We demonstrate that checkerboard magnet-superconductor hybrid systems possess a rich phase diagram exhibiting both strong topological superconducting (STSC) and topological nodal point superconducting (TNPSC) phases. We show that TNPSC phases exist both for ferromagnetic and antiferromagnetic systems, yielding a plethora of qualitatively different edge mode structures. Checkerboard MSH systems also facilitate the emergence of STSC phases which can be induced even in the limit of vanishing magnetization. Our results provide a new path for the quantum engineering of topological superconducting phases using atomic manipulation techniques.
We show that the d-wave ordering in particle-hole channels, dubbed d-wave checkerboard order, possesses important physics that can sufficiently explain the scanning tunneling microscopy (STM) results in cuprates. A weak d-wave checkerboard order can effectively suppress the coherence peak in the single-particle spectrum while leaving the spectrum along the nodal direction almost unaffected. Simultaneously, it generates a Fermi arc with little dispersion around the nodal points at finite temperature that is consistent with the results of angle-resolved photoemission spectroscopy (ARPES) experim…
Numerical study of momentum-dependent gap function is presented to make clear the origin of superconductivity in copper oxides. We claim that antinodal region with pronounced nesting feature of the Fermi contour gives rise to superconducting pairing with large momentum under screened Coulomb repulsion. Such a pairing results in both spatial checkerboard pattern of the superconducting state below Tc and a gapped state of incoherent pairs in a broad temperature range above Tc. We explain the momentum dependence of the coherent spectral weight detected in angle-resolved photoemission spectroscopy…
One of the main challenges in understanding high TC superconductivity is to disentangle the rich variety of states of matter that may coexist, cooperate, or compete with d-wave superconductivity. At center stage is the pseudogap phase, which occupies a large portion of the cuprate phase diagram surrounding the superconducting dome [1]. Using scanning tunneling microscopy, we find that a static, non-dispersive, "checkerboard"-like electronic modulation exists in a broad regime of the cuprate phase diagram and exhibits strong doping dependence. The continuous increase of checkerboard periodicity…
The competing orders in the particle-particle (P-P) channel and the particle-hole (P-H) channel have been proposed separately to explain the pseudogap physics in cuprates. By solving the Bogoliubov-deGennes equation self-consistently, we show that there is a general complementary connection between the d-wave checkerboard order (DWCB) in the particle-hole (P-H) channel and the pair density wave order (PDW) in the particle-particle (P-P) channel. A small pair density localization generates DWCB and PDW orders simultaneously. The result suggests that suppressing superconductivity locally or glob…
We consider competing pair-density-wave (PDW) and $d$-wave superconducting states in a magnetic field. We show that PDW order appears in the cores of $d$-wave vortices, driving checkerboard charge-density-wave (CDW) order in the vortex cores, which is consistent with experimental observations. Furthermore, we find an additional CDW order that appears on a ring outside the vortex cores. This CDW order varies with a period that is twice that of the checkerboard CDW and it only appears where both PDW and $d$-wave order co-exist. The observation of this additional CDW order would provide strong ev…
Inhomogeneous superconductivity in the high quality single crystals of ZrB12 (Tc = 6 K) has been studied using the heat capacity and x-ray diffraction (XRD) data. Evidence of two-band superconductivity with two branches of upper critical field Hc2(Tc) is obtained in a magnetic field applied along the [110] axis of the crystal. On the contrary, at H //[100], the only dependence Hc2(Tc) is observed. This finding is supplemented with the checkerboard-type patterns of the charge stripes in ZrB12 deduced from the detailed analysis of XRD data. These patterns are compared to the structure of the cha…
We introduce a microscopic model aimed at describing the behavior of fermionic excitations in the background of a magnetic texture called "spin-vortex checkerboard". This texture was proposed previously as a possible alternative to stripes to interpret the experimental phenomenology of spin and charge modulations in 1/8-doped lanthanum cuprates. The model involves two kinds of interacting fermionic excitations residing in spin-rich and spin-poor regions of the modulated structure. It is a generalization of another model developed earlier for the so-called "grid checkerboard". The principal ter…
We report measurements of the temperature dependence of the magnetic penetration depth in different quality polycrystalline samples of noncentrosymmetric LaNiC2 down to 0.05 K. This compound has no magnetic phases and breaks time-reversal symmetry. In our highest quality sample we observe a T^2 dependence below 0.4Tc indicative of nodes in the energy gap. We argue that previous results suggesting conventional s-wave behavior may have been affected by magnetic impurities.
By means of the first-principles calculations and magnetic topological quantum chemistry, we demonstrate that the low energy physics in the checkerboard antiferromagnetic (AFM) monolayer FeSe, very close to an AFM topological insulator that hosts robust edge states, can be well captured by a double-degenerate fragile topologically flat band just below the Fermi level. The Wilson loop calculations identify that such fragile topology is protected by the $S_{4z}$ symmetry, which gives rise to an AFM higher-order topological insulator that support the bound state with fractional charge $e/2$ at th…
We consider a quasi two-dimensional superconductor with line nodes in an in-plane magnetic field, and compute the dependence of the specific heat, $C$, and the in-plane heat conductivity, $κ$, on the angle between the field and the nodal direction in the vortex state. We use a variation of the microscopic Brandt-Pesch-Tewordt method that accounts for the scattering of quasiparticles off vortices, and analyze the signature of the nodes in $C$ and $κ$. At low to moderate fields the specific heat anisotropy changes sign with increasing temperature. Comparison with measurements of $C$ and $κ$ in C…
Magneto-oscillations in kinetic and magnetic response functions of a few underdoped cuprates are perhaps one of the most striking observations since many probes of underdoped cuprates clearly point to a non Fermi-liquid normal state. Their observation in the vortex state well below the upper critical field raises a doubt concerning their normal state origin. Here I propose an explanation of the magneto-oscillations as emerging from the quantum interference of the vortex lattice and checkerboard modulations of the electron density of states revealed by STM with atomic resolution in some cuprate…
By performing first-principles electronic structure calculations and analyzing effective magnetic model of alkali-doped iron selenides, we show that the materials without iron vacancies should approach a novel checkerboard phase in which each four Fe sites group together in tetragonal structure. The checkerboard phase is the ground state with a block antiferromagnetic (AFM) order and a small charge density wave order in the absence of superconductivity. Both of them can also coexist with superconductivity. The results explain mysterious $2\times 2$ ordered patterns and hidden orders observed i…
We present a controlled perturbative approach to the low temperature phase diagram of highly inhomogeneous Hubbard models in the limit of small coupling, $t'$, between clusters. We apply this to the dimerized and checkerboard models. The dimerized model is found to behave like a doped semiconductor, with a Fermi-liquid groundstate with parameters ({\it e.g.} the effective mass) which are smooth functions of the Hubbard interaction, $U$. By contrast, the checkerboard model has a nodeless d-wave superconducting state (preformed pair condensate, $d$-BEC) for $0 < U < U_c$, which smoothly crosses …
Spanning a broad range of physical systems, complex symmetry breaking is widely recognized as a hallmark of competing interactions. This is exemplified in superfluid $^3$He which has multiple thermodynamic phases with spin and orbital quantum numbers $S=1$ and $L=1$, that emerge on cooling from a nearly ferromagnetic Fermi liquid. The heavy fermion compound UPt$_3$ exhibits similar behavior clearly manifest in its multiple superconducting phases. However, consensus as to its order parameter symmetry has remained elusive. Our small angle neutron scattering measurements indicate a linear tempera…
Angle-resolved photoemission data on optimally- and under-doped high temperature superconductors reveal a dichotomy between the nodal and antinodal electronic excitations. In this paper we propose an explanation of this unusual phenomenon by employing the coupling between the quasiparticle and the commensurate/incommensurate magnetic excitations.
Motivated by recent work on strain-induced pseudo-magnetic fields in Dirac and Weyl semimetals, we analyze the possibility of analogous fields in two-dimensional nodal superconductors. We consider the prototypical case of a d-wave superconductor, a representative of the cuprate family, and find that the presence of weak strain leads to pseudo-magnetic fields and Landau quantization of Bogoliubov quasiparticles in the low-energy sector. A similar effect is induced by the presence of generic, weak doping gradients. In contrast to genuine magnetic fields in superconductors, the strain- and doping…
Since the discovery of high-Tc LaO_1-xF_xFeAs, and other such systems based on FeAs layers, several proposals have been made for the superconducting order parameter Delta_k, on both phenomenological and microscopic grounds. Here we discuss how the symmetry of Delta_k in the bulk can be determined, assuming that single crystals will soon be available. We suggest that a measurement of the dependence of the low temperature specific heat on the angle of a magnetic field in the FeAs plane is the simplest such method, and calculate representative specific heat vs. field angle oscillations for the va…
Recently it was discovered that superconductivity in transition metal dichalcogenides (TMDs) is strongly affected by an out-of-plane spin-orbit coupling (SOC). In addition, new techniques of fabricating 2d ferromagnets on van der Waals materials are rapidly emerging. Combining these breakthroughs, we propose a realization of nodal topological superconductivity in TMDs by fabricating nanostructured ferromagnets with an in-plane magnetization on the top surface. The proposed procedure does not require application of external magnetic fields and applies to monolayer and multilayer (bulk) systems.…
We report quantum oscillations in underdoped YBa2Cu3O6.56 over a significantly large range in magnetic field extending from 24 to 101 T, enabling three well-spaced low frequencies at 440 T, 532 T, and 620 T to be clearly resolved. We show that a small nodal bilayer coupling that splits a nodal pocket into bonding and antibonding orbits yields a sequence of frequencies, F0 - ΔF, F0, and F0 + ΔF and accompanying beat pattern similar to that observed experimentally, on invoking magnetic breakdown tunneling at the nodes. The relative amplitudes of the multiple frequencies observed experimentally i…
Recently, Ising superconductors which possess in-plane upper critical fields much larger than the Pauli limit field are under intense experimental study. Many monolayer or few layer transition metal dichalcogenides are shown to be Ising superconductors. In this work, we show that in a wide range of experimentally accessible regimes where the in-plane magnetic field is higher than the Pauli limit field but lower than $H_{c2}$, a 2H-structure monolayer NbSe$_2$ or simiarly TaS$_2$ becomes a nodal topological superconductor. The bulk nodal points appear on the $Γ- M$ lines of the Brillouin zone w…
Studying the nodal quasiparticles in superconducting cuprates by photoemission with highly improved momentum resolution, we show that a new "kink" feature in the scattering rate is a key to uncover the nature of electron correlations in these compounds. Our data provide evidence that the main doping independent contribution to the scattering can be well understood in terms of the conventional Fermi liquid model, while the additional doping dependent contribution has a magnetic origin. This sheds doubt on applicability of a phonon-mediated pairing mechanism to high temperature superconductors.
Realizations of Majorana fermions in solid state materials have attracted great interests recently in connection to topological order and quantum information processing. We propose a novel way to create Majorana fermions in superconductors. We show that an incipient non-collinear magnetic order turns a spin-singlet superconductor with nodes into a topological superconductor with a stable Majorana bound state in the vortex core; at a topologically-stable magnetic point defect; and on the edge. We argue that such an exotic non-Abelian phase can be realized in extended t-J models on the triangula…
This paper provides an analysis of neutron inelastic scattering experiments on single crystals of UPd2Al3. The emphasis is on establishing robust, general, inferences on the joint antiferromagnetic-superconducting state which characterises UPd2Al3 at low temperatures. A distinction is drawn between these conclusions and various theoretical perspectives of a more model sensitive nature that have been raised in the literature.
We propose a mechanism for opening a full bulk energy gap and inducing vortex Majorana zero modes (MZMs) in nodal superconductors (SCs). We show that this becomes possible by coupling the nodal SC of interest to a magnetic texture crystal. The latter consists of superpositions of magnetic textures which repeat periodically in space according to suitable wave vectors that enable spin-flip scattering between all pairs of nodes of the SC, and thus open a full gap in its bulk energy spectrum. In this event, MZMs can be trapped in spin or shift vortices introduced in the magnetic texture crystal. O…
We describe a mechanism by which the longitudinal thermal conductivity $κ_{xx}$, measured in an in-plane magnetic field, oscillates as a function of field angle in layered nodal superconductors. These oscillations occur when the spin-orbit splitting at the nodes is larger than the nodal scattering rate, and are complementary to vortex-induced oscillations identified previously. In sufficiently anisotropic materials, the spin-orbit mechanism may be dominant. As a particular application, we focus on the cuprate high-temperature superconductor YBa$_2$Cu$_3$O$_{6+x}$. This material belongs to the …
We have studied nodal tunneling into YBa2Cu3O7-x (YBCO) films under magnetic fields. The films' orientation was such that the CuO2 planes were perpendicular to the surface with the a and b axis at 450 form the normal. The magnetic field was applied parallel to the surface and perpendicular to the CuO2 planes. The Zero Bias Conductance Peak (ZBCP) characteristic of nodal tunneling splits under the effect of surface currents produced by the applied fields. Measuring this splitting under different field conditions, zero field cooled and field cooled, reveals that these currents have different ori…
A characteristic feature of the copper oxide high-temperature superconductors is the dichotomy between the electronic excitations along the nodal (diagonal) and antinodal (parallel to the Cu-O bonds) directions in momentum space, generally assumed to be linked to the "d-wave" symmetry of the superconducting state. Angle-resolved photoemission measurements in the superconducting state have revealed a quasiparticle spectrum with a d-wave gap structure that exhibits a maximum along the antinodal direction and vanishes along the nodal direction. Subsequent measurements have shown that, at low dopi…
We investigate the properties of the coexistence phase of itinerant antiferromagnetism and nodal $d$-wave superconductivity (Q-phase) discovered in heavy fermion CeCoIn5 under applied magnetic field. We solve the minimal model that includes $d$-wave superconductivity and underlying magnetic correlations in real space to elucidate the structure of the $Q$-phase in the presence of an externally applied magnetic field. We further focus on the role of magnetic impurities, and show that they nucleate the Q-phase at lower magnetic fields. Our most crucial finding is that, even at zero applied field,…
The structure of the superconducting order parameter in the iron-pnictide superconductor BaFe$_2$(As$_{0.67}$P$_{0.33}$)$_2$ ($T_c=31$\,K) with line nodes is studied by the angle-resolved thermal conductivity measurements in a magnetic field rotated within the basal plane. We find that the thermal conductivity displays distinct fourfold oscillations with minima when the field is directed at $\pm45^\circ$ with respect to the tetragonal a-axis. We discuss possible gap structures that can account for the data, and conclude that the observed results are most consistent with the closed nodal loops …
We observed quantum oscillations in thermoelectric and magnetic torque signals in non-centrosymmetric superconductor PbTaSe$_2$. One oscillatory frequency stems from the orbits formed by magnetic breakdown, while others are from two-dimensional-like Fermi surfaces near the topological nodal rings. Our comprehensive understanding of the Fermi surface topology of PbTaSe$_2$, including nailing down the Fermi level and detecting the Berry phases near the nodal rings, is crucial for searching plausible topological superconductivity in its bulk and surface states.
Three-dimensional van der Waals ferromagnet Fe$_3$GeTe$_2$ (FGT) is regarded as a candidate for the magnetic topological nodal line semimetal. We investigate lateral electron transport between two 3~$μ$m spaced superconducting In leads beneath a thick three-dimensional FGT exfoliated flake. At low 30~mK temperature, we observe Josephson supercurrent that exhibits unusual critical current $I_c$ suppression by the magnetic field $B$. The overall $I_c(B)$ pattern is asymmetric in respect to the B sign. We demonstrate, that the asymmetry is defined by the magnetic field sweep direction, so the $I_…
A phenomenological model that considers different secondary $id_{xy}$ gap amplitudes and quasiparticle effective charges for each nodal direction, is proposed to explain the observed anisotropic node removal by a magnetic field in high-$T_{c}$ cuprates. Two independent parity-breaking condensates $<\bar{Ψ_{i}}\bigwedgeΨ_{i}>$ develop, implying the induction of a magnetic moment per each nodal direction. The model outcomes are in agreement with the experimentally found relation $Δ_{i}\sim\sqrt{B}$. The secondary gap vanishes through a second-order phase transition at a critical temperature whos…
The superconducting equivalent of giant magnetoresistance, involves placing a thin-film superconductor between two ferromagnetic layers. A change of magnetization-alignment in such a superconducting spin-valve from parallel (P) to antiparallel (AP) creates a positive shift in the superconducting transition temperature (ΔTc) due to an interplay of the magnetic exchange energy and the superconducting condensate. The magnitude of ΔTc scales inversely with the superconductor thickness (dS) and is zero when dS exceeds the superconducting coherence length (ξ) as predicted by de Gennes. Here, we repo…
Topological semimetals with superconducting properties provide an emergent platform to explore the properties of topological superconductors. We report magnetization, and magneto-transport measurements on high quality single crystals of transition metal dichalcogenide SnTaS2. It is a nodal line semimetal with superconducting transition below Tc = 2.9 K. Moderate anisotropy (3.1) is observed in upper critical fields along H||c and H||ab plane. In the normal state we observe large magneto-resistance and weak anti-localization effect that provide unambiguous confirmation of topological features i…
