Sketch of a CdTe/HgTe/CdTe quantum well heterostructure. The lowest conduction band (CB) state is labelled with E1 and the highest valence band (VB) state with H1.
Band structure of a HgTe quantum well of thickness (a). A HgTe nano-ribbon formed out of this quantum well of thickness and height of shows a positive band gap. Fig. 3(c) shows the band structure of an inverted quantum well of thickness . The corresponding quantum wire has a linearly dispersing (Dirac-cone) edge states (d).
Band structure of HgTe quantum well of thickness . At this width, the lowest conduction band (E1) and highest valence band (H1) at the point are equal.
Absolute value of the wave functions of the two edge-states of Fig. 3(d) .
Absolute value of the band gap of a CdTe/HgTe/CdTe quantum well as a function of the well width. Well widths larger than produce inverted band structures and can be exploited for topological insulator devices.
Calculated band gap of bulk as a function of stoichiometry and temperature. At x = 0, the bulk band gap of HgTe ( ) is reproduced.
Critical widths to get inverted band structures of CdTe/Cd1− x Hg x Te/CdTe quantum wells (a) and quantum wells (b) as a function of temperature and stoichiometry x.
Critical widths of CdTe/HgTe/CdTe heterostructures grown along direction as a function of N (a). The band gap closing for , and grown CdTe/HgTe/CdTe at different well widths is shown in (b). Band gap closing at different well dimensions give the corresponding critical width.
Critical widths of CdTe/HgTe/CdTe heterostructures grown along (a), (b), and (c) direction with uniaxial stress applied along (solid), (dashed), and (dashed-dotted) direction. Key observations are summarized in Tables III and IV .
Critical width for CdTe/HgTe/CdTe quantum wells with varying strength of external electric fields in growth direction.
Effective band gap of CdTe/HgTe/CdTe quantum wells of different well thicknesses as a function of applied electric field in growth direction. The dashed line depicts the delimiter between normal and inverted band structures.
8-band k.p parameters for CdTe and HgTe. , and are in units of eV. The remaining Luttinger parameters are dimensionless constants and the effective mass is in units of the free electron mass.
Orbital character of the top most valence band and lowest conduction band in CdTe-HgTe-CdTe heterostructure depending on the well width . The critical well width is the equal to .
The optimal tensile stress and growth conditions for CdTe/HgTe/CdTe quantum wells to achieve the least (L), highest (H), and intermediate (I) critical width, respectively.
The same list of conditions as in Table III but under compressive stress.
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