Date of Award

August 2015

Degree Type


Degree Name

Doctor of Philosophy



First Advisor

Daniel F. Agterberg

Committee Members

Bimal K. Sarma, Dilano K. Saldin, Michael T. Weinert, Prasenjit Guptasarma


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.