Composite fermion liquid to Wigner solid transition in the lowest Landau level of zinc oxide

ARTICLE DOI: 10.1038/s41467-018-06834-6 OPEN Composite fermion liquid to Wigner solid transition in the lowest Landau level of zinc oxide 1234567890():,; D. Maryenko1, A. McCollam2, J. Falson3,4, Y. Kozuka3,5, J. Bruin2,4, U. Zeitler2 & M. Kawasaki1,3 Interactions between the constituents of a condensed matter system can drive it through a plethora of different phases due to many-body effects. A prominent platform for it is a dilute two-dimensional electron system in a magnetic field, which evolves intricately through various gaseous, liquid and solid phases governed by Coulomb interaction. Here we report on the experimental observation of a phase transition between the composite fermion liquid and adjacent magnetic field induced phase with a character of Wigner solid. The experiments are performed in the lowest Landau level of a MgZnO/ZnO two-dimensional electron system with attributes of both a liquid and a solid. An in-plane magnetic field component applied on top of the perpendicular magnetic field extends the Wigner-like phase further into the composite fermion liquid phase region. Our observations indicate the direct competition between a composite fermion liquid and a Wigner solid formed either by electrons or composite fermions. 1 RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan. 2 High Field Magnet Laboratory (HFML-EMFL) and Institute for Molecules and Materials, Radboud University, 6525 ED Nijmegen, The Netherlands. 3 Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), The University of Tokyo, Tokyo 113-8656, Japan. 4Present address: Max Planck Institute for Solid State Research, Stuttgart, Germany. 5Present address: National Institute for Materials Science, Tsukuba, Ibaraki, Japan. Correspondence and requests for materials should be addressed to D.M. (email: ) NATURE COMMUNICATIONS | (2018)9:4356 | DOI: 10.1038/s41467-018-06834-6 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-06834-6 A magnetic field B applied perpendicularly to a twodimensional charge carrier system modifies its density of states and places the charge carriers on a ladder of discrete Landau levels (LL). The Coulomb interaction between the pffiffiffiffiffiffiffiffiffiffi charged particles acting on the magnetic length scale lB ¼  h=eB can be tuned by varying the magnetic field strength. Thereby, the high mobility carriers evolve through the various correlation phases1. When the electrons occupy half of available states in the lowest LL, e.g., filling factor ν = 1/2, the electrons prefer to reduce their interaction by virtue of capturing two magnetic flux quanta resulting in the emergence of new particles, called composite fermions (CF)2,3. These particles form a Fermi surface at ν = 1/2 and move in an effective field Beff = B − Bν = 1/2 (Fig. 1, middle panel) giving rise to magnetoresistance oscillations. At even lower filling factors a Wigner solid, a crystalline phase of charged particles (electrons or CF) driven by the repulsive Coulomb force and yet another manifestation of many-body correlations, emerges as a ground state of the electron system (Fig. 1). Being in the lowest Landau level (LL) the electron system experiences competition between the composite fermion liquid phase and the magnetic field induced Wigner solid phase, which manifests as a large magnetoresistance peak around or below ν = 1/34,6. A liquid-solid transition may follow the Kosterlitz–Thouless model, whereas the particles can form a hexatic phase characterized by bond-oriented nearest-neighbor ordering7–11. An intermediate phase of the liquid-solid transition may also take the form of microemulsion phases associated with a liquid crystalline phase11–13. Departing from the liquid phase of CF at ν = 1/2, a Magnetic field Wigner solid Composite fermions Beff E ν =1/2 CF EF 0 CF k kF Electrons E B EF B=0 k kF Fig. 1 Schematic of the phases of a 2DES in a magnetic field: The different phases of a two-dimensional electron system (2DES) in a magnetic field. At zero magnetic field (bottom panel) the electrons are described as a weakly interacting Fermi gas with a well-defined Fermi surface. In the half-filled lowest LL, e.g., at filling factor ν = 1/2, the electrons reduce their mutual interaction by attaching the two magnetic flux quanta, resulting in the emergence of new particles, so-called composite fermions (middle panel)2,3. These particles form a Fermi surface at ν = 1/2 and move in an effective field Beff = B − Bν = 1/2 giving rise to magnetoresistance oscillations known as the fractional quantum Hall effect (Fig. 2). At even lower filling factors, a Wigner solid, a crystalline phase of electrons arranged by the repulsive Coulomb force and another manifestation of many-body correlations, becomes the ground state, which can be formed either by bare electrons (top left) or composite fermions (top right) 2 formation of both a composite fermion Wigner solid and phase transition to intermediate phases may appear feasible. The idea of realizing a composite fermion Wigner solid was put forward in a number of theoretical works14–19. Recent experiments focusing on GaAs-based 2DES have been gradually accumulating evidence pointing towards the realization of CF Wigner solid20–24. Intuitively the CF crystal is stabilized when the CF of nearby liquid states release two of their vortices to stabilize the crystal, whereas the undressed particles retain their energetically favorable correlations18. Thus a two-flux CF crystal borders the four-flux composite fermion liquid phase, whereas an electron crystal phase is embedded in two-flux composite fermion liquid and forms between filling factors ν = 1/3 and ν = 2/5 for a high enough LL mixing19. Thus the transition between the liquid and the solid can be highly non-trivial and is realized in the lowest LL of a twodimensional charge carrier system by the transformation of the underlying particle type. Here, we study the magnetotransport in a ZnO heterostructure (see: Methods) in the magnetic field region between the CF liquid phase formed at ν = 1/2 and the high resistivity phase appearing at higher field and exhibiting attributes of a Wigner solid25,26. LL mixing, the ratio between electron–electron interaction energy and the cyclotron energy, is 4.2 at ν = 1/2 in this heterostructure and the magnetotransport in the region of interest features a character of both CF liquid and crystalline phase. The presence of such a region with the interlaced character highlights a non-trivial nature of phase transition, the details of which can further be masked by the inhomogeneous potential landscape arising from inevitable crystallographic disorder. The transition between the two phases can be tuned by the application of an in-plane magnetic field. As a result of the phase intermixture, the state at filling factor ν = 1/2 can be formed by a composite fermion liquid and some intermediate state arising in the course of liquid-so (...truncated)