Theoretical Study of Magnetoelectric Effects in Noncentrosymmetric and Cuprate Superconductors

Abstract

A century after the discovery of superconductivity at the lab of Kamerlingh Onnes in 1911, it is noticeable that the phenomenon is quite ubiquitous in nature. In addi- tion to a long list of superconducting alloys and compounds, almost half the elements in the periodic table superconduct. By the late seventies, superconductivity was thought to be well understood. This turned out to be a myth, with the discovery of unconventional superconductors that defied Bardeen-Cooper-Schrieffer (BCS) theory. Cuprates have been the most prominent example among them ever since their discov- ery in 1986 by Bednorz and M ̈uller. Another example of non-compliance with BCS theory lie among noncentrosymmetric superconductors. In this dissertation, mag- netoelectric (ME) effects in these two classes of superconductors have been studied from different perspectives, utilizing Ginzburg-Landau (GL) theory. Even though GL theory was proposed before the BCS theory, it was not given much importance due to its phenomenological nature until Gor’kov proved that it is a limiting form of the microscopic BCS theory. However today, in the absence of any complete microscopic theory to explain superconductivity in unconventional superconductors, Ginzburg- Landau theory is an important tool to move ahead and qualitatively understand the behavior of varied superconducting systems. Noncentrosymmetric superconductors have generated much theoretical interest since 2004 despite been known for long. The absence of inversion symmetry in non- centrosymmetric superconductors allows for extra terms called Lifshitz invariants in the Ginzburg-Landau functional. This leads to magnetoelectric effects that do not exist in centrosymmetric superconductors. One manifestation of this is in the vortex structure in materials with a cubic point group O. In particular, a current is pre- dicted to flow parallel to the applied magnetic field in such a vortex in addition to the usual vortex supercurrents. In this work, we present both analytical and numerical solutions of the Ginzburg-Landau equations that reveal the spatial structure of this current as well as the associated component of the magnetic field for both a single vortex and in the vortex lattice phase near the upper critical field. The discovery of superconductivity in lanthanum barium copper oxide (LBCO) in 1986, was followed by yttrium barium copper oxide (YBCO) in 1987, commenc- ing the era of high temperature superconductivity. The astonishingly rich phase diagram of cuprates includes the pseudogap phase which was earlier thought to be a precursor to superconductivity. Now signatures of broken symmetries have been seen, indicating a true phase transition. Pair density wave (PDW) order has earlier been proposed to account for superconducting correlations and charge density wave (CDW) order in pseudogap phase. There is evidence that the pseudogap phase in the cuprates also breaks time-reversal symmetry. Here we show that pair density wave (PDW) states give rise to a translational invariant nonsuperconducting order param- eter that breaks time-reversal and parity symmetries, but preserves their product. This secondary order parameter has a different origin, but shares the same symme- try properties as a magnetoelectric loop current order that has been proposed earlier in the context of the cuprates to explain the appearance of intracell magnetic or- der. We further show that, due to fluctuations, this secondary loop current order, which breaks only discrete symmetries, can preempt PDW order, which breaks bothcontinuous and discrete symmetries. In such a phase, the emergent loop current or- der coexists with spatial short-range superconducting order and possibly short-range charge density wave (CDW) order. Finally, we propose a PDW phase that accounts for intracell magnetic order and the polar Kerr effect, has CDW order consistent with x-ray scattering and nuclear magnetic resonance observations, and quasiparticle (QP) properties consistent with angle-resolved photoemission spectroscopy. Our work, con- sistently accommodates all observations of broken symmetries in pseudogap phase in a single theory.