Spontaneous Quantum Hall Effect via a Thermally Induced Quadratic Fermi Point

Abstract

Gapless electronic systems containing topologically nontrivial Fermi points are sources of various topological insulators. Whereas most of these special band-crossing points are built in the electronic structure of the non-interacting lattice models, we show that a quadratic Fermi point characterized by a non-zero winding number emerges with a collinear triple-Q spin-density-wave state that arises from a perfectly nested but topologically trivial Fermi surface. We obtain a universal low-energy Hamiltonian for the quadratic Fermi point and show that such collinear orderings are unstable against the onset of scalar spin chirality that opens a gap and induces a spontaneous quantum Hall insulator as the temperature tends to zero.

Exotic magnetic orderings in the kagome Kondo-lattice model

“…This is consistent with the fact that the system remains gapless [ Fig. 10(b)] at the Γ-point [24,26]. To shed light on the selection of the triple-Q order, we note that the couplings between electrons are proportional to the product w Another interesting spectral feature of the B 1 symmetry triple-Q state is the appearance of Dirac nodes at only one of the two inequivalent K-points [ Fig.…”

“…Due to the fact that the collinear A 1 state uses only a single Q η per kagome sublattice, it fulfills the requirement of uniform spin length, whereas the (collinear) B 1,2 states do not. We note that the A 1 state would be the kagome lattice version of the uniaxial spin density wave state reported in [26,53,54]. These collinear spin states all manifestly break translational invariance as a consequence of ordering at finite Q η momentum vectors.…”

“…This mechanism does not require band structures with Dirac points. QAH states may also arise from weakcoupling instabilities at quadratic band crossings [24][25][26][27][28] and nested Fermi surfaces [16]. Nonzero chirality implies broken time-reversal and spatial parity symmetries, a necessary ingredient for QAH states.…”

Multi-Qhexagonal spin density waves and dynamically generated spin-orbit coupling: Time-reversal invariant analog of the chiral spin density wave

“…A number of studies have addressed the effect of interactions between the three flavors of saddle-point electrons, predicting exciting unconventional correlated phases such as topological chiral superconductivity, as well as Cherninsulating chiral spin density waves [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. These works highlight the rich physics expected in a broad class of (doped) hexagonal materials, with doped graphene as a concrete example.…”

Phase diagram of the Shastry-Sutherland Kondo lattice model with classical localized spins: a variational calculation study

“…The chiral nature of these states breaks both parity and time-reversal symmetries. Such non-coplanar spin orderings induce novel quantum phases and phenomena (that are not observed for their coplanar or collinear counterparts) such as the geometric or topological Hall effect (THE) where there is a Hall conductivity even in the absence of an external applied magnetic field [18,19,20,21]. The itinerant electrons acquire an extra Berry phase when its spin follows the spatially varying magnetization present in these spin textures -equivalent to an orbital coupling to a magnetic field.…”