Temperature effects in topological insulators of transition metal dichalcogenide monolayers

We investigate the role of temperature on the topological insulating state of metal dichalcogenide monolayers, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mn>1</a:mn><a:msup><a:mrow><a:mi mathvariant="normal">T</a:mi></a:mrow><a:mo>′</a:mo></a:msup><a:mtext>−</a:mtext><a:msub><a:mrow><a:mi>M</a:mi><a:mi>X</a:mi></a:mrow><a:mn>2</a:mn></a:msub></a:mrow></a:math> (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>M</c:mi><c:mo>=</c:mo><c:mtext>W</c:mtext></c:mrow></c:math>, Mo and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>X</d:mi><d:mo>=</d:mo><d:mtext>S</d:mtext></d:mrow></d:math>, Se). Using first principles calculations based on density functional theory, we consider three temperature-related contributions to the topological band gap: electrons coupling with short-wavelength phonons, with long-wavelength phonons Fröhlich coupling, and thermal expansion. We find that electron-phonon coupling promotes the topology of the electronic structures of all <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mn>1</e:mn><e:msup><e:mrow><e:mi mathvariant="normal">T</e:mi></e:mrow><e:mo>′</e:mo></e:msup><e:mtext>−</e:mtext><e:msub><e:mrow><e:mi>M</e:mi><e:mi>X</e:mi></e:mrow><e:mn>2</e:mn></e:msub></e:mrow></e:math> monolayers, while thermal expansion acts as a counteracting effect. Additionally, we derive the band renormalization from Fröhlich coupling in the two-dimensional context and observe its relatively modest contribution to <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mn>1</g:mn><g:msup><g:mrow><g:mi mathvariant="normal">T</g:mi></g:mrow><g:mo>′</g:mo></g:msup><g:mtext>−</g:mtext><g:msub><g:mrow><g:mi>M</g:mi><g:mi>X</g:mi></g:mrow><g:mn>2</g:mn></g:msub></g:mrow></g:math> monolayers. Finally, we present a simplified physical picture to understand the “inverse Varshni” effect driven by band inversion in topological insulators. Our work reveals that, among the four <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mn>1</i:mn><i:msup><i:mrow><i:mi mathvariant="normal">T</i:mi></i:mrow><i:mo>′</i:mo></i:msup><i:mtext>−</i:mtext><i:msub><i:mrow><i:mi>M</i:mi><i:mi>X</i:mi></i:mrow><i:mn>2</i:mn></i:msub></i:mrow></i:math> studied monolayers, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:msub><k:mi>MoSe</k:mi><k:mn>2</k:mn></k:msub></k:math> is a promising candidate for room-temperature applications because its band gap displays remarkable resilience against thermal expansion, while the topological order of <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:msub><l:mi>WS</l:mi><l:mn>2</l:mn></l:msub></l:math> can be tuned under the combined influence of strain and temperature. Both materials represent novel examples of temperature-promoted topological insulators. Published by the American Physical Society 2024