Random flux is commonly believed to be incapable of driving metal-insulator transitions. Surprisingly, we show that random flux can after all induce a metal-insulator transition in the two-dimensional Su-Schrieffer-Heeger model, thus reporting the fi
rst example of such a transition. Remarkably, we find that the resulting insulating phase can even be a higher-order topological insulator with zero-energy corner modes and fractional corner charges, rather than a conventional Anderson insulator. Employing both level statistics and finite-size scaling analysis, we characterize the metal-insulator transition and numerically extract its critical exponent as $ u=2.48pm0.08$. To reveal the physical mechanism underlying the transition, we present an effective band structure picture based on the random flux averaged Greens function.
Magnetic oscillations of Dirac surface states of topological insulators are expected to be associated with the formation of Landau levels or the Aharonov-Bohm effect. We instead study the conductance of Dirac surface states subjected to an in-plane m
agnetic field in presence of a barrier potential. Strikingly, we find that, in the case of large barrier potentials, the surface states exhibit pronounced oscillations in the conductance when varying the magnetic field, in the textit{absence} of Landau levels or the Aharonov-Bohm effect. These novel magnetic oscillations are attributed to the emergence of textit{super-resonant regimes} by tuning the magnetic field, in which almost all propagating electrons cross the barrier with perfect transmission. In the case of small and moderate barrier potentials, we also identify a positive magnetoconductance which is due to the increase of the Fermi surface by tilting the surface Dirac cone. Moreover, we show that for weak magnetic fields, the conductance displays a shifted sinusoidal dependence on the field direction with period $pi$ and phase shift determined by the tilting direction with respect to the field direction. Our predictions can be applied to many topological insulators, such as HgTe and Bi$_{2}$Se$_{3}$, and provide important insights into exploring and understanding exotic magnetotransport properties of topological surface states.
We propose an intrinsic 3D Fabry-Perot type interferometer, coined higher-order interferometer, that utilizes the chiral hinge states of second-order topological insulators and cannot be equivalently mapped to 2D space because of higher-order topolog
y. Quantum interference patterns in the two-terminal conductance of this interferometer are controllable not only by tuning the strength but also, particularly, by rotating the direction of the magnetic field applied perpendicularly to the transport direction. Remarkably, the conductance exhibits a characteristic beating pattern with multiple frequencies with respect to field strength or direction. Our novel interferometer provides feasible and robust magneto-transport signatures to probe the particular hinge states of higher-order topological insulators.
Chiral Majorana hinge modes are characteristic of a second-order topological superconductor in three dimensions. Here we systematically study pairing symmetry in the point group D_{2h}, and find that the leading pairing channels can be of s-, d-, and
s+id-wave pairing in Dirac materials. Except for the odd-parity s-wave pairing superconductivity, the s+id-wave pairing superconductor is topologically nontrivial and possesses Majorana hinge and surface modes. The chiral Majorana hinge modes can be characterized by a winding number of the quadrupole moment, or quantized quadruple moment at the symmetrically invariant point. Our findings suggest the strong spin-orbital coupling, crystalline symmetries and electron-electron interaction in the Dirac materials may provide a microscopic mechanism to realize chiral Majorana hinge modes without utilizing the proximity effect or external fields.
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.
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 underlyin
g 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.
As the three-dimensional analogs of graphene, Weyl semimetals display signatures of chiral anomaly which arises from charge pumping between the lowest chiral Landau levels of the Weyl nodes in the presence of parallel electric and magnetic fields. In
this work, we study the pseudo chiral anomaly and its transport signatures in graphene ribbon with zigzag edges. Here pseudo refers to the case where the inverse of width of zigzag graphene ribbon plays the same role as magnetic field in three-dimensional Weyl semimetals. The valley chiral bands in zigzag graphene ribbons can be introduced by edge potentials, giving rise to the nonconservation of chiral current, i.e., pseudo chiral anomaly, in the presence of a longitudinal electric field. Further numerical results reveal that pseudo magnetoconductivity of zigzag graphene ribbons is positive and has a nearly quadratic dependence on the pseudofield, which is regarded as the transport signature of pseudo chiral anomaly.
We propose an interferometer for chiral Majorana modes where the interference effect is caused and controlled by a Josephson junction of proximity-induced topological superconductors, hence, a Majorana-Josephson interferometer. This interferometer is
based on a two-terminal quantum anomalous Hall bar, and as such its transport observables exhibit interference patterns depending on both the Josephson phase and the junction length. Observing these interference patterns will establish quantum coherent Majorana transport and further provide a powerful characterization tool for the relevant system.
The robustness of quantum edge transport in InAs/GaSb quantum wells in the presence of magnetic fields raises an issue on the fate of topological phases of matter under time-reversal symmetry breaking. A peculiar band structure evolution in InAs/GaSb
quantum wells is revealed: the electron subbands cross the heavy hole subbands but anticross the light hole subbands. The topologically protected band crossing point (Dirac point) of the helical edge states is pulled to be close to and even buried in the bulk valence bands when the system is in a deeply inverted regime, which is attributed to the existence of the light hole subbands. A sizable Zeeman energy gap verified by the effective g-factors of edge states opens at the Dirac point by an in-plane or perpendicular magnetic field, however it can also be hidden in the bulk valance bands. This provides a plausible explanation for the recent observation on the robustness of quantum edge transport in InAs/GaSb quantum wells subjected to strong magnetic fields.
Graphene is a monolayer of carbon atoms packed into a hexagon lattice to host two pairs of massless two-dimensional Dirac fermions in the absence of or with negligible spin-orbit coupling. It is known that the existence of non-zero electric polarizat
ion in reduced momentum space which is associated with a hidden chiral symmetry will lead to the zero-energy flat band of zigzag nanoribbon. The Adler-Bell-Jackiw chiral anomaly or non-conservation of chiral charges at different valleys can be realized in a confined ribbon of finite width. In the laterally diffusive regime, the finite-size correction to conductivity is always positive and goes inversely with the square of the lateral dimension W, which is different from the finite-size correction inversely with W from boundary modes. This anomalous finite-size conductivity reveals the signature of the chiral anomaly in graphene, and is measurable experimentally.
