We demonstrate that the Berry curvature monopole of nonmagnetic two-dimensional spin-$3/2$ holes leads to a novel Hall effect linear in an applied in-plane magnetic field ${B}_{\ensuremath{\parallel}}$. Remarkably, all scalar and spin-dependent disorder contributions vanish to leading order in ${B}_{\ensuremath{\parallel}}$, while there is no Lorentz force and hence no ordinary Hall effect. This purely intrinsic phenomenon, which we term the anomalous planar Hall effect (APHE), provides a direct transport probe of the Berry curvature accessible in all $p$-type semiconductors. We discuss experimental setups for its measurement.

Generating a Topological Anomalous Hall Effect in a Nonmagnetic Conductor: An In-Plane Magnetic Field as a Direct Probe of the Berry Curvature.

The authors propose a mechanism for superconductivity due to repulsive interactions in Dirac systems based on interference effects arising from the Berry phase and show that this mechanism can be realized in semiconductor artificial graphene.

Artificial graphene: Unconventional superconductivity in a honeycomb superlattice

Higher-order topological superconductors (HOTSs) are topological states possessing gapless modes at the corners (hinges) of 2$d$ (3$d$) samples. While these phases of matter have recently attracted immense theoretical interest, experimental candidates remain scarce. This paper demonstrates a mechanism for HOTSs in doped topological insulators, and provides explicit modeling for a particular realization. The mechanism is effective in materials with localized orbitals. It requires a minimum doping beyond which superconductivity ensues, thus offering a useful criterion in the search for material realizations. 

/pdf/intrinsic-first-and-higher-order-topological-3apipph3.pdf

Intrinsic first- and higher-order topological superconductivity in a doped topological insulator

Recently topological superconductors emerge as a platform to realise Majorana Fermions which has potential application in topological quantum computation. Superconductivity in these materials can be realised by chemical doping, high pressure or proximity effect. Herein we report the emergent superconductivity in single-crystals of Re doped type-II Weyl semimetal NiTe2. The magnetic and transport measurements highlight that Re substitution in Ni-site induces superconductivity at a maximum temperature of 2.36 K. Hall effect and specific heat measurements indicate that Re substitution is doping hole and facilitates the emergence of superconductivity by phonon softening and enhancing the electron-phonon coupling.

Emergent superconductivity by Re doping in type -II Weyl semimetal NiTe2

Topological properties of graphene with nanoholes are theoretically investigated in detail. It is revealed that two types of hole arrangements, honeycomb array and triangular array, give rise to two topologically distinct states. We give a concise two-step strategy for choosing array structures, where two types of Brillouin zone folding, corner-to-corner or corner-to-center, play crucial roles. The topological nontriviality is confirmed by interface states at a domain wall between the honeycomb and triangular hole arrays, which show a cross-shaped band structure resembling helical edge states in quantum spin Hall states. We also diagnose the topology of the states from the view point of the topological crystalline insulator and show that the parity index against the ${C}_{2}$ rotation is a key quantity. These findings indicate that nanotechnology-based geometrical design and manipulation are promising in exploration of topological phases of matter.

Counterpropagating topological interface states in graphene patchwork structures with regular arrays of nanoholes

Gauge theories, while describing fundamental interactions in nature, also emerge in a wide variety of physical systems. Abelian gauge fields have been predicted and observed in a number of novel quantum many-body systems, topological insulators, ultracold atoms, and many others. However, the non-Abelian gauge field, while playing the most fundamental role in particle physics, up to now has remained a purely theoretical construction in many-body physics. In this paper, we report an observation of a non-Abelian gauge field in a spin-orbit coupled quantum system. The gauge field manifests itself in quantum magnetic oscillations of a hole doped two-dimensional (2D) GaAs heterostructure. Transport measurements were performed in tilted magnetic fields, where the effect of the emergent non-Abelian gauge field was controlled by the components of the magnetic field in the 2D plane.

Manifestation of a non-Abelian Berry phase in a p -type semiconductor system

We demonstrate that the combination of an external magnetic field and the intrinsic spin-orbit interaction results in nonadiabatic precession of the electron spin after transmission through a quantum point contact (QPC). We suggest that this precession may be observed in a device consisting of two QPCs situated in series. The pattern of resonant peaks in the transmission is strongly influenced by the non-Abelian phase resulting from this precession. Moreover, an unusual type of resonance which is associated with suppressed, rather than enhanced, transmission (i.e., antiresonance) emerges in the strongly nonadiabatic regime. The shift in the resonant transmission peaks is dependent on the spin-orbit interaction and therefore offers a way to directly measure these interactions in a ballistic one-dimensional system.

One-dimensional spin-orbit interferometer

A semiclassical quantization condition is derived for Landau levels in general spin-orbit coupled systems. This generalizes the Onsager quantization condition via a matrix-valued phase which describes spin dynamics along the classical cyclotron trajectory. We discuss measurement of the matrix phase via magnetic oscillations and electron spin resonance, which may be used to probe the spin structure of the precessing wavefunction. We compare the resulting semiclassical spectrum with exact results which are obtained for a variety of spin-orbit interactions in 2D systems.

Semiclassical Landau quantization of spin-orbit coupled systems

Gauge theories, while describing fundamental interactions in nature, also emerge in a wide variety of physical systems. Abelian gauge fields have been predicted and observed in a number of novel quantum many-body systems, topological insulators, ultracold atoms and many others. However, the non-abelian gauge field, while playing the most fundamental role in particle physics, up to now has remained a purely theoretical construction in many-body physics. In the present paper we report the first observation of a non-abelian gauge field in a spin-orbit coupled quantum system. The gauge field manifests itself in quantum magnetic oscillations of a hole doped two-dimensional (2D) GaAs heterostructure. Transport measurements were performed in tilted magnetic fields, where the effect of the emergent non-abelian gauge field was controlled by the components of the magnetic field in the 2D plane.

Manifestation of a non-abelian gauge field in a p-type semiconductor system

Hexagonally patterned two-dimensional $p$-type semiconductor systems are quantum simulators of graphene with strong and highly tunable spin-orbit interactions. We show that application of purely in-plane magnetic fields, in combination with the crystallographic anisotropy present in low-symmetry semiconductor interfaces, allows Chern insulating phases to emerge from an originally topologically insulating state after a quantum phase transition. These phases are characterized by pairs of co-propagating edge modes and Hall conductivities ${\ensuremath{\sigma}}_{xy}=+\frac{2{e}^{2}}{h},\ensuremath{-}\frac{2{e}^{2}}{h}$ in the absence of Landau levels or cyclotron motion. With current lithographic technology, the Chern insulating transitions are predicted to occur in GaAs heterostructures at magnetic fields of $\ensuremath{\sim}5\phantom{\rule{4.pt}{0ex}}\text{T}$.

Chern insulating state in laterally patterned semiconductor heterostructures

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