The hybrid-order topology of weak topological insulators

We consider weak topological insulators with a twofold rotation symmetry around the dark direction, and show that these systems can be endowed with the topological crystalline structure of a higher-order topological insulator protected by rotation symmetry. These hybrid-order weak topological insulators display surface Dirac cones on all surfaces. Translational symmetry breaking perturbations gap the Dirac cones on the side surfaces leaving anomalous helical hinge modes behind. We also prove that the existence of this topological phase comes about due to a hidden crystalline topological invariant of quantum spin-Hall insulators that can neither be revealed by symmetry indicators nor using Wilson loop invariants. Considering the minimal symmetry requirements, we anticipate that our findings could apply to a large number of weak topological insulators.Comment: 10 pages, 5 figure

The Kilopixel Array Pathfinder Project (KAPPa), a 16 pixel integrated heterodyne focal plane array

KAPPa (the Kilopixel Array Pathfinder Project) is developing key technologies to enable the construction of heterodyne focal plane arrays in the terahertz frequency regime with ~1000 pixels. The leap to ~1000 pixels requires solutions to several key technological problems before the construction of such a focal plane is possible. The KAPPa project will develop a small (16-pixel) 2D integrated heterodyne focal plane array for the 660 GHz atmospheric window as a technological pathfinder towards future kilopixel heterodyne focal plane arrays

Results of using permanent magnets to suppress Josephson noise in the KAPPa SIS receiver

We present the results from the magnetic field generation within the Kilopixel Array Pathfinder Project (KAPPa) instrument. The KAPPa instrument is a terahertz heterodyne receiver using a Superconducting-Insulating- Superconducting (SIS) mixers. To improve performance, SIS mixers require a magnetic field to suppress Josephson noise. The KAPPa test receiver can house a tunable electromagnet used to optimize the applied magnetic field. The receiver is also capable of accommodating a permanent magnet that applies a fixed field. Our permanent magnet design uses off-the-shelf neodymium permanent magnets and then reshapes the magnetic field using machined steel concentrators. These concentrators allow the use of an unmachined permanent magnet in the back of the detector block while two small posts provide the required magnetic field across the SIS junction in the detector cavity. The KAPPa test receiver is uniquely suited to compare the permanent magnet and electromagnet receiver performance. The current work includes our design of a ‘U’ shaped permanent magnet, the testing and calibration procedure for the permanent magnet, and the overall results of the performance comparison between the electromagnet and the permanent magnet counterpart

Classification of crystalline insulators without symmetry indicators : Atomic and fragile topological phases in twofold rotation symmetric systems

Topological crystalline phases in electronic structures can be generally classified using the spatial symmetry characters of the valence bands and mapping them onto appropriate symmetry indicators. These mappings have been recently applied to identify thousands of topological electronic materials. There can exist, however, topological crystalline nontrivial phases that go beyond this paradigm: They cannot be identified using spatial symmetry labels and consequently lack any classification. In this work, we achieve the first of such classifications showcasing the paradigmatic example of two-dimensional crystals with twofold rotation symmetry. We classify the gapped phases in time-reversal invariant systems with strong spin-orbit coupling identifying a set of three Z2 topological invariants, which correspond to nested quantized partial Berry phases. By further isolating the set of atomic insulators representable in terms of exponentially localized symmetric Wannier functions, we infer the existence of topological crystalline phases of the fragile type that would be diagnosed as topologically trivial using symmetry indicators and construct a number of microscopic models exhibiting this phase. Our work is expected to have important consequences given the central role fragile topological phases are expected to play in novel two-dimensional materials such as twisted bilayer graphene

Inversion-symmetry protected chiral hinge states in stacks of doped quantum Hall layers

We prove the existence of higher-order topological insulators with protected chiral hinge modes in quasi-two-dimensional systems made out of coupled layers stacked in an inversion-symmetric manner. In particular, we show that a homogeneous external magnetic field slightly tilted away from the stacking direction drives alternating p- and n-doped honeycomb sheets into a higher-order topological phase, characterized by a nontrivial three-dimensional Z2 invariant. We identify graphene, silicene, and phosphorene multilayers as potential material platforms for the experimental detection of this second-order topological insulating phase

Hybrid-order topology of weak topological insulators

We consider weak topological insulators with a twofold rotation symmetry around their "dark"direction and show that these systems can be endowed with the topological crystalline structure of a higher-order topological insulator protected by rotation symmetry. These hybrid-order weak topological insulators display surface Dirac cones on all surfaces. Translational symmetry breaking perturbations gap the Dirac cones on the side surfaces leaving anomalous helical hinge modes behind. We also prove that the existence of this topological phase comes about due to a novel crystalline topological invariant of quantum spin-Hall insulators that can neither be revealed by symmetry indicators nor using Wilson loop invariants. Considering the minimal symmetry requirements, we anticipate that our findings could apply to a large number of weak topological insulators

Inversion-symmetry protected chiral hinge states in stacks of doped quantum Hall layers

We prove the existence of higher-order topological insulators with protected chiral hinge modes in quasi-two-dimensional systems made out of coupled layers stacked in an inversion-symmetric manner. In particular, we show that a homogeneous external magnetic field slightly tilted away from the stacking direction drives alternating p- and n-doped honeycomb sheets into a higher-order topological phase, characterized by a nontrivial three-dimensional Z2 invariant. We identify graphene, silicene, and phosphorene multilayers as potential material platforms for the experimental detection of this second-order topological insulating phase

Hybrid-order topology of weak topological insulators

We consider weak topological insulators with a twofold rotation symmetry around their "dark"direction and show that these systems can be endowed with the topological crystalline structure of a higher-order topological insulator protected by rotation symmetry. These hybrid-order weak topological insulators display surface Dirac cones on all surfaces. Translational symmetry breaking perturbations gap the Dirac cones on the side surfaces leaving anomalous helical hinge modes behind. We also prove that the existence of this topological phase comes about due to a novel crystalline topological invariant of quantum spin-Hall insulators that can neither be revealed by symmetry indicators nor using Wilson loop invariants. Considering the minimal symmetry requirements, we anticipate that our findings could apply to a large number of weak topological insulators