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Register a new userFilling-enforced Kondo semimetals in two-dimensional non-symmorphic crystals
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We study the competition between Kondo screening and frustrated magnetism on the non-symmorphic Shastry-Sutherland Kondo lattice at a filling of two conduction electrons per unit cell. A previous analysis of this model identified a set of gapless partially Kondo screened phases intermediate between the Kondo-destroyed paramagnet and the heavy Fermi liquid. Based on crystal symmetries, we argue that (i)~both the paramagnet and the heavy Fermi liquid are {it semimetals} protected by a glide symmetry; and (ii)~partial Kondo screening breaks the symmetry, removing this protection and allowing the partially-Kondo-screened phase to be deformed into a Kondo insulator via a Lifshitz transition. We confirm these results using large-$N$ mean field theory and then use non-perturbative arguments to derive a generalized Luttinger sum rule constraining the phase structure of 2D non-symmorphic Kondo lattices beyond the mean-field limit.
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Filling-enforced Dirac semimetals, or those required at specific fillings by the combination of crystalline and time-reversal symmetries, have been proposed and discovered in numerous materials. However, Dirac points in these materials are not generally robust against breaking or modifying time-reversal symmetry. We present a new class of two-dimensional Dirac semimetal protected by the combination of crystal symmetries and a special, antiferromagnetic time-reversal symmetry. Systems in this class of magnetic layer groups, while having broken time-reversal symmetry, still respect the operation of time-reversal followed by a half-lattice translation. In contrast to 2D time-reversal-symmetric Dirac semimetal phases, this magnetic Dirac phase is capable of hosting just a single isolated Dirac point at the Fermi level, and that Dirac point can be stabilized solely by symmorphic crystal symmetries. We find that this Dirac point represents a new quantum critical point, and lives at the boundary between Chern insulating, antiferromagnetic topological crystalline insulating, and trivial insulating phases. We present density functional theoretic calculations which demonstrate the presence of this 2D magnetic Dirac semimetallic phase in FeSe monolayers and discuss the implications for engineering quantum phase transitions in these materials.
Band insulators appear in a crystalline system only when the filling -- the number of electrons per unit cell and spin projection -- is an integer. At fractional filling, an insulating phase that preserves all symmetries is a Mott insulator, i.e. it is either gapless or, if gapped, displays fractionalized excitations and topological order. We raise the inverse question -- at an integer filling is a band insulator always possible? Here we show that lattice symmetries may forbid a band insulator even at certain integer fillings, if the crystal is non-symmorphic -- a property shared by a majority of three-dimensional crystal structures. In these cases, one may infer the existence of topological order if the ground state is gapped and fully symmetric. This is demonstrated using a non-perturbative flux threading argument, which has immediate applications to quantum spin systems and bosonic insulators in addition to electronic band structures in the absence of spin-orbit interactions.
Luttingers theorem is a fundamental result in the theory of interacting Fermi systems: it states that the volume inside the Fermi surface is left invariant by interactions, if the number of particles is held fixed. Although this is traditionally justified using perturbation theory, it can be viewed as arising from a momentum balance argument that examines the response of the ground state to the insertion of a single flux quantum [M. Oshikawa, Phys. Rev. Lett. 84, 3370 (2000)]. This reveals that the Fermi sea volume is a topologically protected quantity. Extending this approach, I show that spinless or spin-rotation-preserving fermionic systems in non-symmorphic crystals possess generalized topological Luttinger invariants that can be nonzero even in cases where the Fermi sea volume vanishes. A nonzero Luttinger invariant then forces energy bands to touch, leading to semimetals whose gaplessness is thus rooted in topology; opening a gap without symmetry breaking automatically triggers fractionalization. The existence of these invariants is linked to the inability of non-symmorphic crystals to host band insulating ground states except at special fillings. I exemplify the use of these new invariants by showing that they distinguish various classes of two- and three-dimensional semimetals.
The variational cluster approach (VCA) based on the self-energy functional theory is applied to the two-dimensional symmetric periodic Anderson model at half filling. We calculate a variety of physical quantities including the staggered moments and single-particle spectra at zero temperature to show that the symmetry breaking due to antiferromagnetic ordering occurs in the strong coupling region, whereas in the weak coupling region, the Kondo insulating state without symmetry breaking is realized. The critical interaction strength is estimated. We thus demonstrate that the phase transition due to competition between antiferromagnetism and Kondo screening in the model can be described quantitatively by VCA.
There is considerable current interest to explore electronic topology in strongly correlated metals, with heavy fermion systems providing a promising setting. Recently, a Weyl-Kondo semimetal phase has been concurrently discovered in theoretical and experimental studies. The theoretical work was carried out in a Kondo lattice model that is time-reversal invariant but inversion-symmetry breaking. In this paper, we show in some detail how nonsymmorphic space-group symmetry and strong correlations cooperate to form Weyl nodal excitations with highly reduced velocity and pin the resulting Weyl nodes to the Fermi energy. A tilted variation of the Weyl-Kondo solution is further analyzed here, following the recent consideration of such effect in the context of understanding a large spontaneous Hall effect in Ce$_3$Bi$_4$Pd$_3$ (Dzsaber et al., arXiv:1811.02819). We discuss the implications of our results for the enrichment of the global phase diagram of heavy fermion metals, and for the space-group symmetry enforcement of topological semimetals in other strongly correlated settings.
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