Topological phase transition and evolution of edge states in In-rich InGaN/GaN quantum wells under hydrostatic pressure

Abstract

Combining the k · p method with the third-order elasticity theory, we perform a theoretical study of the pressure-induced topological phase transition and the pressure evolution of topologically protected edge states in InN/GaN and In-rich InGaN/GaN quantum wells. We show that for a certain range of the quantum well parameters, thanks to a negative band gap pressure coefficient, it is possible to continuously drive the system from the normal insulator state through the topological insulator into the semimetal phase. The critical pressure for the topological phase transition depends not only on the quantum well thickness but also on the width of the Hall bar, which determines the coupling between the edge states localized at the opposite edges. We also find that in narrow Hall bar structures, near the topological phase transition, a significant Rashba-type spin splitting of the lower and upper branches of the edge state dispersion curve appears. This effect originates from the lack of the mirror symmetry of the quantum well potential caused by the built-in electric field, and can be suppressed by increasing the Hall bar width. When the pressure increases, the energy dispersion of the edge states becomes more parabolic-like and the spin splitting decreases. A further increase of pressure leads to the transition to a semimetal phase, which occurs due to the closure of the indirect 2D bulk band gap. The difference between the critical pressure at which the system becomes semimetallic, and the pressure for the topological phase transition, correlates with the variation of the pressure coefficient of the band gap in the normal insulator state.

Topological insulator with negative spin-orbit coupling and transition between Weyl and Dirac semimetals in InGaN-based quantum wells

“…One can see that the E 2 Dg closes first for L b = 15.06 nm due to the TPT originating from the inversion of the CB and LH subbands. Then, the E 2 Dg vanishes for L b larger than 21 nm due to the transition from the TI phase to the nonlocal semimetal (NSM) phase, arising from nonlocal overlapping between the LH and HH subbands 14 . The largest value of the E 2 Dg in the TI state is about 1.25 meV, which is a few times smaller than it was predicted assuming the positive SOC in InN 13 – 15 .…”

“…Here, we note that the coefficients A 5 and A 6 have opposite signs to those in refs 36 , 37 . (The difference in sign of the A 5 and A 6 coefficients was also discussed in refs 38 , 39 ) In order to take into account the coupling between the conduction band and the valence bands, we enlarge the Hamiltonian (2) to the eight-band model using the approach applied in refs 13 , 14 . We reduce the parameter Δ to , since α 5 = 0 for GaN and InN 26 .…”

“…In order to determine the electronic states in a QW grown along [0001] crystallographic direction of the wurtzite structure, we include the strain effects and the built-in electric field originating from the piezoelectric effect and the spontaneous polarization 14 , 15 . Due to large lattice misfit between GaN and InN, we calculate strain and the built-in electric field taking into account the effects of nonlinear elasticity and nonlinear piezoelectricity, according to refs 14 , 15 , 41 . Then, replacing k z in the Hamiltonian H 8×8 by the operator , we get the eight-band Schrödinger-type equation, where and are the energies and the envelope functions of the QW states.…”

“…The positive SOC in GaN and InN was taken into account so far in the study of the TPT in InN/GaN and InGaN/GaN QWs 13 – 15 . In such a case, the TPT is mediated by the DSM arising from the crossing of the HH and CB subbands at k ⊥ = 0 14 . The 2D bulk energy gap ( E 2 Dg ) in the TI state was found to reach about 5 meV 14 , 15 and 10 meV 13 .…”

“…In such a case, the TPT is mediated by the DSM arising from the crossing of the HH and CB subbands at k ⊥ = 0 14 . The 2D bulk energy gap ( E 2 Dg ) in the TI state was found to reach about 5 meV 14 , 15 and 10 meV 13 . These significant values of E 2 Dg allow experimental verification of the edge state transport in InN/GaN and InGaN/GaN QWs and also motivate design of new topological devices based on these structures 24 , 25 .…”