LaPtSi kristal yapıya sahip bazı malzemelerin fiziksel özelliklerinin teorik olarak incelenmesi = Theoretical investigation of the physical properties of some materials crystallized in LaPtSi structure

Abstract

Merkezi simetrik olmayan (noncentrosymmetric (NCS)) LaPtSi yapıdaki birçok bileşiğin süperiletkenliği deneysel olarak 1980'li yıllardan beri bilinmesine rağmen onlar üzerine yapılan teorik çalışmalar yok denecek kadar azdır. Fakat teorik çalışmalar bu tür bileşiklerde süperiletkenliğin orijininin belirlenmesine ışık tutar. Çünkü BCS teorisine göre süperiletkenliğe yol açan Cooper çiftlerinin oluşumunda fononlar aracılık etmektedir. Bu gerçek, süperiletken bileşiklerin elektronik ve fononik özelliklerinin çalışılmasının önemini ortaya koymaktadır. Ayrıca elektron-fonon etkileşimi özellikleri de ayrıntılı bir şekilde çalışılarak hangi elektronik orbitallerin ve hangi fonon modlarının süperiletkenliğe geçişi sağladığı tespit edilmelidir. Yukardaki gerçeklerden yola çıkarak bu tez çalışmasının ilk adımında NCS LaPtSi-tipi kristalleşen LaRhP, LaRhAs, LaIrP, LaIrAs, LaIrGe ve LaPtGe bileşiklerinin yapısal ve elektronik özellikleri günümüzün en geçerli teorik metodu olan yoğunluk fonksiyonel teorisinin yerel yoğunluk yaklaşımı altında spin-orbitsiz ve spin-orbitli (SOC) olarak detaylı bir şekilde incelenmiştir. Böylece bu bileşiklerin elektronik yapıları üzerinde SOC etkisi tespit edilmiştir. Bu etki Ir (veya Pt) içeren bileşiklerde diğer bileşiklere göre az da olsa güçlüdür. Bunun nedeni Ir (veya Pt)'nin Rh'a göre ağır olan kütleleridir çünkü SOC etkisi Z atom numarası olmak üzere Z4 ile doğru orantılıdır. İncelenen bütün bileşiklerde d-elektronları Fermi seviyesi civarında oldukça baskındır bu da onların elektronik yapılarının d-karakterinde olduğuna bir işarettir. Diğer bir işaret ise Cooper çiftlerinin bu elektronlar tarafından oluşturulacağıdır çünkü enerjisi Fermi enerjisine yakın elektronlar momentumun ve enerjinin korunumuna göre bu çiftleri oluşturma potansiyeline sahiplerdir. Elektronik özellikler incelendikten sonra lineer tepki metodu kullanılarak incelenen bileşiklerin fonon spektrumları ve fonon durum yoğunlukları hesaplanmıştır. Yine Ir (veya Pt) içeren bileşiklerde fonon spektrumlarında SOC etkisi daha fazla gözlenmiştir. Bu tezin ana amacı süperiletkenliğin hangi orbitallerden ve de hangi fonon modlarından kaynaklandığını belirlemektir. Bu amaca ulaşmak için tüm bileşikler üzerine elektron-fonon etkileşimi hesaplamaları yapılmıştır. Bu hesaplamalar yapılırken BCS teorisini baz alan Migdal-Eliashberg teorisi kullanılmıştır. Bu teori için gerekli olan elektronik ve fononik sonuçlar ise sırasıyla yoğunluk fonksiyonel teorisi ve lineer tepki metodundan elde edilmiştir. Rh içeren bileşiklerin Eliashberg spektrumunda SOC etkisi yok denecek kadar azdır. Fakat Ir (veya Pt) içeren bileşiklerde bu etki gözlenebilecek mertebededir. Hatta SOC etkisinin dahil edilmesi bu bileşikler için deneyle uyumu iyileştirmektedir. Sonuç olarak, bu tez kapsamında elde edilen sonuçlar, NCS LaPtSi yapıda kristalleşen bu tür bileşiklerin gelecekteki araştırmalara hem deneysel hem de teorik açıdan ilham kaynağı oluşturması beklenmektedir. Bu bulgular, benzer yapıdaki bileşiklerin özelliklerinin daha ayrıntılı bir şekilde anlaşılmasını sağlayarak, bilim dünyasındaki diğer araştırmacıları bu alanda yeni çalışmalara teşvik etmeyi hedeflemektedir.

Although the superconductivity of many compounds crystallizing in the noncentrosymmetric (NCS) LaPtSi structure has been experimentally known since the 1980s, theoretical studies on these materials are notably limited. However, theoretical investigations shed light on the origin of superconductivity in such compounds, as the BCS theory suggests that phonons mediate the formation of Cooper pairs leading to superconductivity. This underscores the importance of studying the electronic and phononic properties of superconducting compounds in detail. Additionally, the electron-phonon interaction characteristics should be thoroughly examined to identify which electronic orbitals and phonon modes facilitate the transition to superconductivity. The computations and simulations in this thesis have been facilitated by the utilization of the open-source software package Quantum Espresso. This powerful computational tool is widely embraced by researchers worldwide and is renowned for its capability to perform electronic structure and phonon calculations for a diverse array of materials. Quantum Espresso operates on the principles of density functional theory, making it an indispensable resource for computational materials science and condensed matter physics. The software harnesses the plane-wave basis set to represent electronic wavefunctions accurately, enabling precise calculations of electronic properties and structural attributes for crystals and nanomaterials, particularly in periodic systems. Additionally, it boasts the capability to leverage high-performance computing clusters (HPC) and supercomputers for large-scale calculations and highly accurate simulations. The computational aspects of this thesis were made achievable through the generous provision of resources by the Uppsala Multidisciplinary Center for Advanced Computational Science (UPPMAX) at Uppsala University in Sweden. Functioning as a central hub for high-performance computing (HPC) resources, UPPMAX offers state-of-the-art computational capabilities to researchers across various fields of study. These sophisticated computational resources have been instrumental in conducting intricate analyses and simulations, serving as a cornerstone for the research endeavors outlined in this study. Building upon these facts, the first step of this thesis involved a detailed investigation of the structural and electronic properties of LaRhP, LaRhAs, LaIrP, LaIrAs, LaIrGe, and LaPtGe compounds crystallizing in the NCS LaPtSi-type structure using the most current theoretical method, the density functional theory (DFT), under local density approximation for both without spin-orbit coupling effect and including spin-orbit-coupling effect (SOC). The results obtained for crystal lattice parameters exhibit excellent agreement with the experimental data in the literature. This provides a significant indication that we are on the right path as we transition to the next step of calculating electronic properties. The electronic structure characteristics were emphasized by combining calculations without SOC obtained from scalar relativistic calculations with SOC included calculations obtained from full relativistic calculations. If present, the impact of spin-orbit interaction was highlighted.Thus, the SOC effect on the electronic structures of these compounds was identified, with Ir (or Pt) containing compounds exhibiting a slightly stronger SOC effect compared to other compounds due to the heavier masses of Ir (or Pt) in proportion to the atomic number Z, where the SOC effect is directly proportional to Z4. In all investigated compounds, d-electrons were found to be dominant around the Fermi level, indicating a d-character in their electronic structures. Another sign is that these electrons are likely to form Cooper pairs since the electrons near the Fermi energy have the potential to create these pairs based on the conservation of momentum and energy. After examining the electronic properties, the phonon spectra and phonon density of states of the studied compounds were calculated using the linear response method. Negative frequencies were not observed in the phonon spectra of all examined compounds, indicating the dynamic stability of all compounds in the LaPtSi crystal structure. Similar to the electronic structure, the phonon spectra of superconductors containing Rh exhibit a relatively weak SOC effect. However, in compounds containing Ir (or Pt), a weak SOC effect has been observed in the phonon spectra. This is, as mentioned above, due to the heavier mass of Ir (or Pt) compared to Rh. The main objective of this thesis is to determine from which orbitals and phonon modes superconductivity originates. To achieve this goal, electron-phonon interaction calculations were performed for all compounds using the Migdal-Eliashberg theory based on the BCS theory. The electronic and phononic results required for this theory were obtained from the density functional theory and linear response method, respectively. The Eliashberg spectrum in compounds containing Rh showed a negligible SOC effect. However, in Ir (or Pt) containing compounds, this effect was observed to a significant extent. In fact, incorporating the SOC effect improves the agreement with experiments for these compounds. Upon comparing the obtained values, it has been determined that the electron-phonon interaction is strongest in LaIrP, resulting in the highest superconducting transition temperature (Tc) of 5,503 K. This value is nearly equal to the experimental value of 5,3 K, demonstrating an excellent agreement that supports the success of the theories utilized in this thesis. In addition to this outstanding match, the calculated Tc values for LaRhP, LaPtGe, and LaIrAs, at 2,476 K, 2,922 K, and 3,123 K respectively, exhibit a satisfactory compatibility with the experimental values of 2,50 K, 3.05 K, and 3.1 K. However, for LaRhAs, no experimental value has been encountered in the literature. We hope that our theoretical study will inspire experimental investigations on this compound. For LaIrGe, the calculated Tc value of 2,182 K is lower than the experimental value of 4,5 K. While excellent agreement is observed for other compounds, the weak match obtained for this compound requires new experimental studies on LaIrGe in our view. The remarkable consistency between theoretical predictions and experimental data, especially for LaIrP, LaRhP, LaPtGe, and LaIrAs, confirms the effectiveness of the theories employed in this thesis. Additionally, the identified differences, particularly for LaIrGe, underscore the necessity for further experimental research on this compound. In summary, the results from this thesis are expected to inspire future studies on materials with the NCS LaPtSi structure. By providing a detailed understanding of these compounds, the results aim to motivate other scientists to explore this field further. This research contributes to our knowledge and encourages researchers to investigate similar materials, encouraging a collaborative pursuit of insights in this type of compounds. The goal is to spark interest and drive further exploration, ultimately leading to advancements in our understanding of these compounds and their potential applications.