Exploring the 4d1analogue of cuprates: theoretical studies on bulk NbF4and NbF4monolayer stabilized on MgO (001) plane.

The recent research in infinite-layer nickelates has inspired new effort in finding the cuprate analogs. Here we propose that NbF4, which contains niobium-centered fluorine octahedra, is a promising 4d1analogue of cuprates. Using the density functional theory, we first show that bulk NbF4is in close proximity tod1configuration, with Nb4dxyorbital nearly half-filled. A single band with dominating4dxycharacter crosses the Fermi level, forming a square-like Fermi surface. The intralayer G-type antiferromagnetic (AFM) order is energetically favored and the Coulomb interaction drives the system into an AFM insulator. Next we demonstrate that the NbF4layer can be stabilized on MgO substrate with main electronic and magnetic features retained, offering an alternative route to realize the NbF4-related high-Tcsuperconductors. Furthermore, we derive effective single orbital models for both systems and investigate the electron correlation effects via functional renormalization group. We find that the G-type AFM dominates near half-filling butdx2-y2-wave superconductivity (SC) prevails upon suitable hole/electron doping. Based on the striking similarities between NbF4and cuprates, we suggest that NbF4-related compounds may be exotic candidates for searching new high-Tcsuperconductors.

Tunable quantum criticalities in an isospin extended Hubbard model simulator.

Studying strong electron correlations has been an essential driving force for pushing the frontiers of condensed matter physics. In particular, in the vicinity of correlation-driven quantum phase transitions (QPTs), quantum critical fluctuations of multiple degrees of freedom facilitate exotic many-body states and quantum critical behaviours beyond Landau's framework1. Recently, moiré heterostructures of van der Waals materials have been demonstrated as highly tunable quantum platforms for exploring fascinating, strongly correlated quantum physics2-22. Here we report the observation of tunable quantum criticalities in an experimental simulator of the extended Hubbard model with spin-valley isospins arising in chiral-stacked twisted double bilayer graphene (cTDBG). Scaling analysis shows a quantum two-stage criticality manifesting two distinct quantum critical points as the generalized Wigner crystal transits to a Fermi liquid by varying the displacement field, suggesting the emergence of a critical intermediate phase. The quantum two-stage criticality evolves into a quantum pseudo criticality as a high parallel magnetic field is applied. In such a pseudo criticality, we find that the quantum critical scaling is only valid above a critical temperature, indicating a weak first-order QPT therein. Our results demonstrate a highly tunable solid-state simulator with intricate interplay of multiple degrees of freedom for exploring exotic quantum critical states and behaviours.

Anisotropic Scattering Caused by Apical Oxygen Vacancies in Thin Films of Overdoped High-Temperature Cuprate Superconductors.

There is a hot debate on the anomalous behavior of superfluid density ρ_{s} in overdoped La_{2-x}Sr_{x}CuO_{4} films in recent years. The linear drop of ρ_{s} at low temperatures implies the superconductors are clean, but the linear scaling between ρ_{s} (in the zero temperature limit) and the transition temperature T_{c} is a hallmark of the dirty limit in the Bardeen-Cooper-Schrieffer (BCS) framework [I. Bozovic et al., Nature (London) 536, 309 (2016)NATUAS0028-083610.1038/nature19061]. This dichotomy motivated exotic theories beyond the standard BCS theory. We show, however, that such a dichotomy can be reconciled naturally by the role of increasing anisotropic scattering caused by the apical oxygen vacancies. Furthermore, the anisotropic scattering also explains the "missing" Drude weight upon doping in the optical conductivity, as reported in the THz experiment [F. Mahmood et al., Phys. Rev. Lett. 122, 027003 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.027003]. Therefore, the overdoped cuprates can actually be described consistently by the d-wave BCS theory with the unique anisotropic scattering.

Reducing autocorrelation time in determinant quantum Monte Carlo using the Wang-Landau algorithm: Application to the Holstein model.

When performing a Monte Carlo calculation, the running time should, in principle, be much longer than the autocorrelation time in order to get reliable results. Among different lattice fermion models, the Holstein model is notorious for its particularly long autocorrelation time. In this paper, we employ the Wang-Landau algorithm in the determinant quantum Monte Carlo to achieve the flat-histogram sampling in the "configuration weight space," which can greatly reduce the autocorrelation time by sacrificing some sampling efficiency. The proposal is checked in the Holstein model on both square and honeycomb lattices. Based on such a Wang-Landau assisted determinant quantum Monte Carlo method, some models with long autocorrelation times can now be simulated possibly.

Observation of Distinct Spatial Distributions of the Zero and Nonzero Energy Vortex Modes in (Li_{0.84}Fe_{0.16})OHFeSe.

The energy and spatial distributions of vortex bound state in superconductors carry important information about superconducting pairing and the electronic structure. Although discrete vortex states, and sometimes a zero energy mode, had been observed in several iron-based superconductors, their spatial properties are rarely explored. In this study, we used low-temperature scanning tunneling microscopy to measure the vortex state of (Li,Fe)OHFeSe with high spatial resolution. We found that the nonzero energy states display clear spatial oscillations with a period corresponding to bulk Fermi wavelength; while in contrast, the zero energy mode does not show such oscillation, which suggests its distinct electronic origin. Furthermore, the oscillations of positive and negative energy states near E_{F} are found to be clearly out of phase. Based on a two-band model calculation, we show that our observation is more consistent with an s_{++} wave pairing in the bulk of (Li, Fe)OHFeSe, and superconducting topological states on the surface.

Tuning Topological Orders by a Conical Magnetic Field in the Kitaev Model.

We show that a conical magnetic field H=(1,1,1)H can be used to tune the topological order and hence, anyon excitations of the Z_{2} quantum spin liquid in the isotropic antiferromagnetic Kitaev model. A novel topological order, featured with Chern number C=4 and Abelian anyon excitations, is induced in a narrow range of intermediate fields H_{c1}≤H≤H_{c2}. On the other hand, the C=1 Ising-topological order with non-Abelian anyon excitations, as previously known to be present at small fields, is found here to survive up to H_{c1}. The results are obtained by developing and applying a Z_{2} mean field theory that works at finite fields and is asymptotically exact in the zero field limit and the associated variational quantum Monte Carlo.

Observation of Discrete Conventional Caroli-de Gennes-Matricon States in the Vortex Core of Single-Layer FeSe/SrTiO_{3}.

Using low-temperature scanning tunneling microscopy (STM), we studied the vortex states of single-layer FeSe film on a SrTiO_{3} (100) substrate, and the local behaviors of superconductivity at sample boundaries. We clearly observed multiple discrete Caroli-de Gennes-Matricon states in the vortex core, and quantitative analysis shows their energies well follow the formula: E=µΔ^{2}/E_{F}, where µ is a half integer (±1/2,±3/2,±5/2…) and Δ is the mean superconducting gap over the Fermi surface. Meanwhile, a fully gapped spectrum without states near zero bias is observed at the [110]_{Fe} oriented boundary of 1 and 2 ML FeSe films, and atomic step edge of 1 ML FeSe. Accompanied with theoretical calculations, our results indicate an s-wave pairing without sign change in the high-T_{C} FeSe/SrTiO_{3} superconductor.

Monolayer NbF4: a 4d1-analogue of cuprates.

The electronic structure and possible electronic orders in monolayer NbF4 are investigated by density functional theory and functional renormalization group. Because of the niobium-centered octahedra, the energy band near the Fermi level is found to derive from the 4dxy orbital, well separated from the other bands. Local Coulomb interaction drives the undoped system into an antiferromagnetic insulator. Upon suitable electron/hole doping, the system is found to develop [Formula: see text] -wave superconductivity with sizable transition temperature. Therefore, the monolayer NbF4 may be an exciting 4d1 analogue of cuprates, providing a new two-dimensional platform for high-Tc superconductivity.

Spectroscopic Imaging of Quasiparticle Bound States Induced by Strong Nonmagnetic Scatterings in One-Unit-Cell FeSe/SrTiO_{3}.

The absence of holelike Fermi pockets in the heavily electron-doped iron selenides (HEDISs) challenges the s_{±}-wave pairing originally proposed for iron pnictides, which consists of opposite signs of the gap function on electron and hole pockets. While the HEDIS compounds have been investigated extensively, a consistent description of the superconducting pairing therein is still lacking. Here, by in situ scanning tunneling spectroscopy and theoretical calculations, we study the effects of strong scatterings from nonmagnetic Pb adatoms on the epitaxially grown HEDIS, one-unit-cell FeSe/SrTiO_{3}(001). Systematic tunneling spectra measured on the Pb adatoms show comprehensive signals of quasiparticle bound states, which can be well explained theoretically within the sign-reversing pairing scenarios. The finding implies that, in addition to previously detected phonons, spin fluctuations play an important role in driving the Cooper pairing in FeSe/SrTiO_{3}(001). The sign reversal in the gap function we revealed here is a significant ingredient in a unified understanding of the high-temperature superconductivity in HEDISs.

Detection of Bosonic Mode as a Signature of Magnetic Excitation in One-Unit-Cell FeSe on SrTiO3.

A "fingerprint" of Cooper pairing mediated by collective bosonic excitation mode is the reconstruction of the quasiparticle-density-of-states (DOS) spectrum with an additional "dip-hump" structure located outside the superconducting coherence peak. Here, we report an in situ scanning tunneling spectroscopy study of one-unit-cell (1-UC) FeSe film on a SrTiO3(001) substrate. In the quasiparticle-DOS spectrum, the bosonic excitation mode characterized by the dip-hump structure is detected outside the larger superconducting gap. Statistically, the excitation mode shows an anticorrelation with pairing strength in magnitude and yields an energy scale upper-bounded by twice the superconducting gap. The observation coincides with the characteristics of magnetic resonance in cuprates and iron-based superconductors. Furthermore, the local response of superconducting spectra to magnetically distinct Se defects all exhibits the induced in-gap quasiparticle bound states, indicating an unconventional sign-reversing pairing over the Fermi surface in 1-UC FeSe. These results clarify the magnetic nature of the bosonic excitation mode and reveal a signature of electron-magnetic-excitation coupling in 1-UC FeSe/SrTiO3(001) besides the previously established pairing channel of electron-phonon interaction.

Directly visualizing the sign change of d-wave superconducting gap in Bi2Sr2CaCu2O8+δ by phase-referenced quasiparticle interference.

The superconducting state is formed by the condensation of Cooper pairs and protected by the superconducting gap. The pairing interaction between the two electrons of a Cooper pair determines the gap function. Thus, it is pivotal to detect the gap structure for understanding the mechanism of superconductivity. In cuprate superconductors, it has been well established that the gap may have a d-wave function. This gap function has an alternative sign change in the momentum space. It is however hard to visualize this sign change. Here we report the measurements of scanning tunneling spectroscopy in Bi2Sr2CaCu2O8+δ and conduct the analysis of phase-referenced quasiparticle interference (QPI). We see the seven basic scattering vectors that connect the octet ends of the banana-shaped contour of Fermi surface. The phase-referenced QPI clearly visualizes the sign change of the d-wave gap. Our results illustrate an effective way for determining the sign change of unconventional superconductors.

Theory of Chiral p-Wave Superconductivity with Near Nodes for Sr_{2}RuO_{4}.

We use the functional renormalization group method to study a three-orbital model for superconducting Sr_{2}RuO_{4}. Although the pairing symmetry is found to be a chiral p wave, the atomic spin-orbit coupling induces near nodes for quasiparticle excitations. Our theory explains a major experimental puzzle between a d-wavelike feature observed in thermal experiments and the chiral p-wave triplet pairing revealed in nuclear-magnetic resonance and the Kerr effect.

Proximity-Induced Superconductivity with Subgap Anomaly in Type II Weyl Semi-Metal WTe2.

Due to the nontrivial topological band structure in type II Weyl semi-metal tungsten ditelluride (WTe2), unconventional properties may emerge in its superconducting phase. While realizing intrinsic superconductivity has been challenging in the type II Weyl semi-metal WTe2, the proximity effect may open an avenue for the realization of superconductivity. Here, we report the observation of proximity-induced superconductivity with a long coherence length along the c axis in WTe2 thin flakes based on a WTe2/NbSe2 van der Waals heterostructure. Interestingly, we also observe anomalous oscillations of the differential resistance during the transition from the superconducting to the normal state. Theoretical calculations show excellent agreement with experimental results, revealing that such a subgap anomaly is the intrinsic property of WTe2 in superconducting state induced by the proximity effect. Our findings enrich the understanding of the superconducting phase of type II Weyl semi-metals and pave the way for their future applications in topological quantum computing.

Possible Pairing Symmetry in the FeSe-Based Superconductors Determined by Quasiparticle Interference.

We study the momentum-integrated quasiparticle interference (QPI) in the FeSe-based superconductors. This method was recently proposed theoretically and has been applied to determine the pairing symmetry in these materials experimentally. Our findings suggest that, if the incipient bands and the superconducting (SC) pairing on them are taken into consideration, then the experimentally measured bound states and momentum-integrated QPI can be well fitted, even if the SC order parameter does not change sign on the Fermi surfaces. Therefore, we offer an alternative explanation to the experimental data, calling for more careful identification of the pairing symmetry that is important for the pairing mechanism.

Possible superconductivity in Sr2IrO4 probed by quasiparticle interference.

Based on the possible superconducting (SC) pairing symmetries recently proposed, the quasiparticle interference (QPI) patterns in electron- and hole-doped Sr2IrO4 are theoretically investigated. In the electron-doped case, the QPI spectra can be explained based on a model similar to the octet model of the cuprates while in the hole-doped case, both the Fermi surface topology and the sign of the SC order parameter resemble those of the iron pnictides and there exists a QPI vector resulting from the interpocket scattering between the electron and hole pockets. In both cases, the evolution of the QPI vectors with energy and their behaviors in the nonmagnetic and magnetic impurity scattering cases can well be explained based on the evolution of the constant-energy contours and the sign structure of the SC order parameter. The QPI spectra presented in this paper can be compared with future scanning tunneling microscopy experiments to test whether there are SC phases in electron- and hole-doped Sr2IrO4 and what the pairing symmetry is.

Experimental detection of a Majorana mode in the core of a magnetic vortex inside a topological insulator-superconductor Bi(2)Te(3)/NbSe(2) heterostructure.

Majorana fermions have been intensively studied in recent years for their importance to both fundamental science and potential applications in topological quantum computing. They are predicted to exist in a vortex core of superconducting topological insulators. However, it is extremely difficult to distinguish them experimentally from other quasiparticle states for the tiny energy difference between Majorana fermions and these states, which is beyond the energy resolution of most available techniques. Here, we circumvent the problem by systematically investigating the spatial profile of the Majorana mode and the bound quasiparticle states within a vortex in Bi(2)Te(3) films grown on a superconductor NbSe(2). While the zero bias peak in local conductance splits right off the vortex center in conventional superconductors, it splits off at a finite distance ∼20 nm away from the vortex center in Bi(2)Te(3). This unusual splitting behavior has never been observed before and could be possibly due to the Majorana fermion zero mode. While the Majorana mode is destroyed by the interaction between vortices, the zero bias peak splits as a conventional superconductor again. This work provides self-consistent evidences of Majorana fermions and also suggests a possible route to manipulating them.

Majorana modes in a topological insulator/s-wave superconductor heterostructure.

In a recent experiment, signatures of Majorana fermion (MF) were found in the vortex core threading a heterostructure composed of n layers of topological insulator (TI) deposited on a bulk s-wave superconductor. Here we provide strong theoretical support to the experiment. First, we demonstrate that MF modes appear on both top and bottom layers of TI, and are well separated for n ~ 6. The top MF becomes more extended with increasing n, in agrement with the experiment. Second, we show both analytically and numerically that right at the vortex core the MF mode is always accompanied by another low energy bound state, leading to a zero-bias peak plus a side peak in the local density of states (LDOS) therein. However, a local scalar impurity at the core can wipe out the accompanying side-peak state while leaving the zero-energy MF mode intact. Consequently the LDOS becomes symmetric about the fermi level, and the peak does not branch near the vortex core, in agreement with the experiment. Finally but unfortunately, while the MF is extremely stable against a single local impurity, the stability in terms of the critical impurity strength is reduced drastically for a moderate concentration (e.g., 10%) of impurities.

In-gap quasiparticle excitations induced by non-magnetic Cu impurities in Na(Fe(0.96) Co(0.03)Cu(0.01))As revealed by scanning tunnelling spectroscopy.

The origin of superconductivity in the iron pnictides remains unclear. One suggestion is that superconductivity in these materials has a magnetic origin, which would imply a sign-reversal s(±) pairing symmetry. Another suggests it is the result of orbital fluctuations, which would imply a sign-equal s(++) pairing symmetry. There is no consensus yet which of these two distinct and contrasting pairing symmetries is the right one in iron pnictide superconductors. Here we explore the nature of the pairing symmetry in the superconducting state of Na(Fe0.97-xCo0.03Cux)As by probing the effect of scattering of Cooper pairs by non-magnetic Cu impurities. Using scanning tunnelling spectroscopy, we identify the in-gap quasiparticle states induced by the Cu impurities, showing signatures of Cooper pair breaking by these non-magnetic impurities-a process that is only consistent with s(±) pairing. This experiment provides strong evidence for the s(±) pairing.

Model for determining the pairing symmetry and relative sign of the energy gap of iron-arsenide superconductors using tunneling spectroscopy.

We demonstrate that tunneling into multiband iron-arsenide superconductors through a wide junction in the transparent limit can provide unambiguous signatures for the symmetry and relative sign nu of the pairing gaps on the Gamma and M Fermi pockets. For antiphase s-wave pairing, Andreev reflections can be thoroughly suppressed by interband destructive interference. This also occurs for tunneling along the antinodal (nodal) direction of antiphase (in-phase) d-wave gaps with distinctive line shapes in the spectra as compared to the s-wave case. If nu is reversed, Andreev reflections survive but are subject to interband decoherence due to quasiparticles.