超導體與半導體在高磁場下的物理性質

Abstract

I. 超強磁場下高溫超導體的傳輸性質與磁性理論 1. 在無序渦漩物質的熱動理學性質和傳輸性質. 高溫超導體的渦旋晶格的表現控制許 多超導體中的特性.理解這些特性對材料的商業應用和基礎研究都非常重要.瞭解無序 與溫度擾動和渦漩物質的交互作用的強關連電子的物理不論在應用或純科學上都有很 佔有很重要的地位。在過去很多年來我的研究群在LLL 近似區內建立了一個量化的理 論來描述溫度效應在相變附近的物理現象，同時的解釋了高溫超導體如YBCO 和層狀 結構的LaSCO。無序效應直到最近理論學家利用「replica method」才將將渦漩物質的理 論發展到實際問題，此後我們才得以解釋無序-有序的相圖. 然而這些方法目前只侷限在 靜態平衡系統上的討論,我計畫將針對動態和不可逆的現象包括玻璃態動力學和記憶效 應.同時的尋找出玻璃態的相變臨界線和無定型及結晶態內不可逆的相變線.一般的統計 力學上ergodic 的假設已不適用,複雜的動態學逼近法可用來應付動態系統在線性反應區 的現象. 2. 渦漩物質結構相變渦漩物質相變理論是目前研究的課題之一.近年來,拜新的實驗技 術如小角度的中子散射或更複雜的介子自旋旋轉技術所賜,渦旋物質的相變在實驗上被 觀察到. Yeshurun 在Bar Ilan 的研究小組最近在高溫超導體LaSCO 的磁性曲線觀察到 第二個峰值,我們認為這是晶格相變的現象. 我們將考慮兩種互補的近似法來研究溫度 擾動和無序的影響對結構相變現象的效應, 一是由變異的Ginzburg –Landau 相變理論, 他考慮了四角型晶格渦漩間偶合的強度的旋轉不變性項.這一部分的研究主要是我博士 班學生林佩真博士論文的主題.我們採用了LLL 和平均場的近似法來計算不同結構之系 統的自由能.在另一個極限下,我們採用了London 理論, 這個近似法將渦漩考慮成為線 狀的物質,這種物質的交互作用力如同d-wave 超導體是沒有旋轉對偁性,最早是由交大電 物的楊宗哲教授所推倒出來的.這個異向性導致在強外場下為晶格呈現正方形的晶格,在 低場下四邊形對偁姓被破壞而形成菱形的晶格.軟化的渦璇靠近相變線導致臨界電流上 產生"peak effect",及突然的增大.我們利用自洽的harmonic approximation 的路徑積分考 慮了溫度和無序效應的影響. 3. 第二類超導的磁束極限動力現象在過去幾年克服了材料和技術上的問題, 在第二類 超導爆炸衝擊波實驗可以利用快閃雷射的脈衝來產生.穩定的磁束前波可以到達10-100 km/sec. 此外,波前有時候會產生樹脂狀的分支.我會用超導渦漩物質的流體動力學方程 式來模擬分析這個現象.由於此一高速接近於破壞超導電流因此在波前部分窄區間會變 成正常態,在前端的能量的損耗和流失到達穩定的終端速度.這個新的領域裡面的發展非 常的我們的理論目前釋目前最能解釋這個爆炸衝擊波的三個主要理論之一. 4. 第二類超導的de Haas-van Alfven 效應近期發現的FFLO態在有機的準二維繫統的 重費米子超導化合物如CeCoIn5, 重新興起了理論學家對自選與軌道交互作用力的在破 壞Cooper對的興趣. 我們將採用加入電子自旋效應修正過的BSC理論來研究在高磁場下 相變附近的effective spin pair breaking第二類超導發生的現象. II.強關聯電子在低維度的半導體系統 1. 低維度的電子氣體之玻璃態在半導體和無序金屬的理論目前已經知道在三維繫統由 於無序所造成金屬絕緣相變是很普遍的行為,但在二維和一維繫統是不可能發生的.在之前的科學家認為1D 和2D 的金屬態是不存在的,即便是系統的雜質非常的稀少.然 而,1995 年Kravchenko 發現這個金屬態存在特殊的半導體系統裡[high mobility Si MOSFET, GaAs/AlGaAs 異相性結構].因此金屬絕緣相變會發生在二維高移動性且低電 子濃度的系統. 這個相當新奇的系統有即使在電子密度很低的情況下還是有著非常強的 電子電子作用力,這意味著標準的Landau liquid 理論需要被修正來解釋這個出乎預料的 結果. 如今世界上很多小組用不同的方法和從不同角度來研究金屬絕緣體相變, 但是一 個圓滿的理論至今還沒有得到.到目前為止,很多令人驚奇的實驗數據顯示了這個奇特的 結果.在熱力學有限溫度的相變中,溫度擾動控制了整個系統的臨界現象,在這裡這裡的臨 界現象是由量子擾動所造成. 量子相變是由其他的參數如外加磁場,無序的強度或是帶 電粒子的密度來調變的,而不是由溫度來控制.我會利用replica symmetry breaking, Keldysh formalism 和GW 近似法來建立低維度無序系統的電子玻璃態裡論. 2. 無序二維電子氣體在強磁場下量子擾動霍爾效應現象吸引了理論和實驗學家投入無 序交互作用電子系統的動力學的研究. 一般來說在強磁場下因為Landau層的能隙變大,可 以有效的採用LLL簡化問題. 這會有效的使有效維度衰減. Mobility edge 的解釋過簡化不 能有效描述實驗發現,因此除了原先的Laughlin』s variational波函數近似法,它需要更多量 化的理論來瞭解這些物理現象.然而多數的理論只考慮到線性反應. 最近非線性的I-V曲 線揭露了值得注意的尺度特性和統一性.我將採用結合無序系統的replica 方法和動力學 的方式來計算無序二維電子氣體系統在LLL區域內的IV特性曲線.這個發法和高溫超導 渦漩物質的理論相似. 我將用數值分析模擬來解析電子結構物質的形成，如:有 關」Wigner 晶格」的一些電子密度之臨界參數，決定量子態轉化的順序和它的 universality class，以及探查金屬相的特性。縱使在純淨的狀況，直到零度樣品仍 能維持在液態，所以零度溫度是個臨界點。一般急速超冷的液體有玻璃態（glass）的 性質，我將利用這臨界性，嚐試去建構玻璃態及存有斥力晶體融化的重整群體 （Renormalization Group）理論。

I. Transport and magnetic properties of high Tc superconductors in magnetic fields" 1. Thermodynamics and transport in disordered vortex matter. Understanding the interplay of disorder and thermal fluctuations in vortex matter of type II superconductors is an important long standing problem in physics of strongly correlated electrons in both pure science and applications. During last several years my group developed a quantitative theory of thermal fluctuations near the upper critical field using the LLL approach in the framework of general Ginzburg –Landau (GL) approach to superconductivity and applied it to a number of systems like YBCO and more layered LaSCO. Recently the theory was expanded using the so called 「replica method」 to include disorder which is crucial in this materials. We were able to explain the unified order –disorder line (including the vortex lattice melting line mainly due to thermal fluctuations and the "second peak" line due mainly to disorder) and the Kauzmann point in BSCCO and its dependence on doping. However the method is generally limited to static equilibrium properties only. I will study dynamic and even irreversible phenomena including glass dynamics and memory phenomena like aging. One of the purposes would be to find the "glass line" or irreversibility line in both the homogeneous and crystalline phases and compare it with the ongoing experiments. This will require calculation of the magnetization along this line. The generalization of statistical physics is required in which the ergodic assumption is no longer valid. Dynamical approach is significantly more complicated by is able to address dynamical questions beyond "linear response". In particular I hope to obtain the "stretched exponential" form of correlations in flux flow exhibiting the memory effects due to disorder. 2. Structural phase transitions in vortex matter. I was working on understanding the transitions between different vortex structure for some time. Recently many structural phase transitions were observed using small angle neutron scattering or a more difficult muon spin rotation technique. Yeshurun's group in Bar Ilan recently measured a second peak line in high Tc superconductor LaSCO, which we reinterpreted as a transition from the square lattice at high fields to a rhombic lattice. At lower fields the fourfold symmetry is spontaneously broken down to the rhombic symmetry. Softening of the vortex lattice near transition leads to the "peak effect" in critical current, namely its large enhancement.We will apply two complementary methods to study the transition. The first is the modified GL approach. Modification consists of the introduction of rotationally noninvariant terms describing the coupling of the vortices to the tetragonal crystal lattice. Both influence of thermal fluctuations and disorder will be considered. We use both the LLL and the mean field approximations to calculate free energies of different lattice configurations. In the opposite limit of low fields we use the London theory. Within this approach vortices are considered to be the line –like objects. The anisotropy leads to ordering of vortices in a square lattice at high fields. 3. Ultrafast dynamics of magnetic flux in type II superconductors. During last two years advance in both materials and measurement techniques made possible the generation of shock waves in type II superconductors by a femtosecond laser pulse. Stable flux front velocities of the scale as high as 10-100 km/sec were obtained. Moreover the front sometimes branches via dendrites. I will use the hydrodynamic equations of vortex matter in superconductors to model this situation numerically. Due to high velocity which is of the order of depairing current the transition to a normal state takes place at a narrow region at the front. The energy is dissipating and flows away from the front at a constant speed after the initial very fast stage at which this steady state was achieved. The field is very new and develops very fast so that our theory is one of three currently competing to explain the phenomenon. 4. The de Haas-van Alfven effect in type II superconductors in strong magnetic field. Recent observation of the Fulde-Ferrell-Larkin-Ovchinnikov state in the organic quasi-two-dimensional heavy-fermion superconducting compound CeCoIn5 have renewed theoretical interest in the interplay between orbital and spin effect in electron pair breaking. We will formulate the LLL microscopic theory at high magnetic fields in strongly type-II SC compounds with effective spin pair breaking. II. Strongly correlated electrons in low dimensional semiconductor systems 1. Electron glass state in disordered 1D and 2D electron gas in semiconductors and disordered metals. While metal-insulator transition due to disorder is quite common in ordinary three dimensional materials, in two or lower dimensions it is impossible. It was therefore generally accepted before recently that a metallic state in 1D and 2D cannot exist with even infinitesimal amount of quenched disorder. However starting 1995 such a state was observed in variety of 2D semiconductor systems (high mobility Si MOSFET, GaAs/AlGaAs heterostructures… ). The system is rather a novel one since about the same density electron – electron interactions become strong. This means that the standard Landau liquid theory should be modified to understand the unexpected results. A host of very surprising experimental data characterizing the transition is available that remains unexplained to date. Unlike in thermal phase transitions at finite temperature where the critical behavior is governed by thermal fluctuations, it is controlled by quantum fluctuations. I will develop the electron glass theory of the disordered low dimensional electron gas. The methods used will include the replica symmetry breaking, Keldysh formalism and the so called GW approximation. 2. Theory of disordered 2D electron gas in strong magnetic field Dynamics of disordered interacting electrons in strong magnetic field attracted great attention both experimentally and theoretically since the discovery of fractional quantum Hall effect. Generally at very high magnetic field the problem simplifies in a sense since the LLL approximation can be used leading to 「dimensional reduction」. The mobility edge explanation is too naive and recently several new experimental discoveries require more quantitative theoretical understanding going far beyond the original Laughlin』s wave function variational approach. Moreover almost all the theories consider linear response only. Recently nonlinear I-V curves were found to exhibit remarkable scaling properties and universality. I will use the LLL approximation combined with the replica theory of disorder to describe the transport in the regime and the dynamical approach to calculate the nonlinear I-V characteristics of the disordered 2D electron gas. The methods used were developed in the work on the vortex matter in high Tc superconductors. I will also describe analytically (as opposed to numerical simulations) the formation of structured electronic matter: the Wigner crystal in weakly disordered 2D electron gas in quantizing magnetic field. Previous study demonstrated that even in the clean samples the overcooled liquid state exists down to zero temperature and becomes critical at zero temperature. Generally overcooled liquid acquires properties of glass. I will use the criticality to construct general renormalization group (RG) theory of the glassy state and of melting of any crystal with repulsive forces.