Anapole superconductivity from PT-symmetric mixed-parity interband pairing

Recently, superconductivity with spontaneous time-reversal or parity symmetry breaking is attracting much attention owing to its exotic properties, such as nontrivial topology and nonreciprocal transport. Particularly fascinating phenomena are expected when the time-reversal and parity symmetry are simultaneously broken. This work shows that time-reversal symmetry-breaking mixed-parity superconducting states generally exhibit an unusual asymmetric Bogoliubov spectrum due to nonunitary interband pairing. For generic two-band models, we derive the necessary conditions for the asymmetric Bogoliubov spectrum. We also demonstrate that the asymmetric Bogoliubov quasiparticles lead to the effective anapole moment of the superconducting state, which stabilizes a nonuniform Fulde-Ferrell-Larkin-Ovchinnikov state at zero magnetic fields. The concept of anapole order employed in nuclear physics, magnetic materials science, strongly correlated electron systems, and optoelectronics is extended to superconductors by this work. Our conclusions are relevant for any multiband superconductors with competing even- and odd-parity pairing channels. Especially, we discuss the superconductivity in UTe₂

Quantum-geometry-induced anapole superconductivity

Anapole superconductivity recently proposed for multiband superconductors [\href{https://www.nature.com/articles/s42005-022-00804-7}{Commun. Phys. $\bm 5$, 39\ (2022)}] is a key feature of time-reversal ($\mathcal{T}$)-symmetry-broken polar superconductors. The anapole moment was shown to arise from the asymmetric Bogoliubov spectrum, which induces a finite center of mass momenta of Cooper pairs at the zero magnetic field. In this paper, we show an alternative mechanism of anapole superconductivity: the quantum geometry induces the anapole moment when the interband pairing and Berry connection are finite. Thus, the anapole superconductivity is a ubiquitous feature of $\mathcal{T}$-broken multiband polar superconductors. Applying the theory to a minimal model of UTe$_2$, we demonstrate the quantum-geometry-induced anapole superconductivity. Furthermore, we show the Bogoliubov Fermi surfaces (BFS) in an anapole superconducting state and predict an unusual temperature dependence of BFS due to the quantum geometry. Experimental verification of these phenomena may clarify the superconducting state in UTe$_2$ and reveal the ubiquitous importance of quantum geometry in exotic superconductors.Comment: 13 pages, 6 figure

Piezoelectric effect and diode effect in anapole and monopole superconductors

Superconductors lacking both inversion symmetry and time-reversal symmetry have been attracting much attention as a platform for exotic superconducting phases and anomalous phenomena, including the superconducting diode effect. Recent studies revealed intrinsic phases with this symmetry, named anapole superconductivity and monopole superconductivity, which are $PT$-symmetric superconducting states with and without Cooper pairs' total momentum, respectively. To explore characteristic phenomena in these states, we calculate and predict the superconducting piezoelectric effect and superconducting diode effect. A close relationship with the finite-$q$ pairing, asymmetric Bogoliubov spectrum, and quantum geometry is discussed. This study reveals the piezoelectric and diode effects as potential probes to elucidate exotic superconducting phases.Comment: 13 pages, 16 figure

Ovarian strumal carcinoid: a case report

Background: Carcinoid tumors of the ovary are rare tumors, histopathologically classified as monodermal teratomas and somatic-type tumors arising from dermoid cysts. Their malignancy varies from borderline to malignant. Carcinoid tumors can occur in young and elderly women, and are sometimes seen in mature teratoma, struma ovarii, or mucinous cystadenoma as a nodule or tumor. Strumal carcinoid and mucinous carcinoid present as special types of carcinoid tumors of the ovary. Case report: This report describes a 56-year-old woman who presented with a large pelvic mass on abdominal ultrasonography during a medical examination. The diameter of the pelvic tumor was approximately 11 cm and was suspected to be ovarian cancer. The values of CA125 and CEA were above their reference intervals on preoperative examination. Abdominal total hysterectomy and bilateral salpingo-oophorectomy were performed. Intraoperative frozen-section histopathology suggested a diagnosis of mucinous adenocarcinoma; therefore, partial omentectomy and pelvic lymphadenectomy were also performed. Permanent-section histopathology led to a final diagnosis of strumal carcinoid of the ovary, stage IA (FIGO 2014). Six years post-operation, the patient had no sign of recurrence

Assessment of Fetal Autonomic Nervous System Activity by Fetal Magnetocardiography: Comparison of Normal Pregnancy and Intrauterine Growth Restriction

Objective. To clarify the developmental activity of the autonomic nervous system (ANS) of the normal fetus and intrauterine growth restriction (IUGR) cases using fetal magnetocardiography (FMCG). Subjects and Methods. Normal pregnancy (n = 35) and IUGR (n = 12) cases at 28–39 and 32–37 weeks of gestation, respectively, were included in this study. The R-R interval variability was used to calculate the coefficient of variance (CVRR) and low frequency/high frequency (LF/HF) ratio. Results. The value of CVRR in the normal pregnancy group displayed a slight increasing trend with gestational age. However, no such trend was observed in the IUGR group. In contrast, the LF/HF ratio in both the normal pregnancy group and the IUGR group clearly increased over the gestational period; the normal group showing statistical significance. Conclusion. The development of fetal ANS activity in IUGR cases might differ from that observed in the normal pregnancy group, and this may facilitate early detection of IUGR