Giant magnetoresistance of edge current between fermion and spin topological systems

A spin-$\frac{1}{2}$ subsystem conjoined along a cut with a subsystem of spinless fermions in the state of topological insulator is studied on a honeycomb lattice. The model describes a junction between a 2D topological insulator and a 2D spin lattice with direction-dependent exchange interactions in topologically trivial and nontrivial phase states. The model Hamiltonian of the complex system is solved exactly by reduction to free Majorana fermions in a static $\mathbb{Z}_2$ gauge field. In contrast to junctions between topologically trivial phases, the junction is defined by chiral edge states and direct interaction between them for topologically nontrivial phases. As a result of the boundary interaction between chiral edge modes, the edge junction is defined by the Chern numbers of the subsystems: such the gapless edge modes with the same (different) chirality switch on (off) the edge current between topological subsystems. The sign of the Chern number of spin subsystem is changed in an external magnetic field, thus the electric current strongly depends both on a direction and a value of an applied weak magnetic field. We have provided a detailed analysis of the edge current and demonstrate how to switch on (off) the electric current in the magnetic field.Comment: 4 pages, 9 figure

Exactly solvable model of topological insulator realized on spin-1/2 lattice

In this paper we propose an exactly solvable model of a topological insulator defined on a spin-1/2 square decorated lattice. Itinerant fermions defined in the framework of the Haldane model interact via the Kitaev interaction with spin-1/2 Kitaev sublattice. The presented model, whose ground state is a non-trivial topological phase, is solved exactly. We have found out that various phase transitions without gap closing at the topological phase transition point outline the separate states with different topological numbers. We provide a detailed analysis of the model's ground-state phase diagram and demonstrate how quantum phase transitions between topological states arise. We have found that the states with both the same and different topological numbers are all separated by the quantum phase transition without gap closing. The transition between topological phases is accompanied by a rearrangement of the spin subsystem's spectrum from band to flat-band states.Comment: 8 pages, 9 figure

Exactly solvable 2D topological Kondo lattice model

A spin-$\frac{1}{2}$ Kitaev sublattice interacting with a subsystem of spinless fermions is studied on a honeycomb lattice when the fermion band is half-filled. The model Hamiltonian describes a topological Kondo lattice with the Kitaev interaction, it is solved exactly by reduction to free Majorana fermions in a static $\mathbb{Z}_2$ gauge field. A yet unsolved problem of a hybridization of fermions and local moments in the Kondo lattice at low temperatures is solved in the framework of the proposed model. The Kondo hybridization gap is opened and the system is fixed in insulator and spin insulator states, due to the spin-fermion nature of the gap. We will show that the hybridization between local moments and itinerant fermions should be understood as hybridization between corresponding Majorana fermions of the spin and charge sectors. The RKKI interaction between local moments is not realized in the model, a system demonstrates a “quasi-Kondo” scenario of behavior with realization chiral gapless edge states in topological nontrivial phases. The ground-state phase diagram of the interacting subsystems calculated in the parameter space is rich