Spin relaxation in a single-electron bilayer graphene quantum dot

We study the spin relaxation in a single-electron bilayer graphene quantum dot due to the spin-orbit coupling. The spin relaxation is assisted by the emission of acoustic phonons via the bond-length change and deformation potential mechanisms and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mn>1</a:mn><a:mo>/</a:mo><a:mi>f</a:mi></a:mrow></a:math> charge noise. In the perpendicular magnetic-field dependence of the spin relaxation rate <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msubsup><b:mi>T</b:mi><b:mn>1</b:mn><b:mrow><b:mo>−</b:mo><b:mn>1</b:mn></b:mrow></b:msubsup></b:math>, we predict a monotonic increase of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msubsup><c:mi>T</c:mi><c:mn>1</c:mn><c:mrow><c:mo>−</c:mo><c:mn>1</c:mn></c:mrow></c:msubsup></c:math> at higher fields where the electron-phonon coupling via the deformation potential plays a dominant role in spin relaxation. We show a less pronounced dip in <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msubsup><d:mi>T</d:mi><d:mn>1</d:mn><d:mrow><d:mo>−</d:mo><d:mn>1</d:mn></d:mrow></d:msubsup></d:math> at lower magnetic fields due to the competition between the electron-phonon coupling due to bond-length change and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mn>1</e:mn><e:mo>/</e:mo><e:mi>f</e:mi></e:mrow></e:math> charge noise. Finally, detailed comparisons of the magnetic-field dependence of the spin relaxation with the existing experiments by Banszerus [] and Gächter [] are reported.