Interaction-Driven Quantum Phase Transitions between Topological and Crystalline Orders of Electrons

Topological and crystalline orders of electrons both benefit from enhanced Coulomb interactions in partially filled Landau levels. In bilayer graphene (BLG), the competition between fractional quantum Hall liquids and electronic crystals can be tuned electrostatically. Applying a displacement field leads to Landau-level crossings, where the interaction potential is strongly modified due to changes in the orbital wave functions. Here, we leverage this control to investigate phase transitions between topological and crystalline orders at constant filling factors in the lowest Landau level of BLG. Using transport measurements in high-quality hBN-encapsulated devices, we study transitions as a function of displacement field near crossings of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>N</a:mi> <a:mo>=</a:mo> <a:mn>0</a:mn> </a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>N</c:mi> <c:mo>=</c:mo> <c:mn>1</c:mn> </c:math> orbitals. The enhanced Landau-level mixing near the crossing stabilizes electronic crystals at all fractional fillings, including a resistive state at <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>ν</e:mi> <e:mo>=</e:mo> <e:mfrac> <e:mn>1</e:mn> <e:mn>3</e:mn> </e:mfrac> </e:math> and a reentrant integer quantum Hall state at <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>ν</g:mi> <g:mo>=</g:mo> <g:mfrac> <g:mn>7</g:mn> <g:mn>3</g:mn> </g:mfrac> </g:math> . On the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>N</i:mi> <i:mo>=</i:mo> <i:mn>0</i:mn> </i:math> side, the activation energies of the crystal and fractional quantum Hall liquid vanish smoothly and symmetrically at the transition, while the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>N</k:mi> <k:mo>=</k:mo> <k:mn>1</k:mn> </k:math> transitions out of the crystal appear discontinuous. Additionally, we observe quantized plateaus forming near the crystal transition at half filling of the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>N</m:mi> <m:mo>=</m:mo> <m:mn>0</m:mn> </m:math> levels, suggesting a paired composite fermion state stabilized by Landau level mixing.