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Design principles for HgTe based topological insulator devices
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Image of FIG. 1.
FIG. 1.

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.

Image of FIG. 2.
FIG. 2.

Bulk band structure of CdTe (a) and HgTe(b). The ordering of the conduction and valence bands near the band gap at the point in HgTe (Fig. 2(b) ) is opposite to the one in CdTe (Fig. 2(a) ). In HgTe, the hole state is above the electron state .

Image of FIG. 3.
FIG. 3.

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).

Image of FIG. 4.
FIG. 4.

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.

Image of FIG. 5.
FIG. 5.

Absolute value of the wave functions of the two edge-states of Fig. 3(d) .

Image of FIG. 6.
FIG. 6.

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.

Image of FIG. 7.
FIG. 7.

Calculated band gap of bulk as a function of stoichiometry and temperature. At  = 0, the bulk band gap of HgTe ( ) is reproduced.

Image of FIG. 8.
FIG. 8.

Critical widths to get inverted band structures of CdTe/Cd HgTe/CdTe quantum wells (a) and quantum wells (b) as a function of temperature and stoichiometry .

Image of FIG. 9.
FIG. 9.

Critical widths of CdTe/HgTe/CdTe heterostructures grown along direction as a function of (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.

Image of FIG. 10.
FIG. 10.

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 .

Image of FIG. 11.
FIG. 11.

Critical width for CdTe/HgTe/CdTe quantum wells with varying strength of external electric fields in growth direction.

Image of FIG. 12.
FIG. 12.

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.


Generic image for table
Table I.

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.

Generic image for table
Table II.

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 .

Generic image for table
Table III.

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.

Generic image for table
Table IV.

The same list of conditions as in Table III but under compressive stress.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Design principles for HgTe based topological insulator devices