Intertwining exotic quantum order and nontrivial topology is at the frontier of condensed matter physics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] . A charge density wave (CDW) like order with orbital currents has been proposed as a powerful resource for topological states in the context of the quantum anomalous Hall effect 5,6 and for the hidden matter in the pseudogap phase of cuprate superconductors 7,8 . However, the experimental realization of such topological charge order is challenging. Here we use high-resolution scanning tunnelling microscopy (STM) to discover a topological charge order in a kagome superconductor 21-25 KV3Sb5. Through both lattice-sensitive topography and electronic-sensitive spectroscopic imaging, we observe a 2×2 superlattice, consistent with the star of David deformation in the underlying kagome lattice. Spectroscopically, an energy gap opens at the Fermi level, across which the charge modulation exhibits an intensity reversal, signaling a charge ordering. The strength of charge modulations further displays a clockwise or anticlockwise chiral anisotropy, which we demonstrate can be switched by an applied magnetic field. Our observations and theoretical analysis point to a topological charge order in the frustrated kagome lattice, which not only leads to a giant anomalous Hall effect, but can also be a strong precursor of unconventional superconductivity.

It has long been speculated that electronic flatband systems can be a fertile ground for hosting novel emergent phenomena including unconventional magnetism and superconductivity 1-14 . Here we use scanning tunnelling microscopy to elucidate the atomically resolved electronic states and their magnetic response in the kagome magnet 15-20 Co3Sn2S2. We observe a pronounced peak at the Fermi level, which is identified to arise from the kinetically frustrated kagome flatband. Increasing magnetic field up to ±8T, this state exhibits an anomalous magnetization-polarized Zeeman shift, dominated by an orbital moment in opposite to the field direction. Such negative magnetism can be understood as spin-orbit coupling induced quantum phase effects 21-25 tied to non-trivial flatband systems. We image the flatband peak, resolve the associated negative magnetism, and provide its connection to the Berry curvature field, showing that Co3Sn2S2 is a rare example of kagome magnet where the low energy physics can be dominated by the spinorbit coupled flatband. Our methodology of probing band-resolved ordering phenomena such as spin-orbit magnetism can also be applied in future experiments to elucidate other exotic phenomena including flatband superconductivity and anomalous quantum transport.

Magnetic topological phases of quantum matter are an emerging frontier in physics and material science [1][2][3][4]. Along these lines, several kagome magnets [5][6][7][8][9] have appeared as the most promising platforms. However, the magnetic nature of these materials in the presence of topological state remains an unsolved issue [5][6][7][8][9]. Here, we explore magnetic correlations in the kagome magnet Co 3 Sn 2 S 2 . Using muon spin-rotation, we present evidence for competing magnetic orders in the kagome lattice of this compound. Our results show that while the sample exhibits an outof-plane ferromagnetic ground state, an in-plane antiferromagnetic state appears at temperatures above 90 K, eventually attaining a volume fraction of 80% around 170 K, before reaching a nonmagnetic state. Strikingly, the reduction of the anomalous Hall conductivity above 90 K linearly follows the disappearance of the volume fraction of the ferromagnetic state. We further show that the competition of these magnetic phases is tunable through applying either an external magnetic field or hydrostatic pressure. Our results taken together suggest the thermal and quantum tuning of Berry curvature field via external tuning of magnetic order. Our study shows that Co 3 Sn 2 S 2 is a rare example where the magnetic competition drives the thermodynamic evolution * Electronic address: zurab.guguchia@psi.ch of the Berry curvature field, thus tuning its topological state.The kagome lattice is a two-dimensional pattern of corner-sharing triangles. With this unusual symmetry and the associated geometrical frustration, the kagome lattice can host peculiar states including flat bands [8], Dirac fermions [5,6] and spin liquid phases [7,10]. In particular, magnetic kagome materials offer a fertile ground to study emergent behaviors resulting from the interplay between unconventional magnetism and band topology. Recently, transition-metal based kagome magnets [5][6][7][8][9][10][11][12][13] are emerging as outstanding candidates for such studies, as they feature both large Berry curvature fields and unusual magnetic tunability. In this family, the kagome magnet Co 3 Sn 2 S 2 is found to exhibit both a large anomalous Hall effect and anomalous Hall angle, and is identified as a promising Weyl semimetal candidate [9,11,14,15]. However, despite knowing the magnetic ground state is ferromagnetic below T C = 177 K [16] with spins aligned along the c-axis [9, 11, 17] (see Figs. 1 a and b) there is no report of its magnetic tunability or phase diagram, and its interplay with the topological band structure. Here we use high-resolution µSR to systematically characterize the phase diagram, uncovering another intriguing in-plane antiferromagnetic phase. The magnetic competition between these two phases is further found to be highly tunable via applying either pressure [18][19][20][21] or magnetic field. Combined with first principles calculations, we discover that the tunable magnetic correlation plays a key role in determining the giant anomalous Hall transp...

In its orthorhombic T d polymorph, MoTe2 is a type-II Weyl semimetal, where the Weyl fermions emerge at the boundary between electron and hole pockets. Non-saturating magnetoresistance and superconductivity were also observed in T d-MoTe2. Understanding the superconductivity in T d-MoTe2, which was proposed to be topologically non-trivial, is of eminent interest. Here, we report high-pressure muon-spin rotation experiments probing the temperature-dependent magnetic penetration depth in T d-MoTe2. A substantial increase of the superfluid density and a linear scaling with the superconducting critical temperature T c is observed under pressure. Moreover, the superconducting order parameter in T d-MoTe2 is determined to have 2-gap s-wave symmetry. We also exclude time-reversal symmetry breaking in the superconducting state with zero-field μSR experiments. Considering the strong suppression of T c in MoTe2 by disorder, we suggest that topologically non-trivial s +− state is more likely to be realized in MoTe2 than the topologically trivial s ++ state.

Pressure, together with temperature and magnetic field, is an important thermodynamical parameter in physics. Investigating the response of a compound or of a material to pressure allows to elucidate ground states, investigate their interplay and interactions and determine microscopic parameters. Pressure tuning is used to establish phase diagrams, study phase transitions and identify critical points. Muon spin rotation/relaxation (muSR) is now a standard technique making increasing significant contribution in condensed matter physics, material science research and other fields. In this review, we will discuss specific requirements and challenges to perform muSR experiments under pressure, introduce the high-pressure muon facility at the Paul Scherrer Institute (PSI, Switzerland) and present selected results obtained by combining the sensitivity of the muSR technique with pressure.Comment: Submitted to High Pressure Research. 26 pages, 17 Figure

or most of its history, the superconductivity of strontium ruthenate (Sr 2 RuO 4) (ref. 1) has been understood in terms of an odd-parity two-component order parameter with equal-spin pairing in the RuO 2 planes: p x ± ip y (refs. 2-5). This order parameter is chiral: the Cooper pairs have angular momentum l = ±1. The evidence for chirality comes from the zero-field muon spin relaxation (ZF-μSR) data 6 , observation of a non-zero Kerr rotation below the critical temperature T c (ref. 7) and signs in the junction experiments of domains in the superconducting state 8,9 , while evidence for equal-spin pairing came from the absence of a change in the Knight shift below T c in nuclear magnetic resonance 10 and polarized neutron scattering 11 measurements. The Knight shift is related to the spin susceptibility; in conventional opposite-spin-pairing superconductors, it is suppressed below T c. However, in new measurements, it has been found that the Knight shift is, in fact, suppressed below T c (refs. 12-14), by a magnitude that is unlikely to be reconcilable with equal-spin pairing. This revision has called into question a number of other results on Sr 2 RuO 4. It raises a particular challenge for experiments that indicate chirality, because opposite-spin pairing implies an even-parity momentum-space gap structure. If the order parameter is constrained to be even parity, chiral, and composed of components that are degenerate on the tetragonal lattice of Sr 2 RuO 4 , the only possibility is d xz ± id yz order 15. Under conventional understanding, this is a highly unlikely order parameter because it

Our experiments unambiguously establish 2H-MoTe2 and 2H-MoSe2 as magnetic, moderate bandgap semiconductors.

We report superconductivity at T(c) ≈ 2.6 K in a new layered bismuth oxyselenide LaO(0.5)F(0.5)BiSe2 with the ZrCuSiAs-type structure composed of alternating superconducting BiSe2 and blocking LaO layers. The superconducting properties of LaO(0.5)F(0.5)BiSe2 were investigated by means of dc magnetization, resistivity and muon-spin rotation experiments, revealing the appearance of bulk superconductivity with a rather large superconducting volume fraction of ≈ 70% at 1.8 K.