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An effective theory is constructed for analyzing a generic phase transitionbetween the quantum spin Hall and the insulator phases. Occurrence ofdegeneracies due to closing of the gap at the transition are carefullyelucidated. For systems without inversion symmetry the gap-closing occurs at\pm k_0(\neq G/2) while for systems with inversion symmetry, the gap can closeonly at wave-numbers k=G/2, where G is a reciprocal lattice vector. In bothcases, following a unitary transformation which mixes spins, the system isrepresented by two decoupled effective theories of massive two-componentfermions having masses of opposite signs. Existence of gapless helical modes ata domain wall between the two phases directly follows from this formalism. Thistheory provides an elementary and comprehensive phenomenology of the quantumspin Hall system.

Tuning phase transition between quantum spin Hall and ordinary insulating phases