Symmetry

Soitinnus: piano.

Manifestation of the pairing symmetry in the vortex core structure in iron-based superconductors

The superconducting gap is a basic character of a superconductor. While the cuprates and conventional phonon-mediated superconductors are characterized by distinct d- and s-wave pairing symmetries with nodal and nodeless gap distributions respectively, the superconducting gap distributions in iron-based superconductors are rather diversified. While nodeless gap distributions have been directly observed in Ba1–xKxFe2As2, BaFe2–xCoxAs2, LiFeAs, KxFe2–ySe2, and FeTe1–xSex, the signatures of a nodal superconducting gap have been reported in LaOFeP, LiFeP, FeSe, KFe2As2, BaFe2–xRuxAs2, and BaFe2(As1–xPx)2. Due to the multiplicity of the Fermi surface in these compounds s± and d pairing states can be both nodeless and nodal. A nontrivial orbital structure of the order parameter, in particular the presence of the gap nodes, leads to effects in which the disorder is much richer in dx2–y2-wave superconductors than in conventional materials. In contrast to the s-wave case, the Anderson theorem does not work, and nonmagnetic impurities exhibit a strong pair-breaking influence. In addition, a finite concentration of disorder produces a nonzero density of quasiparticle states at zero energy, which results in a considerable modification of the thermodynamic and transport properties at low temperatures. The influence of order parameter symmetry on the vortex core structure in iron-based pnictide and chalcogenide superconductors has been investigated in the framework of quasiclassical Eilenberger equations. The main results of the thesis are as follows. The vortex core characteristics, such as, cutoff parameter, ξh, and core size, ξ2, determined as the distance at which density of the vortex supercurrent reaches its maximum, are calculated in wide temperature, impurity scattering rate, and magnetic field ranges. The cutoff parameter, ξh(B; T; Г), determines the form factor of the flux-line lattice, which can be obtained in _SR, NMR, and SANS experiments. A comparison among the applied pairing symmetries is done. In contrast to s-wave systems, in dx2–y2-wave superconductors, ξh/ξc2 always increases with the scattering rate Г. Field dependence of the cutoff parameter affects strongly on the second moment of the magnetic field distributions, resulting in a significant difference with nonlocal London theory. It is found that normalized ξ2/ξc2(B/Bc2) dependence is increasing with pair-breaking impurity scattering (interband scattering for s±-wave and intraband impurity scattering for d-wave superconductors). Here, ξc2 is the Ginzburg-Landau coherence length determined from the upper critical field Bc2 = Φ0/2πξ2 c2, where Φ0 is a flux quantum. Two types of ξ2/ξc2 magnetic field dependences are obtained for s± superconductors. It has a minimum at low temperatures and small impurity scattering transforming in monotonously decreasing function at strong scattering and high temperatures. The second kind of this dependence has been also found for d-wave superconductors at intermediate and high temperatures. In contrast, impurity scattering results in decreasing of ξ2/ξc2(B/Bc2) dependence in s++ superconductors. A reasonable agreement between calculated ξh/ξc2 values and those obtained experimentally in nonstoichiometric BaFe2–xCoxAs2 (μSR) and stoichiometric LiFeAs (SANS) was found. The values of ξh/ξc2 are much less than one in case of the first compound and much more than one for the other compound. This is explained by different influence of two factors: the value of impurity scattering rate and pairing symmetry.

The house that the Court built. The retained powers case law of the European Court of Justice and the constitutional structure of the Union

Euroopan unionin perustamissopimusten katsotaan muodostavan EU:n valtiosäännön, jonka rajat ovat kuitenkin perustamissopimusten määräysten väljän muotoilun sekä Euroopan unionin tuomioistuimen tulkintakäytännön valossa epätarkat. Etenkin kysymys unionin ja sen jäsenvaltioiden välisestä toimivallanjaosta on EU-oikeudellisen tutkimuksen klassikoita. Tarkastelen pro gradu -tutkielmassani unionin valtiosääntörakennetta ja unionioikeuden kokonaisvaikutusta jäsenvaltioiden toimivaltojen käyttöön erityisesti EU-tuomioistuimen ratkaisukäytännössään kehittämän niin kutsutun retained powers -doktriinin valossa. Kyseisen opin mukaan EU-oikeus asettaa vaatimuksia jäsenvaltioiden toimivaltojen käytölle myös niillä aloilla, joilla sääntelytoimivalta on jäänyt jäsenvaltioille eikä sitä ole jaettu unionin kanssa. Aiheen teoreettisen tarkastelun pohjalta analysoin Euroopaun unionin tuomioistuimen ratkaisukäytäntöä erityisesti yhtä säilytetyn toimivallan alaa, koulutusta, koskevissa tapauksissa pyrkien havaitsemaan typologioita tuomioistuimen ratkaisutoiminnassa. Tutkimus noudattaa EU-valtiosääntöoikeuden metodologiaa. Keskeisenä lähdemateriaalina on siten käytetty unionituomioistuimen ratkaisukäytäntöä, joka heijastaa perustamissopimuksia tarkemmin unionin valtiosääntörakennetta. Oikeuskäytännön analyysi ja tulkinta on suoritettu peilaten sitä vasten unionin kehitystä markkinaorientoituneesta organisaatiosta yleismaailmalliseksi poliittiseksi unioniksi. Tutkielmani loppupäätelmä on, että jäsenvaltiot ovat tietyissä rajoissa hyväksyneet unionituomioistuimen kehittämän doktriinin, ja unionituomioistuin on siten saanut aikaan tosiasiallisen muutoksen EU:n valtiosääntörakenteessa. Retained powers -doktriini on omiaan syventämään eurooppalaista integraatiota ja nostaa kysymyksiä toimivallanjaon merkityksestä unionioikeudessa, perustamissopimusten kyvystä heijastaa unionin valtiosääntörakennetta sekä unionituomioistuimen toiminnan poliittisesta luonteesta.

In Search for the European solidarity: The rule of law within the European Union in the framework of constitutional pluralism

The dissertation examines the rule of law within the European Union in the theoretical framework of constitutional pluralism. The leading lines of constitutional pluralism are examined with relation to the traditional and prevailing, monistic and hierarchical conceptions on how to perceive legal orders in Europe. The theoretical part offers also historical perspective by highlighting some of the turning points for the Union constitutional legal order in the framework of European integration. The concept of rule of law is examined in legal terms and its meaning to the Union constitutional constellation as a constitutional principle and a common value is observed. The realization of the rule of law at supranational and national level is explored with a view to discover that recent developments in some of the Member States give rise to concern about the viability of the rule of law within the European Union. It is recognized that the inobservance of the rule of law at national level causes a threat to the supranational constitutional legal order. The relationship between the supranational and national legal orders is significant in this respect and therefore particularly the interaction between the Court of Justice of the European Union (hereinafter the ECJ) and the Member States’ (constitutional/supreme) courts takes focus. It is observed that functioning dialogue between the supranational and national courts based on mutual respect and judicial deference is an important prerequisite for the realization of the rule of law within Europe. In order to afford a concrete example, a recent case C-62/14 Gauweiler v Deutscher Bundestag is introduced and analysed in relation to the notorious relationship between the Federal Constitutional Court of Germany and the ECJ. The implications of the ECJ’s decision in Gauweiler v Deutscher Bundestag is assessed with reference to some of the pressing issues of constitutionalism within Europe and some institutional aspects are also brought forward. Lastly, the feasibility of constitutional pluralism as a theoretical setting is measured against the legal reality of today’s Europe and its many constitutions. The hierarchical idea of one ultimate source of power, stemming from the traditional approaches to legal systems, is then assessed with relation to the requirement of the realization of the rule of law within the European Union from the supranational and national point of view.