Antiferromagnetic Chern Insulators in Noncentrosymmetric Systems

Abstract

We investigate a new class of topological antiferromagnetic (AF) Chern insulators driven by electronic interactions in two-dimensional systems without inversion symmetry. Despite the absence of a net magnetization, AF Chern insulators (AFCI) possess a nonzero Chern number C and exhibit the quantum anomalous Hall effect (QAHE). Their existence is guaranteed by the bifurcation of the boundary line of Weyl points between a quantum spin Hall insulator and a topologically trivial phase with the emergence of AF long-range order. As a concrete example, we study the phase structure of the honeycomb lattice Kane-Mele model as a function of the inversion-breaking ionic potential and the Hubbard interaction. We find an easy z axis C=1 AFCI phase and a spin-flop transition to a topologically trivial xy plane collinear antiferromagnet. We propose experimental realizations of the AFCI and QAHE in correlated electron materials and cold atom systems.

Time-Reversal Symmetry-Breaking Nematic Insulators near Quantum Spin Hall Phase Transitions

“…At large values of A the NI/QSHI transition is not altered by interactions. At intermediate values of A, we find that the NI/QSHI transition proceeds via an intermediate QAHI state that is separated from both NI and QSHI states by first-order phase transitions, similar to the behavior predicted by dynamic mean-field theory for Hubbard model systems [37] and by mean-field theory for interacting Kane-Mele Hubbard models [38]. The QAHI phase is characterized by a U s z τ z mean-field term and has a Φ 2 TRSB order parameter.…”

Interaction-driven topological phase transitions in fermionic SU($3$) systems

“…2(a) that the Hubbard interaction drives the NI into the QHI and subsequently the QHI into the MMI. Similar sequences of phase transitions are found in SU(2) topological systems [29][30][31][32][33][34]. Upon increasing the TSP to ∆ = 11t in Fig.…”

“…In recent years, there has been a large interest in interacting topological insulators [27], with a focus on realizing topological many-body quantum states such as fractional QHI [28] and studying interaction-driven topological phase transitions [29][30][31][32][33][34]. In the time-reversalinvariant Harper-Hofstadter-Hubbard model with a spinmixing hopping term an interaction-driven NI-to-QSHI transition is identified [29], which is found also in an extended Bernevig-Hughes-Zhang-Hubbard model [30,31].…”

“…The competition of the Hubbard interaction and the stag-gered potential in the Haldane-Hubbard model stabilizes an antiferromagnetic Chern insulator (AFCI) where one of the spin components is in the quantum Hall and the other in the normal state [32,33]. Such an AFCI is proposed also for the Kane-Mele-Hubbard model but with a spontaneous breaking of the time-reversal symmetry [34].…”

Correlation Effects in Quadrupole Insulators: a Quantum Monte Carlo Study

“…The predicted Majorana corner/hinge states in such systems are promising building blocks (qubits) for realizing quantum computation [14,15].Attracted by the novel properties and potential applications of HOTIs, many theoretical works have been done to predict HOTIs in realistic systems, such as quasicrystals, sonic crystals, non-hermitian systems, and solid state systems [16][17][18][19][20][21][22][23]. And some experimental works have even shown the direct observation of HOTIs in photonic/phononic crystals, electrical circuits as well as crystalline solids, such as bismuth [24][25][26][27][28][29].Unlike bosonic systems, fermionic systems with spin degrees of freedom are subjected to the Coulumb repulsion which may give rise to many exotic phenomena [30][31][32][33][34][35][36][37]. However, there are only a few studies which discuss correlation effects in HOTIs [38][39][40].…”