Magnetic and topological transitions in three-dimensional topological Kondo insulator

TL;DR

This paper maps the phase diagram of three-dimensional topological Kondo insulators, revealing magnetic and topological phase transitions, including strong and weak topological insulators, and their relation to experimental materials like SmB$_6$.

Contribution

It introduces an extended slave-boson method to identify multiple topological phases and magnetic orders, providing a comprehensive phase diagram including surface states and transitions.

Findings

Identification of four strong and two weak topological insulator phases.

Discovery of an insulator-metal transition with surface Fermi rings.

Classification of antiferromagnetic phases into topological and non-topological based on $\

Abstract

By using an extended slave-boson method, we draw a global phase diagram summarizing both magnetic phases and paramagnetic (PM) topological insulating phases (TI$_s$) in three-dimensional topological Kondo insulator (TKI). By including electron hopping (EH) up to third neighbor, we identify four strong topological insulating (STI) phases and two weak topological insulating (WTI) phases, then the PM phase diagrams characterizing topological transitions between these TI$_s$ are depicted as functions of EH, $f$-electron energy level and hybridization constant. We also find an insulator-metal transition from a STI phase which has surface Fermi rings and spin textures in qualitative agreement to TKI candidate SmB$_6$. In weak hybridization regime, antiferromagnetic (AF) order naturally arises in the phase diagrams, and depending on how the magnetic boundary crosses the PM topological transition lines, AF phases are classified into AF topological insulator (AFTI) and non-topological AF insulator (nAFI), according to their $\mathcal{Z}_2$ indices. In two small regions of parameter space, two distinct topological transition processes between AF phases occur, leading to two types of AFTI, showing distinguishable surface dispersions around their Dirac points.