Shubnikov–de Haas oscillations in two-dimensional hole gases with competing cyclotron and Zeeman energy

Evaluation of the quantum lifetime in two-dimensional hole systems, together with band-structure parameters such as the effective mass and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>g</a:mi> </a:math> factor, becomes challenging when competing energy scales shape Shubnnikov–de Haas oscillations in a magnetic field. Here, we overcome this challenge for holes with pseudospin <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:msub> <b:mi>J</b:mi> <b:mtext>z</b:mtext> </b:msub> <b:mo>=</b:mo> <b:mo>±</b:mo> <b:mfrac> <b:mn>3</b:mn> <b:mn>2</b:mn> </b:mfrac> </b:mrow> </b:math> , confined in low-disorder strained germanium quantum wells. We extract self-consistently the effective mass, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>g</c:mi> </c:math> factor, and quantum lifetime, and estimate a maximum quantum mobility of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mn>133</d:mn> <d:mrow> <d:mo>(</d:mo> <d:mn>3</d:mn> <d:mo>)</d:mo> </d:mrow> <d:mo>×</d:mo> <d:msup> <d:mn>10</d:mn> <d:mn>3</d:mn> </d:msup> <d:mspace width="0.28em"/> <d:msup> <d:mi>cm</d:mi> <d:mn>2</d:mn> </d:msup> <d:mo>/</d:mo> <d:mi mathvariant="normal">V</d:mi> <d:mspace width="0.16em"/> <d:mi mathvariant="normal">s</d:mi> </d:mrow> </d:math> , setting a benchmark for holes in group IV semiconductors. The high quality of the hole gas if further highlighted by observing clean fractional quantum Hall states at low magnetic field and density.