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Electromagnetic field of a fast electric charge in nuclear matter with spatially uniform but random topological charge density is derived. A useful approximation has been developed for the relativistic heavy-ion collisions.
The kagome lattice 1 , which is the most prominent structural motif in quantum physics, benefits from inherent non-trivial geometry so that it can host diverse quantum phases, ranging from spin-liquid phases, to topological matter, to intertwined orders 2,3,4,5,6,7,8 and, most rarely, to unconventional superconductivity 6,9 . Recently, charge sensitive probes have indicated that the kagome superconductors AV 3 Sb 5 (A = K, Rb, Cs) 9,10,11 exhibit unconventional chiral charge order 12,13,14,15,16,17,18,19, which is analogous to the long-sought-after quantum order in the Haldane model 20 or Varma model 21 . However, direct evidence for the time-reversal symmetry breaking of the charge order remains elusive. Here we use muon spin relaxation to probe the kagome charge order and superconductivity in KV 3 Sb 5 . We observe a noticeable enhancement of the internal field width sensed by the muon ensemble, which takes place just below the charge ordering temperature and persists into the superconducting state. Notably, the muon spin relaxation rate below the charge ordering temperature is substantially enhanced by applying an external magnetic field. We further show the multigap nature of superconductivity in KV 3 Sb 5 and that the T c /λ$^{-2}_{ab}$ ratio (where T c is the superconducting transition temperature and λ ab is the magnetic penetration depth in the kagome plane) is comparable to those of unconventional high-temperature superconductors. Our results point to time-reversal symmetry-breaking charge order intertwining with unconventional superconductivity in the correlated kagome lattice.
We analyze the decay of spin waves into Stoner excitations in magnetic Weyl semimetals. The lifetime of a mode is found to have a universal dependence on its frequency and momentum, and on a few parameters that characterize the relativistic Weyl spectrum. At the same time, uniform Gilbert damping by Weyl electrons is absent. Here, the decay rate of spin waves is calculated perturbatively using the s-d model of itinerant Weyl or Dirac electrons coupled to local moments. We show that many details of the Weyl spectrum, such as the momentum-space locations, dispersions, and sizes of the Weyl Fermi pockets, can be deduced indirectly by probing the spin waves of local moments using inelastic neutron scattering.
We derive a Kubo-like formula for the thermal Hall conductance of a 2d lattice systems which is free from ambiguities associated with the definition of energy magnetization. We use it to define a relative topological invariant of gapped 2d lattice systems at zero temperature. Up to a numerical factor, it can be identified with the difference of chiral central charges for the corresponding edge modes. This establishes the bulk-boundary correspondence for the chiral central charge. Here, we also show that for any local commuting projector Hamiltonian, the relative chiral central charge vanishes, while for free fermionic systems, it is related to the zero-temperature electric Hall conductance via the Wiedemann-Franz law.
The main objective of the Louisiana Consortium for Neutron Scattering (LaCNS) is to build a major neutron scattering infrastructure capable of treating both soft and hard materials. The goal is to create a sustainable effort having the quality, breadth, and depth necessary to produce competitive proposals including collaborative and center type proposals. Our scientific aim is to understand the role of coupling in emergent complex materials and its impact on the structure/property relationship and to explore how to tune the key couplings to guide the design of materials with the desired properties. This naturally includes building a base of users of the Spallation Neutron Source (SNS) and the High Flux Isotope Reactor (HFIR) in Louisiana; to train highly talented graduate and post-doctoral students in synthesis, neutron scattering, and simulation and modeling techniques, thereby helping to produce the next generation of scientist who use neutron scattering techniques as a crucial part of their research. The goal of our hard matter program is to understand the interplay between spin, charge, orbital, and lattice degrees of freedom in carefully selected complex materials. We have made considerable progress on number of complex systems including the oxide Sr3(Ru1-xMnx)2O7 where short-range magnetic ordering with anisotropic spin texture is initiated at the metal-insulator transition that clearly indicates a strong spin-charge coupling. Another critical area is in quantum materials. For example, in the topological semimetal BaMnSb2, we found a 3D canted antiferromagnetic Weyl semimetal with a 2D electronic structure and a nontrivial Berry phase. In addition, in the hexagonal chiral Mn1/3NbS2 system, we found soliton/soliton and soliton/antisoliton domain walls where the application of small fields or small currents can be used to control nanoscopic magnetic domains where the control of domain walls is crucially important for information storage. In addition, chemical transformation investigations were performed on the VISION instrument at Spallation Neutron Source (SNS). The soft matter effort was focused on understanding the role of non-covalent interactions on the structure and dynamics of fluid-based soft matter. One key focus was on sequence-defined (SD) amphiphilic peptoid polymers that allow encoding of molecular interactions and thereby systematic investigations of how charge directs the solution self-assembly of amphiphilic polymers in water. Another important area was on the dynamics of lipids self-assembled into membranes for exploring the permeability and mechanical using both neutron spin echo (NSE) spectroscopy and quasielastic neutron scattering (QENS) to distinguished between viscoelasticity and permeability at the molecular scale. Overall, the LaCNS project was quite successful, generating 145 publications and 245 presentations. Our graduate and post-doctoral students were well trained resulting in positions in national laboratories (Oak Ridge National Laboratory (ORNL), Argonne National Laboratory and Los Alamos National Laboratory), major research universities, and industry. We also developed a uniaxial pressure cell along with ORNL for SNS. A critical goal of this project was to establish a foundation for competing nationally in federally funded research programs. To this end, we were quite successful in generating over twenty-two federally and non-federally funded grants including awards from NSF, DOE, and DOD, and two early career awards. Equally important, we were able to secure a key major piece of instrumentation via a large ARO grant for a state-of-the-art electron microscope.
As one of the most intriguing states of matter, the chiral spin liquid (CSL) has attracted much scientific interest while its existence and mechanism in crystalline strongly correlated systems remain hotly debated. On the other hand, strong correlation driven emergent phenomena can be realized in twisted transition metal dichalcogenide bilayers with a tremendously tunable large length scale providing a new platform for the emergence of CSLs. Here, we focus on a strongly correlated model relevant to heterobilayer WSe 2 /MoSe 2 and investigate the Mott insulating phase at half filling under an out-of-plane magnetic field. Considering both its orbital and spin Zeeman effects we identify three conventionally ordered phases including a 120° Néel phase, a stripe phase, and an up-up-down phase. For intermediate fields an emergent quantum spin liquid phase is identified with partial spin polarization. We further characterize its topological nature as the v = 1/2 Laughlin CSL through the topological entanglement spectrum and quantized spin pumping under spin flux insertion. In addition, we map out the quantum phase diagram for different twisted angles in an experimentally accessible parameter regime.
Quantum materials provide a fertile ground in which to test and realize unusual phenomena such as quantum anomalies predicted by quantum field theory. There are three important symmetries that are broken when classical field theory is moved into the quantum regime, the scale anomaly, the axial (chiral) anomaly, and the parity anomaly. Several potential device applications may be realized by the discovery of quantum anomalies in condensed matter, enabled by the new physics they embody, including ultra‐sensitive dark matter detectors, far infrared optical modulators, micro‐bolometric detectors, low‐dissipation ballistic transporters, terahertz‐based qubits, terahertz polarization state controls, passive magnetic field sensors, stable topological superconductors that host Majorana fermions, and qubits topologically protected against decoherence. In this perspective article, the definition of these quantum anomalies is laid out, how little is known in the context of condensed matter, and how quantum anomalies are predicted to manifest as anomalous electronic, thermal, and magnetic behavior in experiments on topological quantum materials, including Weyl and Dirac semimetals. Furthermore, the importance that mechanical strain and defects will play in modifying signatures of quantum anomalies is discussed.
When two parallel coplanar dislocations with opposite Burgers vectors are brought into collision by the action of stress in solid crystals, they annihilate each other. In cholesterics with pitch p, under certain conditions, colliding dislocations with Burgers vectors b = p and b = − p are immune against annihilation and form stable twin-like pairs known as Lehmann clusters. We point out that this immunity is due to the escape of the director field into the third dimension. We show that from a topological point of view, Lehmann clusters can be seen as skyrmion tubes embedded in a helicoidal background, and their extremities have the topology of monopoles.
Recently, unconventional spin-orbit torques (SOTs) with tunable spin generation have opened new pathways for designing novel magnetization control for cutting-edge spintronics innovations. A leading research thrust is to develop field-free deterministic magnetization switching for implementing scalable and energy favorable magnetic recording and storage, which have been demonstrated in conventional ferromagnetic and antiferromagnetic material systems. Here, in this work, we extend this advanced magnetization control strategy to chiral antiferromagnet Mn 3 Sn using spin currents with out-of-plane canted polarization generated from low-symmetry van der Waals (vdW) material WTe 2 . Numerical calculations suggest that dampinglike SOT of spins injected perpendicular to the kagome plane of Mn 3 Sn serves as a driving force to rotate the chiral magnetic order, while the fieldlike SOT of spin currents with polarization parallel to the kagome plane provides the bipolar deterministicity to the magnetic switching in the absence of an external magnetic field. We further introduce scanning quantum microscopy to visualize nanoscale evolutions of Mn 3 Sn magnetic domains during the field-free switching process, corroborating the exceptionally large magnetic switching ratio up to 90%. Our results highlight the opportunities provided by hybrid SOT material platforms consisting of noncollinear antiferromagnets and low-symmetry vdW spin source materials for developing next-generation spintronic logic devices.
Using circularly polarized light to control quantum matter is a highly intriguing topic in physics, chemistry and biology. Previous studies have demonstrated helicity-dependent optical control of chirality and magnetization, with important implications in asymmetric synthesis in chemistry; homochirality in biomolecules; and ferromagnetic spintronics. We report the surprising observation of helicity-dependent optical control of fully compensated antiferromagnetic order in two-dimensional even-layered MnBi 2 Te 4 , a topological axion insulator with neither chirality nor magnetization. Furthermore, to understand this control, we study an antiferromagnetic circular dichroism, which appears only in reflection but is absent in transmission. We show that the optical control and circular dichroism both arise from the optical axion electrodynamics. Our axion induction provides the possibility to optically control a family of PT-symmetric antiferromagnets (P, inversion; T, time-reversal) such as Cr 2 O 3 , even-layered CrI3 and possibly the pseudo-gap state in cuprates. In MnBi 2 Te 4 , this further opens the door for optical writing of a dissipationless circuit formed by topological edge states.
Odd-parity superconductor $\mathrm{UTe_2}$ shows spontaneous time-reversal symmetry breaking and multiple superconducting phases, which imply chiral superconductivity, but only in a subset of samples. Here, we microscopically observe a homogeneous superfluid density $n_s$ on the surface of $\mathrm{UTe_2}$ and an enhanced superconducting transition temperature near the edges. We also detect vortex-antivortex pairs even at zero magnetic field, indicating the existence of a hidden internal field. The temperature dependence of $n_s$, determined independent of sample geometry, does not support point nodes along the $b$ axis for a quasi-2D Fermi surface and provides no evidence for multiple phase transitions in $\mathrm{UTe_2}$.
Understanding topological matter in the fractional quantum Hall (FQH) effect requires identifying the nature of edge state quasiparticles. FQH edge state at the filling factor 𝜈 = 2/3 in the spin-polarized and unpolarized phases is represented by the two modes of composite fermions (CF) with the parallel or opposite spins described by the chiral Luttinger liquids. Tunneling through a quantum point contact (QPC) between different or similar spin phases is solved exactly. With the increase of the applied voltage, the QPC conductance grows from zero and saturates at 𝑒 2 /2ℎ while a weak electron tunneling between the edge modes with the same spin transforms into a backscattering carried by the charge 𝑞 = 𝑒/2 quasiparticles. These unusual quasiparticles and conductance plateau emerge when one or two CF spin-polarized modes in the QPC tunnel into a single mode. Here, we propose experiments on the applied voltage and temperature dependence of the QPC conductance and noise that can shed light on the nature of edge states and FQH transport.
Here, we study plasmonic excitations in the Kane-Mele model, a two-dimensional Z 2 topological insulator on the honeycomb lattice, using the random phase approximation (RPA). In the topologically nontrivial phase, the model has conducting edge states that traverse the bulk energy gap and display spin-momentum locking. Such a state of matter is called the quantum spin hall (QSH) phase, which is robust against time-reversal (TR) invariant perturbations. We find that in the QSH phase, gapless spin-polarized plasmons can be excited on the edges of the system. The propagation of these plasmons is chiral for each individual spin component and shows spin-momentum locking for both spin components on the same edge. Moreover, we study the effect of external magnetic fields on the gapless edge plasmons. Specifically, out-of-plane magnetic fields delocalize edge plasmons propagating in one direction without affecting the other one, while an in-plane magnetic field can be applied to selectively excite a specific spin-plasmon branch with proper doping or gating to the system. Our findings may have potential applications in novel plasmonic and spintronic devices. We also investigate plasmons in the Kane-Mele model on a finite-sized diamond-shaped nanoflake and observe low-energy plasmons circulating the boundary of the material.
Topological states in quantum materials are defined by bulk wave functions that possess nontrivial topological invariants. While edge modes are widely presented as signatures of nontrivial topology, how bulk wave functions can manifest explicitly topological properties remains unresolved. Here, using high-resolution inelastic x-ray spectroscopy (IXS) combined with first principles calculations, we report experimental signatures of chiral wave functions in the bulk phonon spectrum of BaPtGe, which we show to host a previously undiscovered twofold-degenerate quadruple Weyl node. The chirality of the degenerate phononic wave function yields a nontrivial phonon dynamical structure factor, S(Q,ω), along high-symmetry directions, that is in excellent agreement with numerical and model calculations. Furthermore, our results establish IXS as a powerful tool to uncover topological wave functions, providing a key missing ingredient in the study of topological quantum matter.
Topological quantum liquids contain internal degrees of freedom that are coupled to geometric response. Yet, an explicit and microscopic identification of the geometric response remains difficult. Here, taking notable fractional quantum Hall (FQH) states as typical examples, we systematically investigate a promising protocol—the Dehn-twist deformation on the torus geometry—to probe the geometric response of correlated topological states and establish the relation between such response and universal properties of pertinent states. Based on analytical derivations and numerical simulations, we find that the geometry-induced Berry phase encodes features for a broad class of FQH states at the Laughlin, hierarchy, Halperin and non-Abelian Moore-Read fillings. Our findings conclusively demonstrate that the adiabatic Dehn-twist deformation can faithfully capture rich geometric and topological information, including the Hall viscosity and topological spin of the pertinent FQH state and the chiral central charge of the underlying edge conformal field theory. Our approach provides a powerful way to reveal topological orders of generic FQH states and address previously open questions.
We use first-principles methods to demonstrate that, in ZrTe 5 , a layered van der Waals material like graphite, atomic displacements corresponding to five of the six zone-center A g (symmetry-preserving) phonon modes can drive a topological transition from a strong to a weak topological insulator with a Dirac semimetal state emerging at the transition, giving rise to a Dirac topology surface in the multidimensional space formed by the A g phonon modes. This implies that the topological transition in ZrTe 5 , can be realized with many different settings of external stimuli capable of penetrating through the phonon-space Dirac surface without breaking the crystallographic symmetry. Furthermore, we predict that domains with effective mass of opposite signs can be created by laser pumping and will host Weyl modes of opposite chirality propagating along the domain boundaries. Studying phonon-space topology surfaces provides a new route to understanding and utilizing the exotic physical properties of ZrTe 5 , and related quantum materials.
The aim of this Tutorial is to give a pedagogical introduction into realizations of Majorana fermions, usually termed as Majorana bound states (MBSs), in condensed matter systems with magnetic textures. We begin by considering the Kitaev chain model of “spinless” fermions and show how two “half” fermions can appear at chain ends due to interactions. By considering this model and its two-dimensional generalization, we emphasize intricate relation between topological superconductivity and possible realizations of MBS. We further discuss how “spinless” fermions can be realized in more physical systems, e.g., by employing the spin-momentum locking. Next, we demonstrate how magnetic textures can be used to induce synthetic or fictitious spin–orbit interactions, and, thus, stabilize MBS. We describe a general approach that works for arbitrary textures and apply it to skyrmions. We show how MBS can be stabilized by elongated skyrmions, certain higher order skyrmions, and chains of skyrmions. We also discuss how braiding operations can be performed with MBS stabilized on magnetic skyrmions. Furthermore, this Tutorial is aimed at students at the graduate level.
We take advantage of recent improvements in the grand canonical hybrid Monte Carlo algorithm, to perform a precision study of the single-particle gap in the hexagonal Hubbard model, with on-site electron-electron interactions. After carefully controlled analyses of the Trotter error, the thermodynamic limit, and finite-size scaling with inverse temperature, we find a critical coupling of U c /κ = 3.834(14) and the critical exponent zν = 1.185(43). Under the assumption that this corresponds to the expected antiferromagnetic Mott transition, we are also able to provide a preliminary estimate β = 1.095(37) for the critical exponent of the order parameter. We consider our findings in view of the SU(2) Gross-Neveu, or chiral Heisenberg, universality class. Here, we also discuss the computational scaling of the hybrid Monte Carlo algorithm, and possible extensions of our work to carbon nanotubes, fullerenes, and topological insulators.