Nonlinear transport of Wigner solid phase surrounding the two-flux composite fermion liquid

We have investigated the low temperature <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mo>(</a:mo><a:mi>T</a:mi><a:mo>)</a:mo></a:math> transport properties of fractional quantum Hall (FQH) states in a high-mobility two-dimensional hole gas. According to the composite fermion (CF) model, FQH states stemming from a half-filled Landau level, specifically at fillinsg factors <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>ν</b:mi><b:mo>=</b:mo><b:mi>p</b:mi><b:mo>/</b:mo><b:mo>(</b:mo><b:mrow><b:mn>2</b:mn><b:mi>p</b:mi><b:mo>+</b:mo><b:mn>1</b:mn></b:mrow><b:mo>)</b:mo></b:mrow></b:math> (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>p</c:mi><c:mo>=</c:mo><c:mo>±</c:mo><c:mn>1</c:mn><c:mo>,</c:mo><c:mo>±</c:mo><c:mn>2</c:mn><c:mo>,</c:mo><c:mo>±</c:mo><c:mn>3</c:mn><c:mo>,</c:mo><c:mo>...</c:mo></c:mrow></c:math>), can be associated with two-flux-attached CFs at the corresponding Lambda filling factor <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>p</d:mi></d:math>. The zero-resistance minima and Hall plateaus of these states exhibit unusual temperature dependencies, characterized by rapid increases in width below a threshold temperature around <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mspace width="4pt"/><e:mn>100</e:mn><e:mspace width="4pt"/><e:mi>mK</e:mi></e:mrow></e:math>. Differential conductivity measurements from Corbino samples reveal that the regimes surrounding the CF liquid display clear nonlinear transport characteristics. This nonlinearity implies that each CF liquid is surrounded by CF solid phase composed of dilute CF excitations. Quantitatively, the applied electric field <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mi>E</h:mi></h:math> influences the motion of CF solid in a way analogous to <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mi>T</i:mi></i:math>, which is dubbed the “<j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:mi>E</j:mi><j:mo>−</j:mo><j:mi>T</j:mi></j:mrow></j:math> duality.” Our analysis indicates that this <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:mi>E</k:mi><k:mo>−</k:mo><k:mi>T</k:mi></k:mrow></k:math> duality is consistent with the Berezinskii-Kosterlitz-Thouless theory in two-dimensional phase transitions.