Higher-order topological Mott insulator on the pyrochlore lattice

Abstract

We provide the first unbiased evidence for a higher-order topological Mott insulator in three dimensions by numerically exact quantum Monte Carlo simulations. This insulating phase is adiabatically connected to a third-order topological insulator in the noninteracting limit, which features gapless modes around the corners of the pyrochlore lattice and is characterized by a $${\mathbb {Z}}_{4}$$ Z 4 spin-Berry phase. The difference between the correlated and non-correlated topological phases is that in the former phase the gapless corner modes emerge only in spin excitations being Mott-like. We also show that the topological phase transition from the third-order topological Mott insulator to the usual Mott insulator occurs when the bulk spin gap solely closes.

Modification of topological corner excitations at the interplay of boundary geometry and Coulomb interaction

“…Meanwhile the noninteracting topological systems are well described (and fully classified in the case of the conventional topological systems), the properties of interacting topological systems are under active consideration [19][20][21][22] along with the proper topological invariants in such systems [23][24][25]. Nevertheless, the interacting HOTSCs remain yet poorly described, in spite of the quantity of effects to be found in such systems, such as destruction of topological states in 3D systems [26] or appearance of new topological classes [27][28][29].…”

Unconventional ferromagnetism and spin-triplet superconductivity in the imbalanced Kagome-lattice Hubbard model

“…The existing theoretical results in the frustrated lattices are largely obtained by the density matrix renormalization group method on cylinders, since the DQMC method is usually blocked by the infamous sign problem due to the lack of particle-hole symmetry, thus are restricted to rather high temperatures. In the context of higher-order topological Mott insulator on kagome lattice, it is proposed that the sign problem can be avoided by simply changing the sign of the hopping amplitude of one spin species 31,32 . Hence the resulting signproblem-free Hamiltonian becomes an ideal platform to investigate the interplay between geometry frustration and electron-electron correlations for DQMC simulations.…”

Traversing the pyrochlore stability diagram; microwave-assisted synthesis and discovery of mixed B-site Ln$_2$InSbO$_7$ family

“…The flexibility to decorate the frustrated lattice with lanthanide elements of varying single-ion anisotropy, moment size, and radii -combined with the steric and chemical flexibity offered by the B-site -have cemented the pyrochlore family as a fruitful arena for the pursuit of the emergence of exotic and novel magnetic ground states. Experimental and theoretical studies alike have proposed the Ln 2 B 2 O 7 pyrochlores as a means to realize a myriad of properties ranging from unconventional long-range order [2][3][4][5][8][9][10][11][12][13][14][15], unconventional spin-glass behavior [3,[16][17][18][19][20][21][22][23][24][25][26][27], topologically-nontrivial electronic states [28][29][30][31][32][33][34][35][36], spin ices [12,[37][38][39][40][41][42][43][44][45][46][47], magn...…”