京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18058号 / 理博第3936号 / 新制||理||1567(附属図書館) / 30916 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 池田 隆介, 教授 川上 則雄, 教授 石田 憲二 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18060号 / 理博第3938号 / 新制||理||1567(附属図書館) / 30918 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 石田 憲二, 教授 前野 悦輝, 教授 松田 祐司 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18098号 / 理博第3976号 / 新制||理||1573(附属図書館) / 30956 / 京都大学大学院理学研究科化学専攻 / (主査)教授 吉村 一良, 教授 北川 宏, 教授 寺西 利治 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

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In multiband superconductors, different bands at the Fermi surface contribute to the superconductivity with different magnitudes of superconducting gaps on different portions of the Fermi surface. Each band in a multiband superconductor has a condensate with an amplitude and phase that weakly interacts with the other bands’ condensate. The coupling strength between the bands determines whether one or two superconducting transition temperatures are observed, and it is the key to many peculiar properties. In general, if there are two gaps of different magnitude, there are two different length scales associated with the suppression of these gaps in applied magnetic fields, for example. Therefore, effects of multigap superconductivity can be observed in superconducting vortices, which are twirls of supercurrents that are generated when a superconductor is placed in a magnetic field. Furthermore, the two superconducting order parameters in different bands are characterized by a magnitude and phase. In multiband superconductors, there are collective excitations corresponding to fluctuations of the relative phase of two order parameters, so-called the Leggett mode. The first material identified as multiband superconductor is Magnesium Diboride (MgB2) in 2001 with a critical temperature Tc of 39 K. MgB2 is a superconducting material with the highest transition temperature among all conventional BCS superconductors. It has two superconducting gaps \Delta_\pi ~ 2 meV and \Delta_\sigma\ ~ 7 meV and they arise from the existence of two bands \pi and \sigma bands of boron electrons. The discovery of superconductivity in MgB2 renewed interest in the field of multiband superconductivity. MgB2 has attracted many scientists’ attention both for the fundamental importance of understanding the multiband superconductivity and possible applications such as magnets, power cables, bolometers, Josephson junction-based electronic devices, and radio-frequency cavities. Afterward, other materials have been identified as multiband superconductors such as NbSe2, the family of iron-based superconductors, heavy fermion superconductors, multilayer cuprates, borocarbides, etc. This dissertation uses tunneling experiments to highlight multiband superconductivity features in two systems, namely MgB2 thin films and ultrathin films of Pb. Further, we use multiple techniques to study a superconducting material, nitrogen-doped niobium, used for superconducting radio-frequency cavities. For the project on MgB2, MgB2/Native-Oxide/Ag planar junctions are fabricated and characterized down to 2.1 K and in the magnetic field parallel to the sample surface up to 6 Tesla. This work investigates how pairbreaking affects the magnitude and phase of the order parameter in a multiband superconductor. The tunneling spectra are analyzed in the framework of a two-band model developed by our theory collaborator Prof. Alex Gurevich, Old Dominion University. The model allows the extraction of the pair-breaking parameters among other quantities. The analysis shows that the order parameter in the ? band is quickly suppressed in the field, the ? band is cleaner than the ? band. The ratio of pairbreaking parameter in the ? band to the ? band rapidly increases at fields higher than ~0.1 T and then plateau at higher fields. This transition around 0.1 T magnetic field suggests a phase decoupling in the two bands of MgB2. Below the transition, the two bands are phase-locked, so mostly, the superconductivity in the ? band is affected, and after phase decoupling, both bands are affected by the applied field. These results are important for a basic understanding of multiband superconductors and the application implications of this material. This phase decoupling has a new and profound consequence on the superconducting state of a multiband superconductor that has been theoretically predicted and never observed experimentally. For the Pb project, ultrathin films of Pb in ultrahigh vacuum conditions are deposited by e-beam evaporation and characterized with low-temperature scanning tunneling microscopy and spectroscopy (STM/STS). The STM/STS allows measuring the electronic density of states with the highest spatial resolution down to atomic scale. The shape of a superconducting vortex core is determined by the superconducting gap and the Fermi velocity, and the STM allows to map anisotropies of these quantities spatially. The vortex cores of Pb film show a complex shape that evolves from triangular at short distances from the center to a six-fold symmetric star shape farther away from the center. These details are very subtle, and they can be highlighted only if one works within the clean limit (to avoid the averaging effect of the scattering) and by fabricating the heterostructure that pins the vortices spatially. The complex vortex core shape reflects the anisotropy of the two bands that contribute to superconductivity in this material. For the project on Niobium, cold and hot spots from nitrogen-doped Nb cutouts are characterized by low temperature scanning tunneling microscopy and spectroscopy (STM/STS) combined with X-ray photoelectron spectroscopy (XPS) and scanning electron microscopy (SEM). The radiofrequency (RF) measurements of the quality factor and temperature mapping on an N-doped Nb superconducting resonator cavity are carried out at Jefferson Laboratory before cutting out the samples. This work aims to identify possible sources of excess dissipation in hot spots and relate them to the surface chemical composition and superconducting properties. The temperature mapping revealed a strong effect of the cavity cooldown rate on the intensities of hot spots and their spatial distribution, which indicates a significant contribution of trapped vortices to the RF dissipation. SEM images acquired on the cold and hot spots using a secondary electron detector show absence of residual hydride scars and niobium nitrides on their surface. Angle-resolved XPS measurements on the native surface of these samples revealed higher oxidized Nb 3d states on the N-doped Nb cold spots, which is supported by XPS depth profiles done on the samples by Argon ion sputtering. Argon ion sputtering of oxidized Nb removes oxygen preferentially from Nb2O5 and diffuses to bulk, thickening the lower oxidation state layers. The proximity theory framework’s tunneling spectra analysis suggests hot spots have stronger pairbreaking due to a weakly reduced pair potential, a thicker metallic suboxide layer, and a wide distribution of the contact resistance. STM imaging of vortex cores shows a triangular vortex lattice in both samples, and the coherence length is nearly the same in hot and cold spots. The experimental data analysis suggests weakly degraded superconducting properties at the surface of hot spot regions are not the primary sources of RF losses. Instead, they are the regions where vortices nucleate first and get trapped during cooling down. These experimental techniques and findings will be crucial in helping to qualify new recipes for SRF cavity production and to boost their performance. / Physics

This thesis presents a brief synopsis of the derivations of the BCS and Eliashberg equations. An analytic formula for the critical temperature $T_c$ in Eliashberg theory is derived, which contains a sum of iterative integral corrections. These iterative integral corrections are the result of an iterative expression for the gap quotient $\Delta(\iw, T)/\Delta(0,T)$, which is derived. At the critical temperature this expression contains no reference to the critical temperature itself due to the gap approaching zero in this limit, $\lim_{T \rightarrow T_c} \Delta(\iw, T) = 0$. This enables explicit calculation of the critical temperature through the aforementioned iterative expression.\\ \\The behaviour of the iterative expression and its corrections are explored numerically with a toy spectral function $\sF$. Through these numerical experiments, this formula is found to be consistent with, though not equal to the successful McMillan formula for the coupling parameter $\lambda$ in the range $0.3 \leq \lambda \leq 1.5$. Below this value, the McMillan formula is found to approach zero critical temperature $T_c$ more rapidly, raising the future question of which of the two expressions is most successful in predicting the critical temperature $T_c$ in this range. \\ \\ For a toy spectral function with a single mode, the zeroth order correction of the iterative expression for the critical temperature $T_c$ is found to be adequate for most practical purposes due to the magnitude of measurement errors in real life measurements of model parameters. / Detta examensarbete går igenom en kort derivation av BCS och Eliashberg ekvationerna. En analytisk formel för den kritiska temperaturen $T_c$ i Eliashbergteori ges. Denna formel innehåller en summa av iterativa integraler som resulterar från ett uttryckt för energigapets kvot. Vid den kritiska temperaturen så kan man explicit lösa ut denna och på så sätt få ett analytiskt uttryck. Den uttrycket för den kritiska temperaturen utforskas numeriskt med en leksaks-spektralfunktion. Genom dessa numeriska experiment visas det hur det iterativa uttrycket sammanstämmer med McMillans formel för kopplingsparametern $0.3 < \lambda < 1.5$, även om dem ej är lika. Under detta intervall så närmar sig McMillans uttryck noll snabbare, vilket höjer frågan vilken utav dem två uttrycken som fungerar bäst i denna gräns.  För en leksaks-spektralfunktion med ett läge så räcker den nollte korrektionen i det iterativa uttrycket för att få godtagbara resultat, med bakgrund av dem relativt stora mätfelen för riktiga parametrar.

Granular superconductivity at high temperatures in graphite can emerge at certain two-dimensional (2D) stacking faults (SFs) between regions with twisted (around the c-axis) or untwisted crystalline regions with Bernal (ABA…) and/or rhombohedral (ABCABCA…) stacking order. One way to observe experimentally such 2D superconductivity is to measure the frozen magnetic flux produced by a permanent current loop that remains after removing an external magnetic field applied normal to the SFs. Magnetic force microscopy was used to localize and characterize such a permanent current path found in one natural graphite sample out of ∼50 measured graphite samples of different origins. The position of the current path drifts with time and roughly follows a logarithmic time dependence similar to the one for flux creep in type II superconductors. We demonstrate that a ≃10 nm deep scratch on the sample surface at the position of the current path causes a change in its location. A further scratch was enough to irreversibly destroy the remanent state of the sample at room temperature. Our studies clarify some of the reasons for the difficulties of finding a trapped flux in a remanent state at room temperature in graphite samples with SFs.

In this thesis, we study the unconventional superconductivity in Sr2RuO4 (SRO) and related systems. The superconducting state in SRO remains a puzzle after more than 28 years of study. Early experiments had pointed toward a topological non-trivial time-reversal symmetry breaking (TRSB) chiral p-wave order. This pairing candidate has attracted a large amount of attention, partly in relation to the possibility of topological quantum computation, and has stimulated studies on higher chirality superconducting systems. In the first part of this thesis, we study the spontaneous edge current in chiral d- and f-wave superconductors. We show that these currents, which vanish in the continuum limit at zero temperature, are generally non-vanishing but tiny, compared to the simplest chiral p-wave case. In the presence of strong surface roughness, the direction of the edge current in the chiral d-wave case can be reversed, compared with that of a specular ideal surface with specular scattering. However, it is shown that this current reversal is non-universal beyond the continuum limit. The chiral p-wave scenario in SRO is overturned by recent Knight shift measurements, highlighting the importance of exploring different pairing symmetries for SRO. Recently, $d_{x^2-y^2} \pm ig_{(x^2-y^2)xy}$, $s' \pm id_{xy}$ and mixed helical p-wave pairings have been proposed as order parameter candidates. However, the stability of these states, especially of the $d_{x^2-y^2} \pm ig$ pairing, remains unclear. In the second part of the thesis, we study the leading superconducting instabilities in SRO in the presence of sizable atomic spin-orbit coupling (SOC), non-local SOC, and non-local interactions. We find that it is difficult to stabilize chiral p-wave pairing in SRO models; this is because, among the triplet p-wave states, the atomic SOC favors helical states over the chiral state. The presence of both d- and g-wave pairings, including a $d_{x^2-y^2} \pm ig$ state, is found when the second nearest neighbor (in-plane) repulsions, together with orbital-anisotropy of the non-local interactions and/or the B2g channel non-local SOC are included. We further analyze the properties, such as nodal structures, in-plane field spin-susceptibility, and spontaneous edge current, of the realized $d_{x^2-y^2} \pm ig$ pairing and find that this state is more compatible with existing experimental measurements than the $s' \pm id_{xy}$ and the mixed helical p-wave proposals. / Dissertation / Doctor of Philosophy (PhD)

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24176号 / 理博第4867号 / 新制||理||1696(附属図書館) / 京都大学大学院理学研究科化学専攻 / (主査)准教授 倉重 佑輝, 教授 谷村 吉隆, 教授 吉村 一良 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM