Moire heterobilayer transition metal dichalcogenides (TMDs) emerge as an ideal system for simulating the single-band Hubbard model and interesting correlated phases have been observed in these systems. Nevertheless, the moire bands in heterobilayer T
MDs were believed to be topologically trivial. Recently, it was reported that both a quantum valley Hall insulating state at filling $ u=2$ (two holes per moire unit cell) and a valley polarized quantum anomalous Hall state at filling $ u=1$ were observed in AB stacked moire MoTe$_2$/WSe$_2$ heterobilayers. However, how the topologically nontrivial states emerge is not known. In this work, we propose that the pseudo-magnetic fields induced by lattice relaxation in moire MoTe$_2$/WSe$_2$ heterobilayers could naturally give rise to moire bands with finite Chern numbers. We show that a time-reversal invariant quantum valley Hall insulator is formed at full-filing $ u=2$, when two moire bands with opposite Chern numbers are filled. At half-filling $ u=1$, Coulomb interaction lifts the valley degeneracy and results in a valley polarized quantum anomalous Hall state, as observed in the experiment. Our theory identifies a new way to achieve topologically non-trivial states in heterobilayer TMD materials.
In recent years, it has been shown that Berry curvature monopoles and dipoles play essential roles in the anomalous Hall effect and the nonlinear Hall effect respectively. In this work, we demonstrate that Berry curvature multipoles (the higher momen
ts of Berry curvatures at the Fermi energy) can induce higher-order nonlinear anomalous Hall (NLAH) effect. Specifically, an AC Hall voltage perpendicular to the current direction emerges, where the frequency is an integer multiple of the frequency of the applied current. Importantly, by analyzing the symmetry properties of all the 3D and 2D magnetic point groups, we note that the quadrupole, hexapole and even higher Berry curvature moments can cause the leading-order frequency multiplication in certain materials. To provide concrete examples, we point out that the third-order NLAH voltage can be the leading-order Hall response in certain antiferromagnets due to Berry curvature quadrupoles, and the fourth-order NLAH voltage can be the leading response in the surface states of topological insulators induced by Berry curvature hexapoles. Our results are established by symmetry analysis, effective Hamiltonian and first-principles calculations. Other materials which support the higher-order NLAH effect are further proposed, including 2D antiferromagnets and ferromagnets, Weyl semimetals and twisted bilayer graphene near the quantum anomalous Hall phase.
In this work, we demonstrate that making a cut (a narrow vacuum regime) in the bulk of a quantum anomalous Hall insulator (QAHI) creates a topologically protected single helical channel with counter-propagating electron modes, and inducing supercondu
ctivity on the helical channel through proximity effect will create Majorana zero energy modes (MZMs) at the ends of the cut. In this geometry, there is no need for the proximity gap to overcome the bulk insulating gap of the QAHI to create MZMs as in the two-dimensional QAHI/superconductor (QAHI/SC) heterostructures. Therefore, the topological regime with MZMs is greatly enlarged. Furthermore, due to the presence of a single helical channel, the generation of low energy in-gap bound states caused by multiple conducting channels is avoided such that the MZMs can be well separated from other in-gap excitations in energy. This simple but practical approach allows the creation of a large number of MZMs in devices with complicated geometry such as hexons for measurement-based topological quantum computation. We further demonstrate how braiding of MZMs can be performed by controlling the coupling strength between the counter-propagating electron modes.
Recently, it was pointed out that all chiral crystals with spin-orbit coupling (SOC) can be Kramers Weyl semimetals (KWSs) which possess Weyl points pinned at time-reversal invariant momenta. In this work, we show that all achiral non-centrosymmetric
materials with SOC can be a new class of topological materials, which we term Kramers nodal line metals (KNLMs). In KNLMs, there are doubly degenerate lines, which we call Kramers nodal lines (KNLs), connecting time-reversal invariant momenta. The KNLs create two types of Fermi surfaces, namely, the spindle torus type and the octdong type. Interestingly, all the electrons on octdong Fermi surfaces are described by two-dimensional massless Dirac Hamiltonians. These materials support quantized optical conductance in thin films. We further show that KNLMs can be regarded as parent states of KWSs. Therefore, we conclude that all non-centrosymmetric metals with SOC are topological, as they can be either KWSs or KNLMs.
Recent experiments reported gate-induced superconductivity in the monolayer 1T$$-WTe$_2$ which is a two-dimensional topological insulator in its normal state [1, 2]. The in-plane upper critical field $B_{c2}$ is found to exceed the conventional Pauli
paramagnetic limit $B_p$ by 1-3 times. The enhancement cannot be explained by conventional spin-orbit coupling which vanishes due to inversion symmetry. In this work, we unveil some distinctive superconducting properties of centrosymmetric 1T$$-WTe$_2$ which arise from the coupling of spin, momentum and band parity degrees of freedom. As a result of this spin-orbit-parity coupling: (i) there is a first-order superconductor-metal transition at $B_{c2}$ much higher than the Pauli paramagnetic limit $B_p$, (ii) spin-susceptibility is anisotropic with respect to in-plane directions and results in anisotropic $B_{c2}$ and (iii) the $B_{c2}$ exhibits a strong gate dependence as the spin-orbit-parity coupling is significant only near the topological band crossing points. The importance of SOPC on the topologically nontrivial inter-orbital pairing phase is also discussed. Our theory generally applies to centrosymmetric materials with topological band
Recently, it has been pointed out that the twisting of bilayer WSe$_2$ would generate topologically non-trivial flat bands near the Fermi energy. In this work, we show that twisted bilayer WSe$_2$ (tWSe$_2$) with uniaxial strain exhibits a large nonl
inear Hall (NLH) response due to the non-trivial Berry curvatures of the flat bands. Moreover, the NLH effect is greatly enhanced near the topological phase transition point which can be tuned by a vertical displacement field. Importantly, the nonlinear Hall signal changes sign across the topological phase transition point and provides a way to identify the topological phase transition and probe the topological properties of the flat bands. The strong enhancement and high tunability of the NLH effect near the topological phase transition point renders tWSe$_2$ and related moire materials new platforms for rectification and second harmonic generations.
In recent years, signatures of Majorana fermions have been demonstrated experimentally in several superconducting systems. However, finding systems which can be scaled up to accommodate a large number of Majorana fermions for quantum computation rema
ins a major challenge for experimentalists. In a recent work [1], signatures of a pair of Majorana zero modes (MZMs) were found in a new experimental platform formed by EuS islands deposited on top of a gold wire which were made superconducting through proximity coupling to a superconductor. In this work, we provide a theoretical explanation for how MZMs can be formed in EuS/Au/superconductor heterostructures. This simple experimental setup provides a new route for realizing a large number of Majorana fermions for quantum computations.
An external magnetic field is needed to drive a nanowire in proximity to an s-wave superconductor into a topological regime which supports Majorana end states. However, a magnetic field generally suppresses the proximity superconducting gap induced o
n the nanowire. In recent experiments using InSb nanowires coupled to Al, the induced proximity gap vanishes at magnetic fields B~1T. This results in a small superconducting gap on the wire and a narrow topological regime which is proportional to the strength of the magnetic field. In this work, we show that by placing nanowires in proximity to recently discovered Ising superconductors such as the atomically thin transition-metal dichalcogenide(TMD) NbSe2, the topological superconducting gap on the wire can maintain at a large magnetic field as strong as B~10T. This robust topological superconducting gap is induced by the unique equal-spin triplet Cooper pairs of the parent Ising superconductor. The strong magnetic field allows a topological regime ten times larger than those in InSb wires coupled to Al. Our work establishes a realistic platform for building robust Majorana-based qubits.
Quantum anomalous Hall insulator/superconductor heterostructures emerged as a competitive platform to realize topological superconductors with chiral Majorana edge states as shown in recent experiments [He et al. Science {bf 357}, 294 (2017)]. Howeve
r, chiral Majorana modes, being extended, cannot be used for topological quantum computation. In this work, we show that quasi-one-dimensional quantum anomalous Hall structures exhibit a large topological regime (much larger than the two-dimensional case) which supports localized Majorana zero energy modes. The non-Abelian properties of a cross-shaped quantum anomalous Hall junction is shown explicitly by time-dependent calculations. We believe that networks of such quasi-one-dimensional quantum anomalous Hall systems can be easily fabricated for scalable topological quantum computation.
