Topological Metal Research Articles

Concurrence of anomalous Hall effect and charge density wave in a superconducting topological kagome metal

As one of the most fundamental physical phenomena, the anomalous Hall effect (AHE) typically occurs in ferromagnetic materials but is not expected in the conventional superconductors. Here, we have observed a giant AHE in kagome superconductor CsV3Sb5 with transition temperature (Tc) of 2.7 K. The anomalous Hall conductivity reaches up to 2.1*10^4 {\Omega}-1 cm-1 which is larger than those observed in most of the ferromagnetic metals. Strikingly, the emergence of AHE exactly follows the higher-temperature charge-density-wave (CDW) transition with TCDW ~ 94 K, indicating a strong correlation between the CDW state and AHE. Furthermore, AHE disappears when the CDW transition is completely suppressed at high pressure. The origin for AHE is attributed to enhanced skew scattering in CDW state and large Berry curvature arose from the kagome lattice. These discoveries make CsV3Sb5 as an ideal platform to study the interplay among nontrivial band topology, CDW and unconventional superconductivity.

Topological phase transition between a normal insulator and a topological metal state in a quasi-one-dimensional system

We theoretically report the finding of a new kind of topological phase transition between a normal insulator and a topological metal state where the closing-reopening of bandgap is accompanied by passing the Fermi level through an additional band. The resulting nontrivial topological metal phase is characterized by stable zero-energy localized edge states that exist within the full gapless bulk states. Such states living on a quasi-one-dimensional system with three sublattices per unit cell are protected by hidden inversion symmetry. While other required symmetries such as chiral, particle-hole, or full inversion symmetry are absent in the system.

Double Superconducting Dome and Triple Enhancement of T_{c} in the Kagome Superconductor CsV_{3}Sb_{5} under High Pressure.

CsV_{3}Sb_{5} is a newly discovered Z_{2} topological kagome metal showing the coexistence of a charge-density-wave (CDW)-like order at T^{*}=94 K and superconductivity (SC) at T_{c}=2.5 K at ambient pressure. Here, we study the interplay between CDW and SC in CsV_{3}Sb_{5} via measurements of resistivity, dc and ac magnetic susceptibility under various pressures up to 6.6GPa. We find that the CDW transition decreases with pressure and experience a subtle modification at P_{c1}≈0.6-0.9 GPa before it vanishes completely at P_{c2}≈2 GPa. Correspondingly, T_{c}(P) displays an unusual M-shaped double dome with two maxima around P_{c1} and P_{c2}, respectively, leading to a tripled enhancement of T_{c} to about 8K at 2GPa. The obtained temperature-pressure phase diagram resembles those of unconventional superconductors, illustrating an intimated competition between CDW-like order and SC. The competition is found to be particularly strong for the intermediate pressure range P_{c1}≤P≤P_{c2} as evidenced by the broad superconducting transition and reduced superconducting volume fraction. The modification of CDW order around P_{c1} has been discussed based on the band structure calculations. This work not only demonstrates the potential to raise T_{c} of the V-based kagome superconductors, but also offers more insights into the rich physics related to the electron correlations in this novel family of topological kagome metals.

Spin-polarized type-II nodal loop and nodal surface states in hexagonal compounds XTiO2 ( X = Li, Na, K, Rb)

Topological semimetals and metals have been extensively studied in nonmagnetic materials, while those in magnetic materials are still quite rare. Here, based on first-principles calculations, we reveal that a family of hexagonal compounds $X{\mathrm{TiO}}_{2}$ ($X$ = Li, Na, K, Rb) with ferromagnetic ground states host excellent topological electronic structures. In their low-energy band structures, they show two Weyl nodal loops and two Weyl nodal surfaces, where each nodal loop and nodal surface is contributed by the electron states in the same spin channel, namely, spin-polarized nodal loops and nodal surfaces. In particular, the nodal loops in these materials show type-II band dispersions and are robust against spin-orbit coupling because of the protection of the mirror symmetry. These nodal loops are featured with spin-polarized drumhead surface states. We build an effective Hamiltonian, which can well describe the type-II nodal loops in the system. Besides the type-II nodal loops, these materials also possess two spin-polarized nodal surfaces, protected by specific nonsymmorphic symmetry. The findings in this paper can serve as good material platforms to study the fundamental physics of type-II nodal loop and nodal surface fermions in a time-reversal-breaking system.

Unusual competition of superconductivity and charge-density-wave state in a compressed topological kagome metal

Understanding the competition between superconductivity and other ordered states (such as antiferromagnetic or charge-density-wave (CDW) state) is a central issue in condensed matter physics. The recently discovered layered kagome metal AV3Sb5 (A = K, Rb, and Cs) provides us a new playground to study the interplay of superconductivity and CDW state by involving nontrivial topology of band structures. Here, we conduct high-pressure electrical transport and magnetic susceptibility measurements to study CsV3Sb5 with the highest Tc of 2.7 K in AV3Sb5 family. While the CDW transition is monotonically suppressed by pressure, superconductivity is enhanced with increasing pressure up to P1 ≈ 0.7 GPa, then an unexpected suppression on superconductivity happens until pressure around 1.1 GPa, after that, Tc is enhanced with increasing pressure again. The CDW is completely suppressed at a critical pressure P2 ≈ 2 GPa together with a maximum Tc of about 8 K. In contrast to a common dome-like behavior, the pressure-dependent Tc shows an unexpected double-peak behavior. The unusual suppression of Tc at P1 is concomitant with the rapidly damping of quantum oscillations, sudden enhancement of the residual resistivity and rapid decrease of magnetoresistance. Our discoveries indicate an unusual competition between superconductivity and CDW state in pressurized kagome lattice.

Triply degenerate nodal lines in topological and nontopological metals

Topological nodal-line semimetals exhibit double or fourfold degenerate nodal lines, which are protected by symmetries. Here, we investigate the possibility of the existence of triply degenerate nodal lines in metals. We present two types of triply degenerate nodal lines, one topologically trivial and the other nontrivial. The first type is stacked by two-dimensional pseudospin-1 fermions, which can be viewed as an critical case of a tunable band-crossing line structure that contains a symmetry-protected quadratic band-crossing line and a non-degenerate band, and can split into four Weyl nodal lines under perturbations. We find that surface states of the nodal line structure are dependent on the geometry of the lattice and the surface termination. Such a metal has a nesting of Fermi surface in a range of filling, resulting in a density-wave state when interaction is included. The second type is a vortex ring of pseudospin-1 fermions. In this system, the pseudospins form Skyrmion textures, and the surface states are fully extended topological Fermi arcs so that the model exhibits 3D quantum anomalous Hall effect with a maximal Hall conductivity. The vortex ring can evolve into a pair of vortex lines that are not closed in the first Brillouin zone. A vortex line cannot singly exist in the lattice model if it is the only nodal feature of the system.

Fermi surface studies of the topologically nontrivial compound YSi

The Fermi surface properties of a nontrivial system YSi is investigated by de Haas-van Alphen (dHvA) oscillation measurements combined with the first-principle calculations. Three main frequencies ($\alpha$, $\beta$, $\gamma$) are probed up to $14$~T magnetic field in dHvA oscillations. The $\alpha$-branch corresponding to $21$~T frequency possesses non-trivial topological character with $\pi$ Berry phase and a linear dispersion along $\Gamma$ to $Z$ direction with a small effective mass of $0.069~m_e$ with second-lowest Landau-level up to $14$~T. For $B~\parallel$~[010] direction, the 295~T frequency exhibits non-trivial $2D$ character with $1.24\pi$ Berry phase and a high Fermi velocity of $6.7 \times 10^5$~ms$^{-1}$. The band structure calculations reveal multiple nodal crossings in the vicinity of Fermi energy $E_f$ without spin-orbit coupling (SOC). Inclusion of SOC opens a small gap in the nodal crossings and results in nonsymmorphic symmetry enforced Dirac points at some high symmetry points, suggesting YSi to be a symmetry enforced topological metal.

Evidence of nontrivial Berry phase and Kondo physics in SmBi

Realization of semimetals with non-trivial topologies such as Dirac and Weyl semimetals, have provided a boost in the study of these quantum materials. Presence of electron correlation makes the system even more exotic due to enhanced scattering of charge carriers, Kondo screening etc. Here, we studied the electronic properties of single crystalline, SmBi employing varied state of the art bulk measurements. Magnetization data reveals two magnetic transitions; an antiferromagnetic order with a Neel temperature of ~ 9 K and a second magnetic transition at a lower temperature (= 7 K). The electrical resistivity data shows an upturn typical of a Kondo system and the estimated Kondo temperature is found to be close to the Neel temperature. High quality of the crystal enabled us to discover signature of quantum oscillation in the magnetization data even at low magnetic field. Using a Landau level fan diagram analysis, a non-trivial Berry phase is identified for a Fermi pocket revealing the topological character in this material. These results demonstrate an unique example of the Fermiology in the antiferromagnetic state and opens up a new paradigm to explore the Dirac fermion physics in correlated topological metal via interplay of Kondo interaction, topological order and magnetism.

Unified Framework for Charge-Spin Interconversion in Spin-Orbit Materials

Materials with spin-orbit coupling are of great interest for various spintronics applications due to the efficient electrical generation and detection of spin-polarized electrons. Over the past decade, many materials have been studied, including topological insulators, transition metals, Kondo insulators, semimetals, semiconductors, and oxides; however, there is no unifying physical framework for understanding the physics and therefore designing a material system and devices with the desired properties. We present a model that binds together the experimental data observed on the wide variety of materials in a unified manner. We show that in a material with a given spin-momentum locking, the density of states plays a crucial role in determining the charge-spin interconversion efficiency, and a simple inverse relationship can be obtained. Remarkably, experimental data obtained over the last decade on many different materials closely follow such an inverse relationship. We further deduce two figure-of-merits of great current interest: the spin-orbit torque (SOT) efficiency (for the direct effect) and the inverse Rashba-Edelstein effect length (for the inverse effect), which statistically show good agreement with the existing experimental data on wide varieties of materials. Especially, we identify a scaling law for the SOT efficiency with respect to the carrier concentration in the sample, which agrees with existing data. Such an agreement is intriguing since our transport model includes only Fermi surface contributions and fundamentally different from the conventional views of the SOT efficiency that includes contributions from all the occupied states.

Strain modulated quantum spin Hall effect in monolayer NiB

Since boron has diverse coordination chemistry, it is capable of bonding with transition metals to form a new family of two-dimensional (2D) transition metal borides (MBenes) that exhibit rich electronic properties. Here, we propose a 2D planar monolayer NiB with topologically nontrivial electronic structures as the new member of the MBenes family. The NiB monolayer exhibits metallic behavior with two Dirac cones residing slightly below the Fermi level in the absence of spin–orbit coupling (SOC). When a tensile strain of 11% is applied, the NiB monolayer transforms into a semimetal. A gap opening of 18 meV is observed at the Dirac points when SOC is considered. Based on the results of Z2 invariant (Z2=1) and the helical edge states, we identify the pristine NiB as a topological metal, while the stretched monolayer under 11% strain as a quantum spin Hall (QSH) insulator. In addition, the NiB monolayer undergoes a phase transition from topological metal to QSH insulator and then to topological metal with the increase in strain from 0% to 14%. Our findings demonstrate that the electronic properties of NiB, the new member of the MBene family, can be modulated by strain.

Topological gimbal phonons in T -carbon

The topological metal states in electronic systems have been extensively studied, but topological phonons were explored only in few examples so far. Here, we expose for the first time that the topological nodal gimbal phonons, type-I and type-II Weyl phonons are simultaneously present in T-carbon, a recently realized new allotrope of carbon. At about 15.2 THz, we find that there exist three mutually intersecting nodal loops (named as nodal gimbal phonons) around {\Gamma} point, and two pairs of type-I Weyl phonons on the boundary of Brillouin zone around each X point. In addition, there exist three pairs of type-II Weyl phonons at about 14.5 THz around each L point. It is shown that these exotic topological phonons are protected by corresponding symmetries, and lead to topologically nontrivial surface states. Our findings not only afford plenty of intriguing topological phonon states in a simple material like T-carbon but also provide a new platform to study novel properties of topological phonons, which would facilitate further both experimental and theoretical works in future.

Nonlinear Actuation of Casimir Oscillators toward Chaos: Comparison of Topological Insulators and Metals

In the current study, we explore the sensitivity of the actuation dynamics of electromechanical systems on novel materials, e.g., Bi2Se3, which is a well-known 3D Topological Insulator (TI), and compare their response to metallic conductors, e.g., Au, that are currently used in devices. Bifurcation and phase portraits analysis in conservative systems suggest that the strong difference between the conduction states of Bi2Se3 and Au yields sufficiently weaker Casimir force to enhance stable operation. Furthermore, for nonconservative driven systems, the Melnikov function and Poincare portrait analysis probed the occurrence of chaotic behavior leading to increased risk for stiction. It was found that the presence of the TI enhanced stable operation against chaotic behavior over a significantly wider range of operation conditions in comparison to typical metallic conductors. Therefore, the use of TIs can allow sufficient surface conductance to apply electrostatic compensation of residual contact potentials and, at the same time, to yield sufficiently weak Casimir forces favoring long-term stable actuation dynamics against chaotic behavior.

New topological Zn metal organic frameworks as multi-responsive fluorescent sensing materials for detecting Fe3+, Cr2O72−, CrO42− and tetracycline in aqueous system

Three new Zn metal organic frameworks (Zn-MOFs), {[Zn2(L)[H (1,4-bmib)]]·1.5(H2O)}n (1), {[Zn2(HL) (3,5-bip)2]·(H2O)}n (2), and {[Zn2(HL) (4,4′-bbibp)2]·4(H2O)}n (3), have been first synthesized based on a flexible H5L ligand with ether functional group (C–O–C) and successfully characterized (semi-flexible H5L ​= ​3,5-bis(3,5-dicarboxylphenoxy)benzoic acid, flexible 1,4-bmib ​= ​1,4-bis(2-methylimidazol-1-yl)butane, rigid 3,5-bip ​= ​3,5-bis(1-imidazolyl)pyridine, and rigid 4,4′-bbibp ​= ​4,4′-bis(benzoimidazo-1-ly)biphenyl). Zn-MOFs 1–3 are unique topological networks. As multi-responsive fluorescent sensing materials of 1 and 3, they show excellent response and sensitivity for Fe3+, CrO42− and Cr2O72−, and tetracycline (TC) in aqueous system. The quenching mechanism is also investigated in detail.

Topological properties of noncentrosymmetric superconductors TIr2B2 ( T=Nb,Ta )

A recent experiment reported two new non-centrosymmetric superconductors NbIr$_{2}$B$_{2}$ and TaIr$_{2}$B$_{2}$ with respective superconducting transition temperatures of 7.2 K and 5.2 K and further suggested their superconductivity to be unconventional [K. G\'ornicka \textit{et al}., Adv. Funct. Mater. 2007960 (2020)]. Here, based on first-principles calculations and symmetry analysis, we propose that $T$Ir$_{2}$B$_{2}$ ($T$=Nb, Ta) are topological Weyl metals in the normal state. In the absence of spin-orbit coupling (SOC), we find that NbIr$_{2}$B$_{2}$ has 12 Weyl points, and TaIr$_{2}$B$_{2}$ has 4 Weyl points, i.e. the minimum number under time-reversal symmetry; meanwhile, both of them have a nodal net composed of three nodal lines. In the presence of SOC, a nodal loop on the mirror plane evolves into two hourglass Weyl rings, along with the Weyl points, which are dictated by the nonsymmorphic glide mirror symmetry. Besides the rings, NbIr$_{2}$B$_{2}$ and TaIr$_{2}$B$_{2}$ have 16 and 20 pairs of Weyl points, respectively. The surface Fermi arcs are explicitly demonstrated. On the (110) surface of TaIr$_{2}$B$_{2}$, we find extremely long surface Fermi arcs ($\sim$0.6 ${\text{\AA}}^{-1}$) located 1.4 meV below the Fermi level, which should be readily probed in experiment. Combined with the intrinsic superconductivity and the nontrivial bulk Fermi surfaces, $T$Ir$_{2}$B$_{2}$ may thus provide a very promising platform to explore the three-dimensional topological superconductivity.

Planar Hall effect with sixfold oscillations in a Dirac antiperovskite

The planar Hall effect (PHE), wherein a rotating magnetic field in the plane of a sample induces oscillating transverse voltage, has recently garnered attention in a wide range of topological metals and insulators. The observed twofold oscillations in ρyx as the magnetic field completes one rotation are the result of chiral, orbital, and/or spin effects. The antiperovskites A3BO (A=Ca, Sr, Ba; B=Sn, Pb) are topological crystalline insulators whose low-energy excitations are described by a generalized Dirac equation for fermions with total angular momentum J=32. We report unusual sixfold oscillations in the PHE of Sr3SnO, which persisted nearly up to room temperature. Multiple harmonics (twofold, fourfold, and sixfold), which exhibited distinct field and temperature dependencies, were detected in ρxx and ρyx. These observations are more diverse than those in other Dirac and Weyl semimetals and point to a richer interplay of microscopic processes underlying the PHE in the antiperovskites.Received 10 November 2020Accepted 4 March 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013268Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasHall effectMagnetotransportTopological materialsCondensed Matter, Materials & Applied Physics

Saturable Absorption Dynamics of Highly Stacked 2D Materials for Ultrafast Pulsed Laser Production

This review summarizes recent developments of saturable absorbers (SAs) based on 2D materials for nonlinear optical absorption and ultrafast pulsed laser generation. Apart from graphene, various 2D materials such as topological insulators and transition metal dichalcogenides are investigated for SA applications and their important potential as passive mode-lockers for femtosecond laser production are extensively investigated. By selecting appropriate 2D materials, a wide spectral range of passively mode-locked pulsed lasers are obtained, covering visible, midinfrared and a terahertz region. A set of different approaches is used for fabricating SA modules of fiber laser photonics, which include sandwiching, side-polishing and tapering methods. Noticeably, through systematic studies, it is demonstrated that layer-stacking seldom deteriorates the SA performance of 2D materials in the evanescent regime, although their ultrathin nature may improve the efficiency in a transmission mode like sandwich-type SAs. The direction for designing new SAs is presented based on material characterization.

Topology and Symmetry of Quantum Materials via Nonlinear Optical Responses

We review recent progress in the study of photogalvanic effects and optical second-harmonic generation in topological and noncentrosymmetric metals.

Superconductivity in the Z2 kagome metal KV3Sb5

Here we report the observation of bulk superconductivity in single crystals of the two-dimensional kagome metal KV$_3$Sb$_5$. Magnetic susceptibility, resistivity, and heat capacity measurements reveal superconductivity below $T_c = 0.93$K, and density functional theory (DFT) calculations further characterize the normal state as a $\mathbb{Z}_2$ topological metal. Our results demonstrate that the recent observation of superconductivity within the related kagome metal CsV$_3$Sb$_5$ is likely a common feature across the AV$_3$Sb$_5$ (A: K, Rb, Cs) family of compounds and establish them as a rich arena for studying the interplay between bulk superconductivity, topological surface states, and likely electronic density wave order in an exfoliable kagome lattice.

Two-dimensional topological superconductivity candidate in a van der Waals layered material

Two-dimensional (2D) topological superconductors are highly desired because they not only offer opportunities for exploring novel exotic quantum physics, but also possesses potential applications in quantum computation. However, there are few reports on 2D superconductors, let alone topological superconductors. Here, we find a 2D monolayer W$_2$N$_3$, which can be exfoliated from its real van der Waals bulk material with much lower exfoliation energy than MoS$_2$, to be a topological metal with exotic topological states at different energy level. Due to the Van Hove singularities, the density of states near Fermi level are high, making the monolayer a compensate metal. Moreover, the monolayer W$_2$N$_3$ is unveiled to be a superconductor with the superconducting transition temperature Tc $\sim$ 22 K and a superconducting gap of about 5 meV based on the anisotropic Migdal-Eliashberg formalism, arising from the strong electron-phonon coupling around the $\Gamma$ point. Because of the strong electron and lattice coupling, the monolayer displays a non-Fermi liquid behavior in its normal states at temperatures lower than 80 K, where the specific heat exhibit T$^3$ behavior and the Wiedemann-Franz law dramatically violates. Our findings not only provide the platform to study the emergent phenomena in 2D topological superconductors, but also open a door to discover more 2D high-temperature topological superconductors in van der Waals materials.

B4 Cluster-Based 3D Porous Topological Metal as an Anode Material for Both Li- and Na-Ion Batteries with a Superhigh Capacity.

The high rate performance of a battery requires the anode to be conductive not just ionically but also electronically. This criterion has significantly stimulated the study on 3D porous topological metals composed of nonmetal atoms with a light mass. Many carbon-based 3D topological metals for batteries have been reported, while similar work for 3D boron remains missing. Here, we report the first study of a 3D boron topological metal as an anode material for Li or Na ions. Based on systematic calculations, we found that the reported 3D topological metal H-boron composed of B4 cluster shows a low mass density (0.91 g/cm3) with multiple adsorption sites for Li and Na ions due to the electron-deficient feature of boron, leading to an ultrahigh specific capacity of 930 mAh/g for Li and Na ions with a small migration barrier of 0.15 and 0.22 eV, respectively, and small volume changes of 0.6% and 9.8%. These intriguing features demonstrate that B-based 3D topological quantum porous materials are worthy of further study for batteries.