Nuclear magnetic resonance studies of local magnetic, electronic, and dynamic properties in filled single wall carbon nanotubes

In this dissertation, the local magnetic and electronic properties of SWNTs are investigated. Also, one dimensional (1-D) dynamics of C60 fullerenes encapsulated in SWNTs is investigated using Nuclear Magnetic Resonance (NMR) spectroscopy. In order to remove ferromagnetic catalyst particles present in SWNT samples, which interfere with NMR measurements, we have developed a novel magnetic purification method by which 99% of the ferromagnetic particles are removed. With this new method, we could obtain a well-resolved NMR signal with FWHM of ∼20 ppm from natural carbon based SWNTs. Using 25% 13C enriched C60 encapsulated in the magnetically purified SWNTs as an NMR probe, the local magnetic properties of the 1-D inner space of SWNTs are studied. Surprisingly, SWNTs are found to screen the applied magnetic field by tens of ppm. More interestingly, the diamagnetic shielding is found to be tunable by controlling defects or doping. While defects create paramagnetic currents to destroy the diamagnetic shielding, doping enhances the shielding by increase aromaticity in SWNTs to have stronger diamagnetic ring currents. Encapsulated fullerenes in SWNTs show unique dynamics which is related to 1-D geometry. They are found to undergo dynamics transition from free rotation to hindered rotation at ∼100 K, which is lower than that in 3-D bulk fullerenes by as much as ∼160 K. This huge reduction results from the decrease of Van der Waals interaction and the Coulomb interaction between an electron-rich bond and an electron-poor center of a pentagon or a hexagon. DWNTs were made by high temperature annealing of enriched peapods. The isotropic chemical shift of inner nanotubes was found to have shifted diamagnetically by 26.62 ppm due to the magnetic shielding by outer nanotubes. 75% of the inner nanotubes were proven to be metallic due to a strong interaction between inner and outer nanotubes

Realization and ground state properties of topological superconductors in one dimension

Topological superconductors with and without time-reversal symmetry are new phases of matters which host Majorana zero modes at their ends. The possibility of realizing such phases in various kinds of materials that are experimentally accessible, in addition to their unique signatures in simple transport measurements, has brought significant amount of attention from both theorists and experimentalists in condensed matter physics. In this thesis, we extend the previous studies on the realization of topological superconductors and try to answer some of the open questions regarding their transport signatures. First, we study extensions of the realization scheme based on semiconducting nanowires proximity coupled to $s-$wave superconductors \cite{Lutchyn10, Oreg10} by replacing the s-wave superconductor with high temperature superconductors. We show that significant amount of induced superconducting gap in a nanowire can be achieve for a special interface geometry. The existence of gapless nodal excitations in the cuprate superconductors lead to a finite lifetime of Majorana zero modes when they are coupled to fermionic bath. We also consider the topological superconductivity in the Yu-Shiba-Rusinov states in chains of magnetic atoms at the surface of two dimensional $s-$wave superconductors with strong spin-orbit coupling. We study the generalization of the single Shiba state problem into a multiple Shiba states problem in the presence of spin-orbit coupling. We show that spin-orbit coupling induces the mixing of Shiba states correspond to different angular momentum channels and leads to interesting effects such as angular dependence of Shiba spectrum on the direction of magnetic moment. Based on these newly discovered effects, we propose new experimental methods to analyze and tune the physical parameters of the magnetic atom chains which can be applied to the ongoing experiments \cite{nadj2014, pawlak15, Ruby15}. Using the formalism developed for a single impurity, we study the magnetic atom chains with multiple Shiba state bands and present the topological phase diagram.Next, we study the transport signatures of time-reversal invariant topological superconductors which support Kramers pair of Majorana modes. Especially, we explore the effects of interactions on the transport signatures in tunnel junctions involving Majorana Kramers pairs by considering two types of junction geometries. We first consider a junction between Majorana Kramers pair and Luttinger liquid. Using renormalization group (RG) analysis, we study the boundary conditions of the infrared fixed points where system flows to as a function of interaction strength. In the presence of weak repulsive interactions in the Luttinger liquid, two channel Andreev reflection is stable in contrast to the junction between an interacting lead and a conventional $s-$wave superconductor. Second, we study the ground state properties of Majorana Kramers pair-quantum dot-normal lead junction using weak coupling RG and slave-boson mean-field theory. We find that the Kodno interaction between the lead electrons and the quantum dot and the Majorana-quantum dot interaction compete each other. We find a new strong coupling fixed point characterized by strong correlation between impurity spin and Majorana Kramers pair, and we study its signatures in differential tunneling conductance

Ground states of a two-dimensional frustrated quantum antiferromagent Cs₂CuCl₄

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2008.Includes bibliographical references (leaf 43).The properties of a frustrated quantum antiferromagnet are interesting topics in condensed matter theory. Among the quantum antiferromagnets, Cs₂CuCl₄ gains attention as one of the candidates for materials with ground state spin liquid phase. The recent experimental results show that there exist several ground state phases in the presence of magnetic field which cannot be explained with classical Hamiltonian. In the thesis, I numerically studied the ground state of Cs₂CuCl₄ using a modified classical Hamiltonian, and I compared the result with previous experiments and classical analysis. The resulted magnetic phase diagram contains two phases, cone and ferromagnetic phase, which are separated by second order transition and a first order transition line for intermediate longitudinal field which ends up with a critical point.by Younghyun Kim.S.B

Signatures of Majorana Kramers pairs in superconductor-Luttinger liquid and superconductor-quantum dot-normal lead junctions

Time-reversal invariant topological superconductors are characterized by the presence of Majorana Kramers pairs localized at defects. One of the transport signatures of Majorana Kramers pairs is the quantized differential conductance of $4e^2/h$ when such a one-dimensional superconductor is coupled to a normal-metal lead. The resonant Andreev reflection, responsible for this phenomenon, can be understood as the boundary condition change for lead electrons at low energies. In this paper, we study the stability of the Andreev reflection fixed point with respect to electron-electron interactions in the Luttinger liquid. We first calculate the phase diagram for the Luttinger liquid-Majorana Kramers pair junction and show that its low-energy properties are determined by Andreev reflection scattering processes in the spin-triplet channel, i.e. the corresponding Andreev boundary conditions are similar to that in a spin-triplet superconductor - normal lead junction. We also study here a quantum dot coupled to a normal lead and a Majorana Kramers pair and investigate the effect of local repulsive interactions leading to an interplay between Kondo and Majorana correlations. Using a combination of renormalization group analysis and slave-boson mean-field theory, we show that the system flows to a new fixed point which is controlled by the Majorana interaction rather than the Kondo coupling. This Majorana fixed point is characterized by correlations between the localized spin and the fermion parity of each spin sector of the topological superconductor. We investigate the stability of the Majorana phase with respect to Gaussian fluctuations.Comment: 26 pages, 8 figure

Hydra: Multi-head Low-rank Adaptation for Parameter Efficient Fine-tuning

The recent surge in large-scale foundation models has spurred the development of efficient methods for adapting these models to various downstream tasks. Low-rank adaptation methods, such as LoRA, have gained significant attention due to their outstanding parameter efficiency and no additional inference latency. This paper investigates a more general form of adapter module based on the analysis that parallel and sequential adaptation branches learn novel and general features during fine-tuning, respectively. The proposed method, named Hydra, due to its multi-head computational branches, combines parallel and sequential branch to integrate capabilities, which is more expressive than existing single branch methods and enables the exploration of a broader range of optimal points in the fine-tuning process. In addition, the proposed adaptation method explicitly leverages the pre-trained weights by performing a linear combination of the pre-trained features. It allows the learned features to have better generalization performance across diverse downstream tasks. Furthermore, we perform a comprehensive analysis of the characteristics of each adaptation branch with empirical evidence. Through an extensive range of experiments, encompassing comparisons and ablation studies, we substantiate the efficiency and demonstrate the superior performance of Hydra. This comprehensive evaluation underscores the potential impact and effectiveness of Hydra in a variety of applications. Our code is available on \url{https://github.com/extremebird/Hydra