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The modern theory of electric polarization has recently been extended to higher multipole moments, such as quadrupole and octupole moments. The higher electric multipole insulators are essentially topological crystalline phases protected by underlying crystalline symmetries. Henceforth, it is natural to ask what are the consequences of symmetry breaking in these higher multipole insulators. In this work, we investigate topological phases and the consequences of symmetry breaking in generalized electric quadrupole insulators. Explicitly, we generalize the Benalcazar-Bernevig-Hughes model by adding specific terms in order to break the crystalline and non-spatial symmetries. Our results show that chiral symmetry breaking induces an indirect gap phase which hides corner modes in bulk bands, ruining the topological quadrupole phase. We also demonstrate that quadrupole moments can remain quantized even when mirror symmetries are absent in a generalized model. Furthermore, it is shown that topological quadrupole phase is robust against a unique type of disorder presented in the system.
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We investigate disorder-driven topological phase transitions in quantized electric quadrupole insulators. We show that chiral symmetry can protect the quantization of the quadrupole moment $q_{xy}$, such that the higher-order topological invariant is well-defined even when disorder has broken all crystalline symmetries. Moreover, nonvanishing $q_{xy}$ and consequent corner modes can be induced from a trivial insulating phase by disorder that preserves chiral symmetry. The critical points of such topological phase transitions are marked by the occurrence of extended boundary states even in the presence of strong disorder. We provide a systematic characterization of these disorder-driven topological phase transitions from both bulk and boundary descriptions.
We consider a three-dimensional topological insulator (TI) wire with a non-uniform chemical potential induced by gating across the cross-section. This inhomogeneity in chemical potential lifts the degeneracy between two one-dimensional surface state subbands. A magnetic field applied along the wire, due to orbital effects, breaks time-reversal symmetry and lifts the Kramers degeneracy at zero-momentum. If placed in proximity to an $s$-wave superconductor, the system can be brought into a topological phase at relatively weak magnetic fields. Majorana bound states (MBSs), localized at the ends of the TI wire, emerge and are present for an exceptionally large region of parameter space in realistic systems. Unlike in previous proposals, these MBSs occur without the requirement of a vortex in the superconducting pairing potential, which represents a significant simplification for experiments. Our results open a pathway to the realisation of MBSs in present day TI wire devices.
Higher-rank electric/magnetic multipole moments are attracting attention these days as candidate order parameters for exotic material phases. However, quantum-mechanical formulation of those multipole moments is still an ongoing issue. In this paper, we propose a thermodynamic definition of electric quadrupole moments as a measure of symmetry breaking, following previous studies of orbital magnetic dipole moments and magnetic quadrupole moments. The obtained formulas are illustrated with a model of orbital-ordered nematic phases of iron-based superconductors.
A quadrupole topological insulator, being one higher-order topological insulator with nontrivial quadrupole quantization, has been intensely investigated very recently. However, the tight-binding model proposed for such emergent topological insulators demands both positive and negative hopping coefficients, which imposes an obstacle in practical realizations. Here we introduce a feasible approach to design the sign of hopping in acoustics, and construct the first acoustic quadrupole topological insulator that stringently emulates the tight-binding model. The inherent hierarchy quadrupole topology has been experimentally confirmed by detecting the acoustic responses at the bulk, edge and corner of the sample. Potential applications can be anticipated for the topologically robust in-gap states, such as acoustic sensing and energy trapping.
We consider extended Hubbard models with repulsive interactions on a Honeycomb lattice and the transitions from the semi-metal phase at half-filling to Mott insulating phases. In particular, due to the frustrating nature of the second-neighbor repulsive interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spinful fermion models, respectively. We present the mean-field phase diagram and consider the effects of fluctuations within the random phase approximation (RPA). Functional renormalization group analysis also show that these states can be favored over the topologically trivial Mott insulating states.
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