Quantum Monte Carlo simulations are used to study the magnetic and transport properties of the Hubbard Model, and its strong coupling Heisenberg limit, on a one-third depleted square lattice. This is the geometry occupied, after charge ordering, by t
he spin-$frac{1}{2}$ Ni$^{1+}$ atoms in a single layer of the nickelate materials La$_4$Ni$_3$O$_8$ and (predicted) La$_3$Ni$_2$O$_6$. Our model is also a description of strained graphene, where a honeycomb lattice has bond strengths which are inequivalent. For the Heisenberg case, we determine the location of the quantum critical point (QCP) where there is an onset of long range antiferromagnetic order (LRAFO), and the magnitude of the order parameter, and then compare with results of spin wave theory. An ordered phase also exists when electrons are itinerant. In this case, the growth in the antiferromagnetic structure factor coincides with the transition from band insulator to metal in the absence of interactions.
Topological insulators in three dimensions are characterized by a Z2-valued topological invariant, which consists of a strong index and three weak indices. In the presence of disorder, only the strong index survives. This paper studies the topologica
l invariant in disordered three-dimensional system by viewing it as a super-cell of an infinite periodic system. As an application of this method we show that the strong index becomes non-trivial when strong enough disorder is introduced into a trivial insulator with spin-orbit coupling, realizing a strong topological Anderson insulator. We also numerically extract the gap range and determine the phase boundaries of this topological phase, which ?ts well with those obtained from self-consistent Born approximation (SCBA) and the transport calculations.
Disorder, ubiquitously present in solids, is normally detrimental to the stability of ordered states of matter. In this letter we demonstrate that not only is the physics of a strong topological insulator robust to disorder but, remarkably, under cer
tain conditions disorder can become fundamentally responsible for its existence. We show that disorder, when sufficiently strong, can transform an ordinary metal with strong spin-orbit coupling into a strong topological `Anderson insulator, a new topological phase of quantum matter in three dimensions.
Electrons on the surface of a strong topological insulator, such as Bi2Te3 or Bi1-xSnx, form a topologically protected helical liquid whose excitation spectrum contains an odd number of massless Dirac fermions. A theoretical survey and classification
is given of the universal features, observable by the ordinary and spin-polarized scanning tunneling spectroscopy, in the interference patterns resulting from the quasiparticle scattering by magnetic and non-magnetic impurities in such a helical liquid. Our results confirm the absence of backscattering from non-magnetic impurities observed in recent experiments and predict new interference features, uniquely characteristic of the helical liquid, when the scatterers are magnetic.
Itinerant electrons in a two-dimensional Kagome lattice form a Dirac semi-metal, similar to graphene. When lattice and spin symmetries are broken by various periodic perturbations this semi-metal is shown to spawn interesting non-magnetic insulating
phases. These include a two-dimensional topological insulator with a non-trivial Z_2 invariant and robust gapless edge states, as well as dimerized and trimerized `Kekule insulators. The latter two are topologically trivial but the Kekule phase possesses a complex order parameter with fractionally charged vortex excitations. A charge density wave is shown to couple to the Dirac fermions as an effective axial gauge field.
