近年來，具有類方鈷礦結構之三元錫化物在凝態物理領域持續受到關注，由於其擁有許多像是超導現象、結構相變、熱電效應及磁特性等等有趣的物理特性。。為了瞭解超導相變與結構相變之間的電子-聲子交互作用影響，本篇論文將透過X-ray繞射、電性量測、熱電量測以及錫原子的核磁共振等實驗方法，來討論 (Sr1-xCax)3Rh4Sn13與Ce3Rh4Sn13這兩個相似卻擁有不同相變系統的物理特性。本論文的第一個部分，對於Sr3Rh4Sn13摻雜鈣之系列樣品，在電阻率的量測中，結構相變的溫度T*隨著Ca摻雜的比例增加而下降。而霍爾係數的結果指出，在Ca3Rh4Sn13樣品中，呈現負號的霍爾係數代表n-type的載子主導著其電子的傳輸，相對於較複雜的Sr3Rh4Sn13樣品，其經過138 K的結構性相變後，低溫部分的霍爾係數出現劇烈的轉折並變成正值，表示在Sr3Rh4Sn13樣品中的結構相變連帶影響費米面(Fermi surfaces)上的態密度(Density of state)，而此結果也與Seebeck係數、熱電性質的量測結果一致。接著我們透過量測Sr3Rh4Sn13樣品的119Sn核磁共振線型，觀察到119Sn核磁共振譜線中呈現具有不對稱性的結構，此結構由佔據不同對稱位置的軸對稱Sn1與非軸對稱的Sn2所組成，譜線在經過結構相變後Sn2的譜線部分有明顯變化。最後，在自旋晶格鬆弛速率1/T1 (Spin lattice relaxation rate)的量測中，(Sr1-xCax)3Rh4Sn13系列樣品皆呈金屬特性的Korringa行為與溫度成線性變化，所以藉著Korringa relation關係式便可估算出各樣品游離電子之費米面上的態密度。對於Sr3Rh4Sn13樣品，結構性相變使得其費米面有微小的變化而且態密度在相變後減少約13 %。不僅如此，根據計算的結果，我們發現Sn的5s電子在費米面上所貢獻的態密度會隨著Ca摻雜的比例增加而變大，這個趨勢與此系列樣品的超導溫度隨Ca元素比例增加而提高的趨勢是一致的。對於(Sr1-xCax)3Rh4Sn13這個系統，本論文的電性和核磁共振分析對電子態密度變化提供了一個微觀的證據，並討論電子態密度與結構相變之間的影響效應。
本論文第二個部分，對於Ce3Rh4Sn13的量測結果中，我們藉由同步輻射X-ray繞射實驗觀察到Ce3Rh4Sn13在T* 350 K處有一個結構相變產生。在比熱的實驗中，由於樣品的比熱數據在升溫與降溫的過程中重疊，意即此相變前後不具有熱滯的現象，因此可以定義此相變為二階的結構相變。在熱電性質的量測中，熱導係數顯示Ce3Rh4Sn13在相變前後聲子的貢獻有較大的改變，此點與第一部分所討論的(Sr1-xCax)3Rh4Sn13系統不同。在核磁共振的分析中，佔據不同對稱位置的Sn原子受到f-s超精細耦合作用的變化反映在核磁共振的線型之中。此現象可以歸因於Ce與Sn原子間的平均距離減少所致。特別是對於Sn2原子來說，Ce與Sn2的鍵長從高溫結構經相變成低溫結構後較為縮短。本論文對於Ce3Rh4Sn13在T*的二階結構相變，本質上是由於聲子的不穩定引起結構的扭曲變化，提供一個基本的物理圖像。

Ternary stannides with Yb3Rh4Sn13-type structure continuously attract a lot of attention due to it interesting electronic, thermodynamic, magnetic properties in condensed matter physics. To shed the light on the instability between superconductivity and structural phase transition involving the interaction of electron-phonon, in this thesis, we report the results of two systems of Rh-based ternary stannides (Sr1-xCax)3Rh4Sn13 and Ce3Rh4Sn13, respectively. In this two-similar system, there is phase transition at normal state but different mechanisms. In the first part of this thesis, we discuss the electronic properties of the single crystalline (Sr1-xCax)3Rh4Sn13 by means of the electrical resistivity, Hall coefficient, thermal electric properties, as well as 119Sn nuclear magnetic resonance (NMR) measurements. In our results, the negative sign of the Hall coefficient and Seebeck coefficient at low temperatures suggest that the n-type carriers dominate the electrical transport in Ca3Rh4Sn13, in contrast to the observations in Sr3Rh4Sn13 which exhibits a dramatic change around T*and presents positive RH at the regime of T<T*. Such a finding indicates a significant difference in the electronic features between these two stannides. Furthermore, we analyzed the temperature-dependent 119Sn NMR spin-lattice relaxation rate for Ca doped Sr3Rh4Sn13 to examine the change of the electronic Fermi-level density of states (DOS) in (Sr1-xCax)3Rh4Sn13. It indicates that the Sn 5s partial Fermi-level DOS enhances with increasing the Ca content, being consistent with the trend of the superconducting temperature. With this respect, the NMR analysis provides microscopic evidence for the correlation between the electronic DOS and superconductivity of the (Sr1-xCax)3Rh4Sn13 system.
In the second part of this thesis, we report an observation of a phase transition in Ce3Rh4Sn13 with the transition temperature T* 350 K by means of synchrotron X-ray powder diffraction, specific heat, electrical resistivity, Seebeck coefficient, thermal conductivity, as well as 119Sn NMR measurements. The phase transition has been characterized by marked features near T* in all measured physical quantities. The lack of thermal hysteresis in the specific heat indicates a second-order phase transition in nature. Different from the system of (Sr1-xCax)3Rh4Sn13 we discussed in the first part, the result of thermal conductivity in Ce3Rh4Sn13 reveals that phonon plays an important role in the phase transition. From the NMR analysis, the change in the transferred hyperfine coupling constant for two tin sites has been resolved. The obtained results have been associated with the reduction in the averaged interatomic distance between Ce and Sn atoms, particularly for the Sn2 atoms. It indicates that the displacement of the Sn2 atoms, which deforms the high-temperature structure, shortens the Ce-Sn2 bond length at low temperatures. We therefore provide a concise picture that the observed second-order phase transition at T* of Ce3Rh4Sn13 should be characterized by a structural modulation essentially due to lattice distortions arising from phonon instability.

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