The nontrivial ground state topology in the coexistence phase of chiral d-wave superconductivity and 120 degrees magnetic order on a triangular lattice
Valery V. Val'kov, Anton O. Zlotnikov, Maxim S. Shustin
备注：
6 pages, 4 figures, prepaired after the report on the Moscow International Symposium on Magnetism 2017, submitted to Journal of Magnetism and Magnetic Materials
The Z2 topological invariant is defined in the chiral d-wave superconductor having a triangular lattice in the presence of the 120 degrees magnetic ordering. By analyzing the Z2 invariant, we determine the conditions of implementing nontrivial phases in the model with regard to superconducting pairings between nearest and next nearest neighbors. It is often supposed in such system that the pairing parameter between nearest neighbors should be equal to zero due to influence of the intersite Coulomb interaction. We show that taking into account even weak pairings in the first coordination sphere leads to the disappearance of the gapless excitations of the bulk spectrum in the wide region of the parameter space. Thus topological invariants can be defined in such region. Solving the problem of open edges it is shown that the zero energy modes are realized basically in the topologically nontrivial phases. Such zero modes are topologically protected Majorana modes. A connection between the Z2 invariant calculated at the symmetric points of the Brillouin zone with respect to the electron-hole symmetry and the integer topological invariant of the ground state of the 2D lattice expressed in terms of the Green functions is established in the presence of noncollinear magnetic ordering.
We show that the quantum charge and spin fluctuations, while sufficiently renormalizing the magnetic order parameter, do not destroy the coexistence phase of chiral d+id superconductivity and 120-degree spin ordering in a strongly correlated 2D system with a triangular lattice. The nontrivial topology characterized by the topological invariant N3 is also preserved. It is shown that the Majorana mode exist among edge states in the topologically nontrivial phase. The spatial structure of such mode is determined. The spin and charge fluctuations shift the critical values of electron density at wh…
We study a model for the depinning and driven steady state phases of a solid tuned across a polymorphic phase transition between ground states of triangular and square symmetry. These include pinned states which may have dominantly triangular or square correlations, a plastically flowing liquid-like phase, a moving phase with hexatic correlations, flowing triangular and square states and a dynamic coexistence regime characterized by the complex interconversion of locally square and triangular regions. We locate these phases in a dynamical phase diagram. We demonstrate that the apparent power-l…
Superconductivity in crystals without inversion symmetry has received extensive attention due to its unconventional pairing and possible nontrivial topological properties. Using first-principles calculations, we systemically study the electronic structure of noncentrosymmetric superconductors $A_2$Cr$_3$As$_3$ ($A$=Na, K, Rb and Cs). Topologically protected triply degenerate points connected by one-dimensional arcs appear along the $C_{3}$ axis, coexisting with strong ferromagnetic (FM) fluctuations in the non-superconducting state. Within random phase approximation, our calculations show that…
The intersection of two-dimensional superconductivity and topologically nontrivial states hosts a wide range of quantum phenomena, including Majorana fermions. Coexistence of topologically nontrivial states and superconductivity in a single material, however, remains elusive. Here, we report on the observation of two-dimensional superconductivity and weak anti-localization at the TiOx/KTaO3(111) interfaces. A remnant, saturating resistance persists below the transition temperature as superconducting puddles fail to reach phase coherence. Signatures of weak anti-localization are observed below …
Substitution modulated transition from semimetal to superconductor in ZrTe$_{2-x}$Se$_x$ with coexistence of nontrivial electronic topology
Escola de Engenharia de Lorena - DEMAR, Universidade de São Paulo（圣保罗大学洛雷纳工程学院-DEMAR）；Universidade Federal do ABC, Centro de Ciências Naturais e Humanas（ABC联邦大学自然与人文中心）；Instituto de Ciências Tecnológicas e Exatas, Universidade Federal do Triângulo Mineiro（米纳斯吉拉斯三角区联邦大学技术与科学研究所）；Chair of Computational Condensed Matter Physics, Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理学院计算凝聚态物理讲席）
Over the past fifteen years, tremendous efforts have been devoted to realizing topological superconductivity in realistic materials and systems, predominately propelled by their promising application potentials in fault-tolerant quantum information processing. In this article, we attempt to give an overview on some of the main developments in this field, focusing in particular on two-dimensional crystalline superconductors that possess either intrinsic p-wave pairing or nontrivial band topology. We first classify the three different conceptual schemes to achieve topological superconductor (TSC…
We study the magnetic structures and their connections with topological superconductivity due to proximity effect for coupled magnetic atomic chains deposited on a superconductor. Several magnetic phases are self-consistently determined, including both the coplanar and non-coplanar ones. For a $N$-chain triangular atomic ladder, topologically nontrivial superconducting states can always be realized, but strongly depend on its magnetic structure and the number of atomic chains. When $N$ is even, the topologically nontrivial states with noncoplanar structures are characterized by $\mathbb{Z}_{2}…
We show that finite angular momentum pairing chiral superconductors on the triangular lattice have point zeroes in the complex gap function. A topological quantum phase transition takes place through a nodal superconducting state at a specific carrier density $x_c$ where the normal state Fermi surface crosses the isolated zeros. For spin singlet pairing, we show that the second nearest neighbor $d+id$-wave pairing can be the dominant pairing channel. The gapless critical state at $x_c\simeq0.25$ has six Dirac points and is topologically nontrivial with a $T^3$ spin relaxation rate below $T_c$.…
The behavior of thermal fluctuations of a superconducting order parameter with extended $ s $ and chiral $ d + id $ symmetry is investigated. The study is carried out on a triangular lattice within the framework of the quasi-two-dimensional single-band model with attraction between electrons at neighboring sites. The method of consistent consideration of the order parameter fluctuations and the charge carrier scattering by fluctuations of coupled electron pairs, based on the theory of functional integration is used. The distribution functions of the phase fluctuation probabilities depending on…
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 recently discovered layered kagome metals AV$_3$Sb$_5$(A=K, Rb, Cs) have attracted much attention because of their unique combination of superconductivity, charge density wave (CDW) order, and nontrivial band topology. The CDW order with an in-plane 2x2 reconstruction is found to exhibit exotic properties, such as time-reversal symmetry breaking and rotational symmetry breaking. However, the nature of the CDW, including its dimensionality, structural pattern, and effect on electronic structure, remains elusive despite intense research efforts. Here, using angle-resolved photoemission spect…
Three-component fermion beyond the conventional Dirac Weyl Majorana classification attracts extensive attentions recently and many efforts have been paid to explore their superconductivity. Based on first-principles calculations, we systematically investigate the electron-phonon coupling (EPC) in the three-component fermion materials WN, WC and TaN. The EPC in pristine and pressured WC and TaN are to small to induce superconductivity. Electron doping can efficiently enhance the EPC strength and the predicted Tcs reach the value of experiments. Upon 0.6 electron/unitcell doping, the EPC strengt…
Pairing-channel reconstruction by Ising spin-orbit coupling in a multiorbital triangular-lattice model
Anhui Provincial Key Laboratory of Low-Energy Quantum Materials and Devices, High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences（中国科学院合肥物质科学研究院强磁场科学中心安徽省低能量子材料与器件重点实验室）；Science Island Branch of Graduate School, University of Science and Technology of China（中国科学技术大学研究生院科学岛分院）
Many-body instabilities and topological physics are two attractive topics in condensed matter physics. It is intriguing to explore the interplay between these phenomena in a single quantum material. Here, using the prototypical charge density wave (CDW) material monolayer 1H-NbSe$_2$ as an example, we show how momentum-dependent electron-phonon coupling drives the CDW transition from $3\times3$ to $2\times2$ phase under electron doping. More interestingly, we find the coexistence of superconductivity and nontrivial topology in one of the two $2\times2$ CDW phases, the latter of which is identi…
