Continuous Quantum Phase Transitions in 2D Topological Insulators Driven by Strain

We develop a novel framework to study quantum phase transitions in two-dimensional topological insulators (TIs) driven by strain-induced perturbations. Using a new perturbation Hamiltonian that couples mechanical strain to topological edge states, we derive formulations for the continuous transition from topological to trivial insulator phases via an intermediate critical phase. Our model introduces critical exponents (v = 1, z = 1), a universal scaling law for the energy gap, and a real-space correlation function, validated through analytical and numerical methods. Phase diagrams, density of states, and correlation functions, visualized in four figures, illustrate the transition dynamics. This work addresses a key gap in controlling topological phases via external fields, offering insights for quantum device engineering and experimental realization in strain-tunable systems like HgTe quantum wells.