Interplay of Cooper Pairs and Zero-Energy Quasiparticles in a Gapless Superconductor.

The interplay between Cooper pairs and Bogoliubov-de Gennes (BdG) quasiparticles is a topic of considerable interest in the quantum properties of solids, but its important ingredient, the sufficient amount of low-energy quasiparticles to interact with Cooper pairs remains elusive in conventional superconductors. Here a gapless superconductor with coupled paramagnetic atomic layers is used to generate a significant amount of zero-energy quasiparticles that Anderson-localize and bifurcate into regions of high and low zero-energy quasiparticle density of states. The enriched zero-energy quasiparticles induce puddled superconductivity and Josephson vortices. This discovery not only advances the understanding of the mutual interaction of Cooper pairs and BdG quasiparticles but also opens a new avenue for exploring and controlling exotic quantum phenomena where superconductivity, disorder, and spin degrees of freedom are entangled.

Emergent Quantum Phenomena of a Noncentrosymmetric Charge Density Wave in 1T-Transition Metal Dichalcogenides.

1T-transition metal dichalcogenides (TMDs) have been an exciting platform for exploring the intertwinement of charge density waves and strong correlation phenomena. While the David star structure has been conventionally considered as the underlying charge order in the literature, recent scanning tunneling probe experiments on several monolayer 1T-TMD materials have motivated a new, alternative structure, namely, the anion-centered David star structure. In this Letter, we show that this novel anion-centered David star structure manifestly breaks inversion symmetry, resulting in flat bands with pronounced Rashba spin-orbit couplings. These distinctive features unlock novel possibilities and functionalities for 1T-TMDs, including the giant spin Hall effect, the emergence of Chern bands, and spin liquid that spontaneously breaks crystalline rotational symmetry. Our findings establish promising avenues for exploring emerging quantum phenomena of monolayer 1T-TMDs with this novel noncentrosymmetric structure.

High-temperature concomitant metal-insulator and spin-reorientation transitions in a compressed nodal-line ferrimagnet Mn3Si2Te6.

Symmetry-protected band degeneracy, coupled with a magnetic order, is the key to realizing novel magnetoelectric phenomena in topological magnets. While the spin-polarized nodal states have been identified to introduce extremely-sensitive electronic responses to the magnetic states, their possible role in determining magnetic ground states has remained elusive. Here, taking external pressure as a control knob, we show that a metal-insulator transition, a spin-reorientation transition, and a structural modification occur concomitantly when the nodal-line state crosses the Fermi level in a ferrimagnetic semiconductor Mn3Si2Te6. These unique pressure-driven magnetic and electronic transitions, associated with the dome-shaped Tc variation up to nearly room temperature, originate from the interplay between the spin-orbit coupling of the nodal-line state and magnetic frustration of localized spins. Our findings highlight that the nodal-line states, isolated from other trivial states, can facilitate strongly tunable magnetic properties in topological magnets.

Topological Complex Charge Conservation in Nontrivial Z2 × Z2 Domain Walls.

Localized topological modes such as solitons, Majorana Fermions, and skyrmions are attracting great interest as robust information carriers for future devices. Here, a novel conserved quantity for topological domain wall networks of a Z2 × Z2 order generated with spin-polarized current in Sr2VO3FeAs is discovered. Domain walls are mobilized by the scanning tunneling current, which also observes in atomic scale active dynamics of domain wall vertices including merge, bifurcation, pair creation, and annihilation. Within this dynamics, the product of the topological complex charges defined for domain wall vertices is conserved with a novel boundary-charge correspondence rule. These results may open an avenue toward topological electronics based on domain wall vertices in generic Z2 × Z2 systems.

Dual Higgs modes entangled into a soliton lattice in CuTe.

Recently discovered Higgs particle is a key element in the standard model of elementary particles and its analogue in materials, massive Higgs mode, has elucidated intriguing collective phenomena in a wide range of materials with spontaneous symmetry breaking such as antiferromagnets, cold atoms, superconductors, superfluids, and charge density waves (CDW). As a straightforward extension beyond the standard model, multiple Higgs particles have been considered theoretically but not yet for Higgs modes. Here, we report the real-space observations, which suggest two Higgs modes coupled together with a soliton lattice in a solid. Our scanning tunneling microscopy reveals the 1D CDW state of an anisotropic transition metal monochalcogenide crystal CuTe is composed of two distinct but degenerate CDW structures by the layer inversion symmetry broken. More importantly, the amplitudes of each CDW structure oscillate in an out-of-phase fashion to result in a regular array of alternating domains with repeating phase-shift domain walls. This unusual finding is explained by the extra degeneracy in CDWs within the standard Landau theory of the free energy. The multiple and entangled Higgs modes demonstrate how novel collective modes can emerge in systems with distinct symmetries broken simultaneously.

Kinkless Electronic Junction along 1D Electronic Channel Embedded in a Van Der Waals Layer.

Here, the formation of type-I and type-II electronic junctions with or without any structural discontinuity along a well-defined 1 nm-wide 1D electronic channel within a van der Waals layer is reported. Scanning tunneling microscopy and spectroscopy techniques are employed to investigate the atomic and electronic structure along peculiar domain walls formed on the charge-density-wave phase of 1T-TaS2 . Distinct kinds of abrupt electronic junctions with discontinuities of the band gap along the domain walls are found, some of which even do not have any structural kinks and defects. Density-functional calculations reveal a novel mechanism of the electronic junction formation; they are formed by a kinked domain wall in the layer underneath through substantial electronic interlayer coupling. This work demonstrates that the interlayer electronic coupling can be an effective control knob over nanometer-scale electronic property of 2D atomic monolayers.

Robust Luttinger Liquid State of 1D Dirac Fermions in a Van der Waals System Nb9Si4Te18.

We report on the Tomonaga-Luttinger liquid (TLL) behavior in fully degenerate 1D Dirac Fermions. A ternary van der Waals material Nb9Si4Te18 incorporates in-plane NbTe2 chains, which produce a 1D Dirac band crossing Fermi energy. Tunneling conductance of electrons confined within NbTe2 chains is found to be substantially suppressed at Fermi energy, which follows a power law with a universal temperature scaling, hallmarking a TLL state. The obtained Luttinger parameter of ∼0.15 indicates a strong electron-electron interaction. The TLL behavior is found to be robust against atomic-scale defects, which might be related to the Dirac electron nature. These findings, combined with the tunability of the compound and the merit of a van der Waals material, offer a robust, tunable, and integrable platform to exploit non-Fermi liquid physics.

Control over a Wide Phase Diagram of 2D Correlated Electrons by Surface Doping; K/1T-TaS2.

We demonstrate the systematic tuning of a trivial insulator into a Mott insulator and a Mott insulator into a correlated metallic and a pseudogap state, which emerge in a quasi-two-dimensional electronic system of 1T-TaS2 through strong electron correlation. The band structure evolution is investigated upon surface doping by alkali adsorbates for two distinct phases occurring at around 220 and 10 K by angle-resolved photoelectron spectroscopy. We find contrasting behaviors upon doping that corroborate the fundamental difference of two electronic states: while the antibonding state of the spin-singlet insulator at 10 K is partially occupied to produce an emerging Mott insulating state, the presumed Mott insulating state at 220 K evolves into a correlated metallic state and then a pseudogap state. The work indicates that surface doping onto correlated 2D materials can be a powerful tool to systematically engineer a wide range of correlated electronic phases.

Alternative Structure Model of Correlated Charge Density Wave in Monolayer 1T-Nb(Ta)Se2.

The putative Mott charge density wave (CDW) phases of monolayer 1T-NbSe2 and 1T-TaSe2 have attracted a lot of recent interest due to the unexpected orbital texture of their Mott-Hubbard states and the superstructure related to an exotic possibility of a quantum spin liquid with a spinon Fermi surface. The origins of the orbital texture and the superstructure have been, however, elusive. We find by using density functional theory calculations that these CDW phases can have an alternative metastable structure, an anion (Se) centered cluster, in contrast to the prevailing model of a cation (Nb or Ta) centered David star cluster. This structure can be stabilized by the charge transfer from the bilayer graphene/SiC substrate used commonly in the experiments. The anion-centered structure has a similar electronic band structure of a charge transfer insulator to that of DS clusters but naturally explains the orbital texture of the upper Hubbard band from simply its atomic structure. Moreover, this band structure exhibits a Fermi surface nesting to possibly break the symmetry spontaneously into a 3×3-R30° superstructure observed experimentally. The resulting ground state of the superstructure is shown to be a trivial band insulator, in contrast to exotic proposals. This result emphasizes the huge structural flexibility of these heteroexpitaxial monolayers, for which careful studies on atomic structures and interactions with substrates are highly requested.

Topological soliton molecule in quasi 1D charge density wave.

Soliton molecules, bound states of two solitons, can be important for the informatics using solitons and the quest for exotic particles in a wide range of physical systems from unconventional superconductors to nuclear matter and Higgs field, but have been observed only in temporal dimension for classical wave optical systems. Here, we identify a topological soliton molecule formed spatially in an electronic system, a quasi 1D charge density wave of indium atomic wires. This system is composed of two coupled Peierls chains, which are endowed with a Z4 topology and three distinct, right-chiral, left-chiral, and non-chiral, solitons. Our scanning tunneling microscopy measurements identify a bound state of right- and left-chiral solitons with distinct in-gap states and net zero phase shift. Our density functional theory calculations reveal the attractive interaction of these solitons and the hybridization of their electronic states. This result initiates the study of the interaction between solitons in electronic systems, which can provide novel manybody electronic states and extra data-handling capacity beyond the given soliton topology.

Realizing a Superconducting Square-Lattice Bismuth Monolayer.

Interplay of crystal symmetry, strong spin-orbit coupling (SOC), and many-body interactions in low-dimensional materials provides a fertile ground for the discovery of unconventional electronic and magnetic properties and versatile functionalities. Two-dimensional (2D) allotropes of group 15 elements are appealing due to their structures and controllability over symmetries and topology under strong SOC. Here, we report the heteroepitaxial growth of a proximity-induced superconducting 2D square-lattice bismuth monolayer on superconducting Pb films. The square lattice of monolayer bismuth films in a C4 symmetry together with a stripey moiré structure is clearly resolved by our scanning tunneling microscopy, and its atomic structure is revealed by density functional theory (DFT) calculations. A Rashba-type spin-split Dirac band is predicted by DFT calculations to exist at the Fermi level and becomes superconducting through the proximity effect from the Pb substrate. We suggest the possibility of a topological superconducting state in this system with magnetic dopants/field. This work introduces an intriguing material platform with 2D Dirac bands, strong SOC, topological superconductivity, and the moiré superstructure.

Mobile Kink Solitons in a Van der Waals Charge-Density-Wave Layer.

Kinks, point-like geometrical defects along dislocations, domain walls, and DNA, are stable and mobile, as solutions of a sine-Gordon wave equation. While they are widely investigated for crystal deformations and domain wall motions, electronic properties of individual kinks have received little attention. In this work, electronically and topologically distinct kinks are discovered along electronic domain walls in a correlated van der Waals insulator of 1T-TaS2 . Mobile kinks and antikinks are identified as trapped by pinning defects and imaged in scanning tunneling microscopy. Their atomic structures and in-gap electronic states are unveiled, which are mapped approximately into Su-Schrieffer-Heeger solitons. The twelvefold degeneracy of the domain walls in the present system guarantees an extraordinarily large number of distinct kinks and antikinks to emerge. Such large degeneracy together with the robust geometrical nature may be useful for handling multilevel information in van der Waals materials architectures.

Tunable Mott Dirac and Kagome Bands Engineered on 1T-TaS2.

Strongly interacting electrons in hexagonal and kagome lattices exhibit rich phase diagrams of exotic quantum states, including superconductivity and correlated topological orders. However, material realizations of these electronic states have been scarce in nature or by design. Here, we theoretically propose an approach to realize artificial lattices by metal adsorption on a 2D Mott insulator 1T-TaS2. Alkali, alkaline-earth, and group 13 metal atoms are deposited in (√3 × âˆš3)R30° and 2 × 2 TaS2 superstructures of honeycomb- and kagome-lattice symmetries exhibiting Dirac and kagome bands, respectively. The strong electron correlation of 1T-TaS2 drives the honeycomb and kagome systems into correlated topological phases described by Kane-Mele-Hubbard and kagome-Hubbard models. We further show that the 2/3 or 3/4 band filling of Mott Dirac and flat bands can be achieved with a proper concentration of Mg adsorbates. Our proposal may be readily implemented in experiments, offering an attractive condensed-matter platform to exploit the interplay of correlated topological order and superconductivity.

Z3 Charge Density Wave of Silicon Atomic Chains on a Vicinal Silicon Surface.

An ideal one-dimensional electronic system is formed along atomic chains on Au-decorated vicinal silicon surfaces, but the nature of its low-temperature phases has been puzzling for last two decades. Here, we unambiguously identify the low-temperature structural distortion of this surface using high-resolution atomic force microscopy and scanning tunneling microscopy. The most important structural ingredient of this surface, the step-edge Si chains, are found to be strongly buckled, every third atom down, forming trimer unit cells. This observation is consistent with the recent model of rehybridized dangling bonds and rules out the antiferromagnetic spin ordering proposed earlier. The spectroscopy and electronic structure calculation indicate a charge density wave insulator with a Z3 topology, making it possible to exploit topological phases and excitations. The tunneling current was found to substantially lower the energy barrier between three degenerate CDW states, which induces a dynamically fluctuating CDW at very low temperature.

Creation and annihilation of mobile fractional solitons in atomic chains.

Localized modes in one-dimensional (1D) topological systems, such as Majonara modes in topological superconductors, are promising candidates for robust information processing. While theory predicts mobile integer and fractional topological solitons in 1D topological insulators, experiments so far have unveiled immobile, integer solitons only. Here we observe fractionalized phase defects moving along trimer silicon atomic chains formed along step edges of a vicinal silicon surface. By means of tunnelling microscopy, we identify local defects with phase shifts of 2π/3 and 4π/3 with their electronic states within the band gap and with their motions activated above 100 K. Theoretical calculations reveal the topological soliton origin of the phase defects with fractional charges of ±2e/3 and ±4e/3. Additionally, we create and annihilate individual solitons at desired locations by current pulses from the probe tip. Mobile and manipulable topological solitons may serve as robust, topologically protected information carriers in future information technology.

Enhanced Berry Curvature Dipole and Persistent Spin Texture in the Bi(110) Monolayer.

Nonvanishing Berry curvature dipole (BCD) and persistent spin texture (PST) are intriguing physical manifestations of electronic states in noncentrosymmetric 2D materials. The former induces a nonlinear Hall conductivity while the latter offers a coherent spin current. Based on density-functional-theory (DFT) calculations, we demonstrate the coexistence of both phenomena in a Bi(110) monolayer with a distorted phosphorene structure. Both effects are concurrently enhanced due to the strong spin-orbit coupling of Bi while the structural distortion creates internal in-plane ferroelectricity with inversion asymmetry. We further succeed in fabricating a Bi(110) monolayer in the desired phosphorene structure on the NbSe2 substrate. Detailed atomic and electronic structures of the Bi(110)/NbSe2 heterostructure are characterized by scanning tunneling microscopy/spectroscopy and angle-resolved-photoemission spectroscopy. These results are consistent with DFT calculations which indicate the large BCD and PST are retained. Our results suggest the Bi(110)/NbSe2 heterostructure as a promising platform to exploit nonlinear Hall and coherent spin transport properties together.

Engineering Domain Wall Electronic States in Strongly Correlated van der Waals Material of 1T-TaS2.

Although a few physical methods were demonstrated for domain wall engineering in various electronic or ferroic materials with broken discrete symmetries, the direct control over the electronic properties of individual domain walls has been extremely limited. Here, we introduce a chemical method to tune the electronic property of domain walls in 1T tantalum disulfide. By using scanning tunneling microscopy and spectroscopy techniques, we find that indium adatoms on 1T-TaS2 have distinct behaviors on the domains with different bulk terminations. Moreover, the adatoms form their own chains along the edges of neighboring domains. The density functional theory calculations reveal a 1D Mott insulating state on a modified domain wall, resulting from the degenerated spin-polarized bands with electron doping from adsorbates and charge transfer from neighboring domains. This work suggests that chemical decoration by adsorbates can be widely used to tune local electronic states of domain walls and various 2D materials.

Colossal angular magnetoresistance in ferrimagnetic nodal-line semiconductors.

Efficient magnetic control of electronic conduction is at the heart of spintronic functionality for memory and logic applications1,2. Magnets with topological band crossings serve as a good material platform for such control, because their topological band degeneracy can be readily tuned by spin configurations, dramatically modulating electronic conduction3-10. Here we propose that the topological nodal-line degeneracy of spin-polarized bands in magnetic semiconductors induces an extremely large angular response of magnetotransport. Taking a layered ferrimagnet, Mn3Si2Te6, and its derived compounds as a model system, we show that the topological band degeneracy, driven by chiral molecular orbital states, is lifted depending on spin orientation, which leads to a metal-insulator transition in the same ferrimagnetic phase. The resulting variation of angular magnetoresistance with rotating magnetization exceeds a trillion per cent per radian, which we call colossal angular magnetoresistance. Our findings demonstrate that magnetic nodal-line semiconductors are a promising platform for realizing extremely sensitive spin- and orbital-dependent functionalities.

Distinguishing a Mott Insulator from a Trivial Insulator with Atomic Adsorbates.

In an electronic system with various interactions intertwined, revealing the origin of its many-body ground state is challenging and a direct experimental way to verify the correlated nature of an insulator has been lacking. Here we demonstrate a way to unambiguously distinguish a paradigmatic correlated insulator, a Mott insulator, from a trivial band insulator based on their distinct chemical behavior for a surface adsorbate using 1T-TaS_{2}, which has been debated between a spin-frustrated Mott insulator or a spin-singlet trivial insulator. We start from the observation of different sizes of spectral gaps on different surface terminations and show that potassium adatoms on these two surface layers behave in totally different ways. This can be straightforwardly understood from distinct properties of Mott and band insulators due to the fundamental difference of the half- and full-filled orbitals involved, respectively. This work not only solves an outstanding problem in this particularly interesting material but also provides a simple touchstone to identify the correlated ground state of electrons experimentally.