arXiv subjects

Predrag Nikolić

Publications and source records attributed to Predrag Nikolić.

15 recordsLinked to original sources

arXiv2025

Hedgehog lattices induced by chiral spin interactions

We analyze a classical Heisenberg spin model on the simple cubic lattice which is invariant under time reversal and contains multiple chiral spin interactions. The modelled dynamics is appropriate either for local moments coupled to itinerant Weyl electrons, or localized electrons with a strong spin-orbit coupling that would produce a Weyl spectrum away from half filling. Using a Monte Carlo method, we find a robust $4Q$ bipartite lattice of hedgehogs and antihedgehogs which melts through a first order phase transition at a critical temperature in certain segments of the phase diagram. The density of hedgehogs is a non-linear function of the Dzyaloshinskii-Moriya interaction, and a linear function of the multiple-spin chiral interaction which plays the fundamental role of a ``magnetic flux'' or a hedgehog chemical potential. These findings are related to the observations of hedgehog lattices in MnGe, MnSi$_{1-x}$Ge$_x$ and SrFeO$_3$, and indirectly support the possible existence of incompressible quantum-disordered hedgehog liquids.

cond-mat.str-el↗

arXiv2025

Theory of non-resonant Raman scattering from electrons in nodal and flat bands

Raman scattering is emerging as a surprising probe of electron topology in quantum materials. It has been used recently to detect and characterize a topological phase transition that accompanies the magnetic transition in Nd$_2$Ir$_2$O$_7$. Here we present a theory of Raman scattering from nodal electrons with Weyl and quadratic band touching spectra, which has to reach beyond the standard effective mass approximation. After reviewing and providing the details of our previous theory development, we discuss several new results. We show that the light-polarization dependence of Raman scattering is universal in the case of Weyl electrons and given by an analytic expression, while it contains symmetry-protected features in the case of quadratic band-touching nodes. We also analyze modifications of the Raman signal due to the ubiquitous tilting of the Weyl spectrum, and argue that universality is lost only in a finite frequency range that springs out of the threshold frequency for untilted nodes. Finally, we explore the frequency dependence of Raman scattering for the case of Dirac electrons coexisting with a flat band in the same region of the first Brillouin zone, which is inspired by the material V$_{1/3}$NbS$_2$.

cond-mat.mtrl-sci↗

arXiv2024

Magnetic excitations and interactions in the Weyl ferrimagnet NdAlSi

Weyl fermions can arise from time-reversal symmetry-breaking magnetism, but their impact on magnetic order is a source of ongoing research. Using high-precision neutron diffraction and spectroscopy, we present a comprehensive exploration of the magnetic structure and excitation spectrum of Weyl semimetal and helical magnet NdAlSi. We use Luttinger-Tisza, classical mean-field, and random-phase approximation techniques to model the dispersive crystal field excitons. We find extended-ranged and sign-changing interactions, suggesting a coupling between conduction electrons and the local moments. We demonstrate that low-symmetry anisotropic Dzyaloshinskii-Moriya interactions, in contrast with higher-symmetry interactions enabled by Weyl fermions, play an important role in stabilizing the complex spin spiral ground state of NdAlSi. Our work provides a first detailed view of microscopic interactions in a Weyl magnet, and constrains the role of Weyl electrons and their chirality on the spiral magnetism.

cond-mat.str-el↗

arXiv2024

Instanton confinement-deconfinement transitions: The stability of pseudogap phases and topological order

We explore the stability of certain many-body quantum states which may exist at zero or finite temperatures, may lack long-range order and even topological order, and still are thermodynamically distinct from uncorrelated disordered phases. We sharply characterize such states by the conservation of topological charge, or equivalently confinement of instantons, using a generalization of the Wilson loop and the correlation length of an emergent gauge field. Our main conclusions are: (i) topological orders can exist at finite temperatures, (ii) relativistic liquids of topological defects can also exist as stable phases at finite temperatures, and (iii) there are two universality classes of instanton suppression. We also relate the instanton dynamics to the problem of the pseudogap state in underdoped cuprates. A universal experimental signature of the instanton deconfinement transition is a change of the quantum noise spectrum, which can perhaps be measured in some situations, for example via a quantum anomaly, or indirectly detected with a specific heat jump. The method of analysis is a functional renormalization group that generalizes the Coulomb gas treatment of Kosterlitz and Thouless to arbitrary interactions and dimensions. In particular, we construct an exact non-perturbative technique for confining interactions between instantons, which introduce irreparable infra-red divergences in the standard perturbative approaches.

cond-mat.str-el↗

arXiv2024

Pseudogap phases, chiral anomaly and topological order with quantum loop entanglement

A many-body quantum system whose topological defects are conserved, abundant and mobile is a correlated quantum liquid. Since topological defects can be classified by homotopy groups, each homotopy identifies a class of quantum liquids. Here we explore the quantum liquids based on the $π_3(S^2)$ homotopy group, i.e. Hopf fibration. Their topologically non-trivial dynamics emerges from the interlinking between magnetic flux or skyrmion loops in the charge and spin sectors respectively. We lay down a field theory foundation for analyzing such states by naturally incorporating the well-known framing regularization into the theory, and constructing the appropriate topological Lagrangian terms. We show that at least two strongly correlated phases of interlinked loops can exist in $d=3$ spatial dimensions at zero and low finite temperatures. These phases are closely related to the chiral quantum anomaly and do not have an obvious topological order, but they are distinguished from the trivial disordered phase with a generalization of the Wilson loop operator. In $d=4$ spatial dimensions, interlinked loops are able to produce topological order at zero temperature, featuring charge, angular momentum and braiding fractionalization. We discuss some possible experimental signatures of loop entanglement in the quantum noise of charge currents.

cond-mat.str-el↗

arXiv2024

Topological order in spin nematics from the quantum melting of a disclination lattice

The topological defects of Spin($n+1$) nematics in two spatial dimensions, known as disclinations, are characterized by the $\pi_1(\mathbb{R}P^n) = \textrm{Z}_2$ homotopy group for $n\ge2$. We argue that incompressible quantum liquids of disclinations can exist as stable low-temperature phases and host composite quasiparticles which combine a fractional amount of fundamental Z$_2$ charge with a unit of topological charge. The four-fold topological ground state degeneracy on a torus admits a fermionic or semionic quasiparticle exchange statistics. The topological non-triviality of these states is visible in the existence of protected gapless edge modes. While the fermionic nematic and gapped Z$_2$ spin liquids have equivalent topological orders, they are still thermodynamically distinct due to having different edge modes, in analogy to the topologically non-trivial and trivial states of quantum spin-Hall systems. The analysis proceeds by recasting the Z$_2$ gauge theory of spin nematics as a continuum limit theory with a larger gauge structure. Nematic fractionalization parallels that of a quantum Hall liquid, but the large gauge symmetry restores the time-reversal symmetry and restricts the quasiparticle fusion rules and statistics. The conclusions from field theory analysis are complemented with the construction of plausible host microscopic models.

cond-mat.str-el↗

arXiv2022

Weyl-Luttinger phase transition in pyrochlore iridates revealed by Raman scattering

Pyrochlore iridates are thought to be a fertile ground for the realization of topologically non-trivial and strongly correlated states of matter. Here we provide a compelling evidence of interacting Weyl electrons in Nd$_2$Ir$_2$O$_7$ and quadratic band touching in Pr$_2$Ir$_2$O$_7$ by Raman scattering. We observe a magnetically-driven phase transition between the topological Weyl semimetal and a Luttinger semimetal with quadratic band touching in Nd$_2$Ir$_2$O$_7$. Our theoretical analysis of the Raman scattering from Weyl and Luttinger quasiparticles agrees with experimental observations, and enables a characterization of the material parameters while revealing interaction and disorder effects through a relatively short quasiparticle lifetime.

cond-mat.mtrl-sci↗

arXiv2021

Universal spin wave damping in magnetic Weyl semimetals

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, Gilbert damping by Weyl electrons is absent. 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.

cond-mat.str-el↗

arXiv2021

The dynamics of local magnetic moments induced by itinerant Weyl electrons

We derive the effective interactions between local magnetic moments which are mediated by Weyl electrons in magnetic topological semimetals. The resulting spin dynamics is governed by the induced Heisenberg, Kitaev and Dzyaloshinskii-Moriya (DM) interactions with extended range and oscillatory dependence on the distance between the spins. These interactions are realized in multiple competing channels shaped by the multitude of Weyl nodes in the electron spectrum. Microscopic spins need to be spatially modulated with a channel-dependent wavevector in order to take advantage of the interactions. The DM vector is parallel to the displacement between the two interacting spins, and requires the presence of Weyl electron Fermi surfaces. We also derive the Weyl-induced chiral three-spin interaction in the presence of an external magnetic field. This interaction has an extended range as well, and acts upon the spatially modulated spins in various channels. Its tendency is to produce a skyrmion lattice or a chiral spin liquid which exhibits topological Hall effect. Ultimately, the theory developed here addresses magnetic dynamics in relativistic metals even when chiral magnetism is microscopically precluded. We discuss insights into the ordered state of the magnetic Weyl semimetal NdAlSi.

cond-mat.str-el↗

arXiv2020

Incommensurate magnetism mediated by Weyl fermions in NdAlSi

Emergent relativistic quasiparticles in Weyl semimetals are the source of exotic electronic properties such as surface Fermi arcs, the anomalous Hall effect, and negative magnetoresistance, all observed in real materials. Whereas these phenomena highlight the effect of Weyl fermions on the electronic transport properties, less is known about what collective phenomena they may support. Here, we report a new Weyl semimetal, NdAlSi that offers an example. Using neutron diffraction, we report a long-wavelength magnetic order in NdAlSi whose periodicity is linked to the nesting vector between two topologically non-trivial Fermi pockets, which we characterize using density functional theory and quantum oscillation measurements. Our work provides a rare example of Weyl fermions driving collective magnetism.

cond-mat.str-el↗

arXiv2020

Finite momentum condensate brought on by Zeeman field

We study superfluid states in a two-dimensional fermionic attractive Hubbard model with Zeeman coupling to an external field. Focusing our attention on singlet pairing in both weak and strong coupling regimes, we reveal a rich phase diagram of finite momentum condensates which exhibits both Fulde-Ferrell and Larkin-Ovchinnikov orders at zero temperature. The latter are commensurate stripe states that spontaneously break a lattice symmetry; many stable ordering wavevectors are found as a function of particle density and Zeeman field. Stronger coupling significantly enhances the stability of the finite momentum condensates, but our numerical mean-field calculations underestimate the effect of fluctuations and indicate a possible localization near half-filling.

cond-mat.str-el↗

arXiv2020

Topological orders of monopoles and hedgehogs: From electronic and magnetic spin-orbit coupling to quarks

Topological states of matter are, generally, quantum liquids of conserved topological defects. We establish this by constructing and analyzing topological field theories which describe the dynamics of field singularities using gauge fields. Homotopy groups are utilized to identify topologically protected singularities, and the conservation of their protected number is captured by a topological action term that unambiguously obtains from the given set of symmetries. Stable phases of these theories include quantum liquids with emergent massless Abelian and non-Abelian gauge fields, as well as topological orders with long-range quantum entanglement, fractional excitations, boundary modes and unconventional responses to external perturbations. This paper focuses on the derivation of topological field theories and basic phenomenological characterization of topological orders associated with homotopy groups $π_n(S^n)$, $n\ge 1$. These homotopies govern monopole and hedgehog topological defects in $d=n+1$ dimensions, and enable the generalization of both weakly-interacting and fractional quantum Hall liquids of vortices to $d>2$. Hedgehogs have not been in the spotlight so far, but they are particularly important defects of magnetic moments because they can be stimulated in realistic systems with spin-orbit coupling, such as chiral magnets and $d=3$ topological materials. We predict novel topological orders in systems with U(1)$\times$Spin($d$) symmetry in which fractional electric charge attaches to hedgehogs. Monopoles, the analogous defects of charge or generic U(1) currents, may bind to hedgehogs via Zeeman effect, or effectively emerge in purely magnetic systems. The latter can lead to spin liquids with different topological orders than that of the RVB spin liquid. Charge fractionalization of quarks in atomic nuclei is also seen as possibly arising from the charge-hedgehog attachment.

cond-mat.str-el↗

arXiv2020

Quantum field theory of topological spin dynamics

We develop a field theory of quantum magnets and magnetic (semi)metals, which is suitable for the analysis of their universal and topological properties. The systems of interest include collinear, coplanar and general non-coplanar magnets. At the basic level, we describe the dynamics of magnetic moments using smooth vector fields in the continuum limit. Dzyaloshinskii-Moriya interaction is captured by a non-Abelian vector gauge field, and chiral spin couplings related to topological defects appear as higher-rank antisymmetric tensor gauge fields. We distinguish type-I and type-II magnets by their equilibrium response to the non-Abelian gauge flux, and characterize the resulting lattices of skyrmions and hedgehogs, the spectra of spin waves, and the chiral response to external perturbations. The general spin-orbit coupling of electrons is similarly described by non-Abelian gauge fields, including higher-rank tensors related to the electronic Berry flux. Itinerant electrons and local moments exchange their gauge fluxes through Kondo and Hund interactions. Hence, by utilizing gauge fields, this theory provides a unifying physical picture of ``intrinsic'' and ``topological'' anomalous Hall effects, spin-Hall effects, and other correlations between the topological properties of electrons and moments. We predict ``topological'' magnetoelectric effect in materials prone to hosting hedgehogs. Links to experiments and model calculations are provided by deriving the couplings and gauge fields from generic microscopic models, including the Hubbard model with spin-orbit interactions. We establish the possible existence of novel quantum spin liquids that exhibit a fractional magnetoelectric effect, and discuss a few applications to topological magnetic conductors like Mn$_3$Sn and Pr$_2$Ir$_2$O$_7$.

cond-mat.str-el↗

arXiv2014

Two-dimensional heavy fermions on the strongly correlated boundaries of Kondo topological insulators

Samarium hexaboride (SmB$_6$), a representative Kondo insulator, has been characterized recently as a likely topological insulator. It is also a material with strong electron correlations, evident by the temperature dependence of its bandgap and the existence of a nearly flat collective mode whose energy lies within the bandgap. Similar strong correlations can affect or even destabilize the two-dimensional metallic state of topological origin at the crystal boundary. Here we construct the minimal lattice model of the correlated boundary of topological Kondo insulators, and make phenomenological predictions for its possible ground states. Depending on the microscopic properties of the interface between the topological Kondo material and a conventional insulator, the boundary metal can exhibit a varied degree of hybridization between the $d$ and $f$ orbitals of the rare earth element, yielding a rich two-dimensional heavy fermion phenomenology. A pronounced participation of the $f$ orbitals is expected to create a heavy fermion Dirac metal, possibly unstable to a spin density wave, electron localization or even superconductivity. The opposite limit of "localized magnetic moments" helped by the partial Kondo screening on the crystal boundary can bring about a non-Fermi liquid of $d$ electrons that exhibits two-dimensional quantum electrodynamics, or other unconventional states. In addition, ultra-thin films made from topological Kondo insulators could open the possibility of creating exotic incompressible quantum liquids with non-Abelian fractional excitations, whose dynamics shaped by the strong Rashba spin-orbit coupling resembles that of fractional quantum Hall systems.

cond-mat.str-el↗

arXiv2014

Vortices and vortex states in Rashba spin-orbit-coupled condensates

The Rashba spin-orbit coupling is equivalent to the finite Yang-Mills flux of a static SU(2) gauge field. It gives rise to the protected edge states in two-dimensional topological band-insulators, much like magnetic field yields the integer quantum Hall effect. An outstanding question is which collective topological behaviors of interacting particles are made possible by the Rashba spin-orbit coupling. Here we addresses one aspect of this question by exploring the Rashba SU(2) analogues of vortices in superconductors. Using the Landau-Ginzburg approach and conservation laws, we classify the prominent two-dimensional condensates of two- and three-component spin-orbit-coupled bosons, and characterize their vortex excitations. There are two prominent types of condensates that take advantage of the Rashba spin-orbit coupling. Their vortices exist in multiple flavors whose number is determined by the spin representation, and interact among themselves through logarithmic or linear potentials as a function of distance. The vortices that interact linearly exhibit confinement and asymptotic freedom similar to quarks in quantum chromodynamics. One of the two condensate types supports small metastable neutral quadruplets of vortices, and their tiles as metastable vortex lattices. Quantum melting of such vortex lattices could give rise to non-Abelian fractional topological insulators, SU(2) analogues of fractional quantum Hall states. The physical systems in which these states could exist are trapped two- and three-component bosonic ultra-cold atoms subjected to artificial gauge fields, as well as solid-state quantum wells made either from Kondo insulators such as SmB$_6$ or conventional topological insulators interfaced with conventional superconductors.

cond-mat.quant-gas↗