Strain-tunable type-II to type-III & Gimbal nodal line transition in Imm2-phase of Cu$_2$SnS$_3$: An ab-initio study

TL;DR

This study uses ab-initio calculations to explore how various strains can induce transitions between different topological nodal line phases in Cu$_2$SnS$_3$, revealing strain-controlled topological phase transitions and complex nodal structures.

Contribution

It provides a detailed theoretical analysis of strain-induced topological phase transitions in Cu$_2$SnS$_3$, including the emergence of gimbal nodal loops and the complete vanishing of nodal lines.

Findings

Uniaxial compressive strain shifts the nodal line plane.

Equi-biaxial tensile strain creates multiple nodal rings.

Strain can induce gimbal nodal loops and topological transitions.

Abstract

Topological nodal line semimetals (NLSMs) represent an intriguing quantum phase, opening new avenues in materials science for practical applications such as anisotropic transport devices, high-mobility conductors, unconventional thermoelectrics, and nonlinear optical devices. Recently, Cu$_2$SnS$_3$ has been theoretically proposed as a type-II NLSM, with its Fermi surface containing only one nodal ring. Here, we demonstrate how uniaxial, equi-biaxial, and equi-triaxial strains affect the nodal line state of the $Imm2$-phase of Cu$_2$SnS$_3$ by using state-of-the-art ab-initio calculations. Under the application of uniaxial compressive strain (UCS) along the a-direction, the plane of the nodal line evolves from the $k_x$-$k_z$ to $k_y$-$k_z$ for 6\%$\leq$UCS$\leq$8\%. In contrast, under uniaxial tensile strain (UTS), the nodal line remains in the ($k_x$-$k_z$) plane across the entire studied range of UTS. Interestingly, on the application of equi-biaxial tensile strain (EBTS) along a-b (a-c) directions, it hosts only one nodal ring below 8\% ($<$6\%), which further evolves into three (seven) nodal-ring for EBTS of 8\% (6\%$\leq$EBTS$\leq$8\%). Upon the application of EBTS along a-c directions, we found two sets of three mutually orthogonal, intersecting nodal loops (topological gimbals). Apart from this, under the application of equi-biaxial compressive strain (EBCS) along the a-b (a-c) directions, it exhibits only one nodal ring up to 8\% (7\%). Beyond this, the nodal line completely vanishes and does not reappear at higher values of EBCS. Under equi-triaxial tensile strain (ETTS), Cu$_2$SnS$_3$ exhibits only one nodal-ring $<$6\%, which subsequently transforms into five nodal-ring for 6\%$\leq$ETTS$\leq$8\%. However, under the application of equi-triaxial compressive strain (ETCS), as in EBCS, only one nodal line exists up to 6\% ETCS.