HgTe is inconvenient because the heavy holes! Unstrained HgTe - PowerPoint PPT Presentation

HgTe is inconvenient because the heavy holes! Unstrained HgTe Strained HgTe Γ − point Γ − point L − point HgTe z>0 SnTe z>0 𝑨 𝑨 CdTe z<0 PbTe z<0

Surface states in IV-VI heterostructures “Ideal” -Dirac Hamiltonian ℏ𝑙 𝑨 𝑤 ℏ𝑙 − 𝑤 𝐹 ↑ Δ 0 ℏ𝑙 + 𝑤 −ℏ𝑙 𝑨 𝑤 0 Δ 𝐹 ↓ Valid at low energy ℏ𝑙 𝑨 𝑤 ℏ𝑙 − 𝑤 𝐼 ↑ – Δ 0 Orbital mixing very strong ℏ𝑙 + 𝑤 −ℏ𝑙 𝑨 𝑤 𝐼 ↓ 0 – Δ 𝐹 PbTe SnTe z>0 𝐼 Pb 0.2 Sn 0.8 Se 𝑨 PbSe z<0

|𝐹 ↑ > ℏ𝑙 𝑨 𝑤 ℏ𝑙 − 𝑤 Δ 0 |𝐹 ↓ > ℏ𝑙 + 𝑤 −ℏ𝑙 𝑨 𝑤 0 Δ |𝐼 ↑ > ℏ𝑙 𝑨 𝑤 ℏ𝑙 − 𝑤 – Δ 0 ℏ𝑙 + 𝑤 −ℏ𝑙 𝑨 𝑤 |𝐼 ↓ > 0 – Δ Bulk solution PbTe SnTe Δ = 𝐹 2 Δ = −𝐹 1 Δ 2 + ℏ𝑙 𝑨 𝑤 2 + ℏ𝑙 𝑠 𝑤 2 𝐹 =

𝜔(𝑦, 𝑧, 𝑨) = 𝜓𝑓 𝑗𝑙 𝑨 𝑨 𝑓 𝑗(𝑙 𝑦 𝑦+𝑙 𝑧 𝑧) |𝐹 ↑ > ℏ𝑙 𝑨 𝑤 ℏ𝑙 − 𝑤 Δ 0 𝑙 𝑨 = 𝑙 1 SnTe z>0 |𝐹 ↓ > ℏ𝑙 + 𝑤 −ℏ𝑙 𝑨 𝑤 0 Δ Δ = −𝐹 1 Pb 0.2 Sn 0.8 Se |𝐼 ↑ > ℏ𝑙 𝑨 𝑤 ℏ𝑙 − 𝑤 – Δ 0 𝑨 ℏ𝑙 + 𝑤 −ℏ𝑙 𝑨 𝑤 0 – Δ |𝐼 ↓ > 𝑙 𝑨 = 𝑙 2 PbSe z<0 Δ = 𝐹 2 2 = 𝑙 𝑦 2 + 𝑙 𝑧 2 𝑙 𝑠 Δ 2 + ℏ𝑙 𝑨 𝑤 2 + ℏ𝑙 𝑠 𝑤 2 𝐹 = Boundary conditions: 2 − ℏ𝑙 𝑠 𝑤 2 𝐹 2 − 𝐹 1 Pb 0.2 Sn 0.8 Se: 𝑙 1 = ℏ𝑤 𝜔 𝑄𝑐𝑇𝑓 (0) = 𝜔 𝑄𝑐𝑇𝑜𝑇𝑓 (0) 𝑒𝜔 𝑄𝑐𝑇𝑓 𝑒𝜔 𝑄𝑐𝑇𝑜𝑇𝑓 ቤ = − ቤ 2 − ℏ𝑙 𝑠 𝑤 2 𝐹 2 − 𝐹 2 𝐹 2 𝑒𝑨 𝐹 1 𝑒𝑨 PbSe: 𝑨=0 𝑨=0 𝑙 2 = ℏ𝑤

Bound Dirac state from boundary conditions interface PbSnSe At z<0 2 2 𝑙 1 2 = 𝑙 2 PbSe 𝐹 ± = ± ℏ𝑤𝑙 𝑠 2 𝐹 1 𝐹 2 2 −𝐹 1 = 𝑗𝐹 1 𝑙 1 = ℏ𝑤 ℏ𝑤 2 − ℏ𝑙 𝑠 𝑤 2 𝐹 2 − 𝐹 1 𝑙 1 = ℏ𝑤 𝑙 2 = 𝑗𝐹 2 ℏ𝑤 𝜔 2 2 − ℏ𝑙 𝑠 𝑤 2 𝐹 2 − 𝐹 2 𝜔(𝑦, 𝑧, 𝑨) = 𝜓 1 𝑓 −𝑙 1 𝑨 𝑓 𝑗(𝑙 𝑦 𝑦+𝑙 𝑧 𝑧) 𝑙 2 = ℏ𝑤 𝜓 2 𝑓 𝑙 2 𝑨 𝑓 𝑗(𝑙 𝑦 𝑦+𝑙 𝑧 𝑧) 𝑨

Which one is topological PbSe or PbSnSe (HgTe or CdTe) HgTe interface PbSnSe PbSe

Observation of bound surface state – angle resolved photoemission Pb 0.9 Sn 0.1 Se Bi 2 Se 3 - 1 Dirac cones at gamma point Analytis et al .Phys. Rev. B 81 , 205407 (2010) Pb 0.8 Sn 0.2 Se Phys. Rev. Lett. 119 106602 (2017) ARPES by group of O. Rader