Cooper instability associated with superconductivity in the two-dimensional semi-Dirac semimetals is attentively studied in the presence of attractive Cooper-pairing interaction, which is the projection of an attractive fermion-fermion interaction. Performing the standard renormalization group analysis shows that the Cooper theorem is violated at zero chemical potential but instead Cooper instability can be generated only if the absolute strength of fermion-fermion coupling exceeds certain critical value and transfer momentum is restricted to a confined region, which is determined by the initial conditions. Rather, the Cooper theorem would be instantly restored once a finite chemical potential is introduced and thus a chemical potential-tuned phase transition is expected. Additionally, we briefly examine the effects of impurity scatterings on the Cooper instability at zero chemical potential, which in principle are harmful to Cooper instability although they can enhance the density of states of systems. Furthermore, the influence of competition between a finite chemical potential and impurities upon the Cooper instability is also simply investigated. These results are expected to provide instructive clues for exploring unconventional superconductors in the kinds of semimetals.
The interplay of nontrivial topology and superconductivity in condensed matter physics gives rise to exotic phenomena. However, materials are extremely rare where it is possible to explore the full details of the superconducting pairing. Here, we investigate the momentum dependence of the superconducting gap distribution in a novel Dirac material PdTe. Using high resolution, low temperature photoemission spectroscopy, we establish it as a spin-orbit coupled Dirac semimetal with the topological Fermi arc crossing the Fermi level on the (010) surface. This spin-textured surface state exhibits a …
The behavior of three-dimensional (3D) semimetals under strong magnetic fields is a topic of recurring interest in condensed matter physics. Recently, the advent of Weyl and Dirac semimetals has brought about an interesting platform for potentially uncovering phases of matter that combine nontrivial band topology and interactions. While electronic instabilities of such semimetals at strong magnetic fields have been explored theoretically and experimentally, the role of electron-phonon interactions therein has been largely neglected. In this paper, we study the interplay of electron-electron an…
Superconductivity from Coulomb repulsion in three-dimensional quadratic band touching Luttinger semimetals
研究了具有二次带接触和强自旋轨道耦合的三维Luttinger半金属中屏蔽库仑排斥驱动的超导电性。在这些半金属中，库珀对是由自旋为3/2的费米子与非平凡波函数形成的。通过数值求解线性Eliashberg方程，得到了单重态s波带隙函数的临界温度与掺杂的关系，并考虑了自旋轨道修正和自能修正.为了理解超导的基本机制，我们计算了临界温度对介电函数$ε(iΩ_n,q)$变化的敏感性。我们将我们的结果与等离子体激元和Kohn-Luttinger机制。最后，我们讨论了我们的方法的有效性，并将我们的结果与文献进行比较。我们发现很好的协议与一些铋基半Heuslers，如YPtBi，并推测在铱酸盐Pr 2 Ir 2 O 7的超导性。
Resilient $j$=3/2 superconductivity in topological semimetal YPtBi
University of Maryland, College Park（马里兰大学帕克分校）；Missouri University of Science and Technology（密苏里科技大学）；National High Magnetic Field Laboratory（国家高磁场实验室）
We study superconductivity in a three-dimensional zero-density Dirac semimetal in proximity to a ferroelectric quantum critical point. We find that the interplay of criticality, inversion-symmetry breaking, and Dirac dispersion gives rise to a robust superconducting state at the charge-neutrality point, where no Fermi surface is present. Using Eliashberg theory, we show that the ferroelectric quantum critical point is unstable against the formation of a ferroelectric density wave (FDW), whose fluctuations, in turn, lead to a first-order superconducting transition. Surprisingly, long-range supe…
Electrons with large kinetic energy have a superconducting instability for infinitesimal attractive interactions. Quenching the kinetic energy and creating a flat band renders an infinitesimal repulsive interaction the relevant perturbation. Thus, flat band systems are an ideal platform to study the competition of superconductivity and magnetism and their possible coexistence. Recent advances in the field of twisted bilayer graphene highlight this in the context of two-dimensional materials. Two dimensions, however, put severe restrictions on the stability of the low-temperature phases due to …
We study numerically, in the framework of the Cooper approach from 1956, mechanisms of pair formation in a model of La-based cuprate superconductors with longer-ranged hopping parameters reported in the literature at different values of center of mass momentum. An efficient numerical method allows to study lattices with more than a million sites. We consider the cases of attractive Hubbard and d-wave type interactions and a repulsive Coulomb interaction. The approach based on a frozen Fermi sea leads to a complex structure of accessible relative momentum states which is very sensitive to the t…
Novel attractive pairing interaction in strongly correlated superconductors
传统和非传统的超导性，分别产生于吸引（电子-声子）和排斥（多体库仑）相互作用与固定符号和符号反转配对对称性。虽然重费米子、铜酸盐和磷属元素化物被广泛认为是非传统的超导体，但最近在一种重费米子超导体（CeCu $_2$ Si $_2$）中的证据表明，除了电子-声子耦合之外，还存在一种新的传统类型的配对对称性。提出了强关联混合价化合物中电子间吸引势的一种新的机制，即由玻色子场（真空或holon）介导的吸引势。在强耦合极限下，定域电子位不受双占据的影响，从而产生出一个新的holon规范场。然而，holon态可以通过价涨落通道吸引传导电子，由此产生的具有局域电子和传导电子的双占据态凝聚为具有现场固定符号的$s$波配对对称性的库珀对。我们发展了相应的超导自洽理论，并与实验结果进行了比较。我们的理论提供了一种新的超导机制，其适用性扩展到更广泛的金属间化合物/混合价材料和其他平带金属。
We examine the existence and characteristics of the exotic Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase in a one-dimensional Fermi gas with attractive Hubbard interactions, in the presence of spin-orbit coupling (SOC) and Zeeman field. We show that a robust FFLO phase can be created in the presence of attractive on-site interactions and Zeeman field, and that the addition of SOC suppresses the FFLO order and enhances the pair formation. In absence of SOC, the system shows four phases: Bardeen-Cooper-Schrieffer (BCS), FFLO, multi- mode pairing and fully polarized phases by tuning the Zeeman fie…
We determine the fate of interacting fermions described by the Hamiltonian $H=\textbf{p}\cdot \textbf{J}$ in three-dimensional topological semimetals with linear band crossing, where $\textbf{p}$ is momentum and $\textbf{J}$ are the spin-$j$ matrices for half-integer pseudospin $j\geq 3/2$. While weak short-range interactions are irrelevant at the crossing point due to the vanishing density of states, weak long-range Coulomb interactions lead to a renormalization of the band structure. Using a self-consistent perturbative renormalization group approach, we show that band crossings of the type …
