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A number of strongly correlated heavy-fermion compounds, such as samarium (Sm), ytterbium (Yb), plutonium (Pu) hexaboride, are predicted to become topological insulators at low temperatures. These systems support massless Dirac fermions near certain (three) points of the surface Brillouin zone, hereafter referred to as the valleys. In strong perpendicular magnetic fields, the conical Dirac dispersions of these surface states quench onto three sets of Landau levels and we predict various possible hierarchies of incompressible quantum Hall states on the surface of hexaborides. In addition, we address the effects of strong electron-electron interaction within the surface zeroth Landau levels. Specifically, we show that depending on the relative strength of the long-range (Coulomb-type) and the finite-range (Hubbard-type) interactions, the ground state can display either a valley-polarized or a valley-coherent distribution of electronic density. We also show that the transition between two valley-polarized states is always discontinuous, while that between a valley-polarized and a valley-coherent phase is continuous. The Zeeman splitting and/or an applied uniaxial strain on the surface can drive the system through various quantum phase transitions and place it in different broken-symmetry phases. Application of uniaxial strain is also shown to considerably modify the precise sequence of quantum Hall states. We also highlight the role of topology in determining the broken-symmetry phases, disorder on the surface of topological hexaborides in strong magnetic fields. [ABSTRACT FROM AUTHOR]

We consider the gapless modes along the vortex line of the fully gapped, momentum independent paired states of three-dimensional Dirac fermions. For this, we require the solution of fermion zero modes of the corresponding two-dimensional problem in the presence of a point vortex, in the plane perpendicular to the vortex line. Based on the spectral symmetry requirement for the existence of the zero mode, we identify the appropriate generalized Jackiw-Rossi Hamiltonians for different paired states. A four-dimensional generalized Jackiw-Rossi Hamiltonian possesses spectral symmetry with respect to an antiunitary operator, and gives rise to a single zero mode only for the odd vorticity, which is formally described by a Z2 index. In the presence of generic perturbations such as chemical potential, Dirac mass, and Zeeman couplings, the associated two-dimensional problem for the odd party topological superconducting state maps onto m-o copies of generalized Jackiw-Rossi Hamiltonian, and consequently an odd vortex binds two Majorana fermions. In contrast, there are no zero-energy states for the topologically trivial 5-wave superconductor in the presence of any chiral symmetry breaking perturbation in the particle-hole channel, such as regular Dirac mass. We show that the number of one-dimensional dispersive modes along the vortex line is also determined by the index of the associated two-dimensional problem. For an axial superfluid state in the presence of various perturbations, we discuss the consequences of the Z2 index on the anomaly equations. [ABSTRACT FROM AUTHOR]

We investigate the nature of the ordering among magnetic adatoms, randomly deposited on the surface of topological insulators. Restricting ourselves to dilute impurity and weak coupling (between itinerant fermion and magnetic impurities) limit, we show that for arbitrary amount of chemical doping away from the apex of the surface Dirac cone the magnetic impurities tend to arrange themselves in a spin-density-wave pattern, with the periodicity approximately π/kF, where kF is the Fermi wave vector, when magnetic moment for impurity adatoms is isotropic. However, when magnetic moment possesses strong Ising or easy-axis anisotropy, pursuing both analytical and numerical approaches we show that the ground state is ferromagnetic for low to moderate chemical doping, despite the fragmentation of the system into multiple ferromagnetic islands. For high doping away from the Dirac point as well, the system appears to fragment into many ferromagnetic islands, but the magnetization in these islands is randomly distributed. Such magnetic ordering with net zero magnetization is referred to here as ferromagnetic spin glass, which is separated from the pure ferromagnet state by a first order phase transition. We generalize our analysis for cubic topological insulators (supporting three Dirac cones on a surface) and demonstrate that the nature of magnetic orderings and the transition between them remains qualitatively the same. We also discuss the possible relevance of our analysis to recent experiments. [ABSTRACT FROM AUTHOR]

We theoretically address the effects of strong magnetic fields in three-dimensional Weyl semimetals (WSMs) built out of Weyl nodes with a monopole charge n. For n=1, 2, and 3 we realize single, double, and triple WSM, respectively, and the monopole charge n determines the integer topological invariant of the WSM. Within the linearized continuum description, the quasiparticle spectrum is then composed of Landau levels (LLs), containing exactly n number of chiral zeroth Landau levels (ZLLs), irrespective of the orientation of the magnetic field. In the presence of strong backscattering, for example (due to quenched disorder associated with random impurities), these systems generically give rise to longitudinal magnetotransport. Restricting ourselves to the quantum limit (and assuming only the subspace of the ZLLs to be partially filled) and mainly accounting for Gaussian impurities, we show that the longitudinal magnetoconductivity (LMC) in all members of the Weyl family displays a positive linear-B scaling when the field is applied along the axis that separates the Weyl nodes. But, in double and triple WSM, LMC displays a smooth crossover to a nonlinear B dependence as the field is tilted away from such a high-symmetry direction. In addition, due to the enhanced density of states, the LL quantization can trigger instabilities toward the formation of translational symmetry-breaking density-wave orderings for sufficiently weak interaction (BCS instability), which gaps out the ZLLs. Concomitantly as the temperature (magnetic field) is gradually decreased (increased) the LMC becomes negative. Thus WSMs with arbitrary monopole charge (n) can host an intriguing interplay of LL quantization, longitudinal magnetotransport (a possible manifestation of one-dimensional chiral or axial anomaly), and density-wave ordering, when placed in a strong magnetic field. [ABSTRACT FROM AUTHOR]

Driven quantum materials often feature emergent topology, otherwise absent in static crystals. Dynamic bulk-boundary correspondence, encoded by nondissipative gapless modes residing near the Floquet zone center and/or boundaries, is its most prominent example. Here we show that topologically robust gapless dispersive modes appear along the grain boundaries, embedded in the interior of Floquet topological crystals, when the Floquet-Bloch band inversion occurring at a finite momentum ( K inv Flq ) and the Burgers vector ( b ) of the constituting array of dislocations satisfy K inv Flq · b = π (modulo 2 π ). Such nondissipative gapless states can be found near the center and/or edges of the Floquet Brillouin zone, irrespective of the drive protocol. We showcase these general outcomes for two-dimensional driven time-reversal symmetry breaking insulators. Promising experimental platforms hosting such dynamic topological dispersive bands in real materials are discussed., Competing Interests: Declarations. Competing interests: The authors declare no competing interests., (© 2025. The Author(s).)