒng)長(zhǎng)度無關(guān)。此時(shí),對(duì)應(yīng)Majorana模在鏈的同一端來回振蕩。以上行為依賴于淬火路徑,反映了不同拓?fù)湎嘧兿?Majorana模變化的不同。當(dāng)變化到新的拓?fù)湎鄷r(shí),如果之前的零(或π)邊緣模依然存在并保持為原來的能量,則對(duì)應(yīng)的Majorana邊緣模在這種淬火下是穩(wěn)定的,否則它將退相干。特別的,如果新的拓?fù)湎嘀羞吘壞Ｄ芰坎辉贋榱?或π),則Majorana殘存幾率隨時(shí)間周期性振蕩。通過分析這種路徑依賴的淬火動(dòng)力學(xué)行為,可反饋得到系統(tǒng)拓?fù)湎嘧兊男畔�。最�?我們研究了電子-電子相互作用對(duì)周期性驅(qū)動(dòng)拓?fù)涑瑢?dǎo)體的影響。相互作用主要帶來兩個(gè)效應(yīng)：一種是抑制Majorana邊緣模,使系統(tǒng)發(fā)生拓?fù)湎嘧�；另一種是引起混沌效應(yīng)。混沌效應(yīng)與拓?fù)涫窍到y(tǒng)兩種相對(duì)立的性質(zhì)。其中,前者很容易受擾動(dòng)的影響,而后者則對(duì)擾動(dòng)不敏感。在驅(qū)動(dòng)頻率與系統(tǒng)帶寬以及相互作用強(qiáng)度在同一量級(jí)時(shí),基于高頻與低頻展開的解析方法不再適用。我們用精確對(duì)角化方法,根據(jù)系統(tǒng)的準(zhǔn)能譜與淬火動(dòng)力學(xué)行為,研究了相互作用對(duì)其拓?fù)湫再|(zhì)的影響。而混沌效應(yīng)則通過準(zhǔn)能譜的能隙統(tǒng)計(jì)性質(zhì)加以分析。結(jié)果表明,對(duì)于V較小的情形,y引起的弱混沌效應(yīng)可以與拓?fù)湫再|(zhì)共存。而強(qiáng)相互作用在引起系統(tǒng)強(qiáng)混沌效應(yīng)的同時(shí),也破壞系統(tǒng)的拓?fù)湫再|(zhì),使其相變到拓?fù)淦接箲B(tài)。
[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.
【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類號(hào)】：O469
本文編號(hào)：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.
【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類號(hào)】：O469
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