1 / 23

Electronic Liquid Crystals Novel Phases of Electrons in Two Dimensions

Electronic Liquid Crystals Novel Phases of Electrons in Two Dimensions. Alan Dorsey University of Florida Collaborators: Leo Radzihovsky (U Colorado) Carlos Wexler (U Missouri) Mouneim Ettouhami (UF) Support from the NSF. Competing interactions. Long range repulsive force: uniform phase

shae
Download Presentation

Electronic Liquid Crystals Novel Phases of Electrons in Two Dimensions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Electronic Liquid CrystalsNovel Phases of Electrons in Two Dimensions Alan Dorsey University of Florida Collaborators: Leo Radzihovsky (U Colorado) Carlos Wexler (U Missouri) Mouneim Ettouhami (UF) Support from the NSF NYU Colloquium

  2. Competing interactions • Long range repulsive force: uniform phase • Short range attractive force: compact structures • Competition between forcesinhomogeneous phase. • Ferromagnetic films, ferrofluids, type-I superconductors, block copolymers NYU Colloquium

  3. Ferrofluid in a Hele-Shaw cell • Ferrofluid: colloid of 1 micron spheres. Fluid becomes magnetized in an applied field. • Hele-Shaw cell: ferrofluid between two glass plates Surface tension competes with dipole-dipole interaction… NYU Colloquium

  4. Results courtesy of Ken Cooper http://www.its.caltech.edu/~jpelab/Ken_web_page/ferrofluid.html NYU Colloquium

  5. Modulated phases Langmuir monolayer (phospholipid and cholesterol) Ferromagnetic film (magnetic garnet) NYU Colloquium

  6. Liquid crystals T smectic-C smectic-A nematic isotropic NYU Colloquium

  7. Outline • Overview of the two dimensional electron gas and the quantum Hall effect • Theoretical and experimental evidence for a charge density wave? • Liquid crystal physics in quantum Hall systems—smectics and nematics • Quantum theory of the nematic phase NYU Colloquium

  8. AlGaAs B 3 2 E 1 F N=0 Two-dimensional electron gas (2DEG) • Created in GaAs/AlGaAs heterostructures • Magnetic field quantizes electron motion into highly degenerate Landau levels • Magnetic length • Experiments at NYU Colloquium

  9. The quantum Hall effect • Filling fraction (per spin): • State of the art mobility reveals interaction effects • No Hall effect at half filling NYU Colloquium

  10. Charge density wave in 2D? CDWs proposed by Fukuyama et al. (1979) as the ground state of a partially filled LL, but the Laughlin liquid has a lower energy. What happens in higher LLs (lower magnetic fields)? Hartree-Fock [Fogler et al. (1996)] predicts a CDW in higher LLs. Shown to be exact by Moessner and Chalker (1996). NYU Colloquium

  11. Hartree-Fock treatment of CDW • Direct vs. exchange balance leads to stripes or bubbles direct or “Hartree” term exchange or “Fock” term • Direct: repulsive long range Coulomb interaction • Exchange: attractive short range interaction NYU Colloquium

  12. Experimental evidence Microwave conductivity: R. Lewis & L. Engel (NHMFL) dc transport: Lilly et al. (1999) NYU Colloquium

  13. Experimental details • Anisotropy can be reoriented with an in-plane field (new features at 5/2, 7/2) • Transition at 100 mK • “Easy” direction [110] • “Native” anisotropy energy about 1 mK • No QHE: “compressible” state NYU Colloquium

  14. A charge density wave? • Transport anisotropy consistent with CDW state • BUT: • Transport in static CDW would be too anisotropic • Formation energy of several K, not mK • Data also consistent with an anisotropic liquid Fluctuations must be important [Fradkin&Kivelson (1999), MacDonald&Fisher (2000)]! NYU Colloquium

  15. The quantum Hall smectic • Classical smectic is a “layered liquid” • Stripe fluctuations lead to a “quantum Hall smectic” • Wexler&ATD (2001): find elastic properties from HFA NYU Colloquium

  16. Order in two dimensions Problem: in 2D phonons destroy the positional order but preserve the orientational order. However, this ignores dislocations (=half a layer inserted into crystal). • Topological character. • Dislocation energy in a smectic is finite, there will be a nonzero density. • Dislocations further reduce the orientational order. NYU Colloquium

  17. The quantum Hall nematic • Dislocations “melt” the smectic [Toner&Nelson (1982)]. • Algebraic orientational order: NYU Colloquium

  18. Nematic to isotropic transition • Low temperature phase is better described as a nematic [Cooper et al (2001)]. Local stripe order persists at high temperatures. • Nematic to isotropic transition occurs via a disclination unbinding (Kosterlitz-Thouless) transition. • Wexler&ATD: start from HFA and find transition at 200 mK, vs. 70-100 mK in experiments. NYU Colloquium

  19. Quantum theory of the QHN • Classical theory overestimates anisotropy below 20 mK. Are quantum fluctuations the culprit? • Quantum fluctuations can unbind dislocations at T=0. Radzihovsky&ATD (PRL, 2002): use dynamics of local smectic layers as a guide. Make contact with hydrodynamics. NYU Colloquium

  20. Theoretical digression… • The collective degrees of freedom are the rotations of the dislocation-free domains (nematogens). Their angular momenta and directors are conjugate. • Commutation relations are derived in the high field limit, and lead to an unusual quantum rotor model. • Broken rotational symmetry leads to a Goldstone mode with anisotropic dispersion: • Note that NYU Colloquium

  21. Predictions • QHN exhibits true long range order at zero temperature; quantum fluctuations important below 20 mK. • QHN unstable to weak disorder. Glass phase? • Tunneling probes low energy excitations. See a pseudogap at low bias. • Damping of Goldstone mode due to coupling to quasiparticles. • Resistivity anisotropy proportional to nematic order parameter [conjectured by Fradkin et al. (2000)]. NYU Colloquium

  22. New directions • Start from half-filled fermi liquid state. Can interactions cause the FS to spontaneously deform? • Variational wavefunctions? • Experimental probes: tunneling, magnetic focusing, surface acoustic waves. • Relation to nanoscale phase separation in other systems (e.g., cuprate superconductors)? NYU Colloquium

  23. Summary Fascinating problem of orientationally ordered point particles! NYU Colloquium

More Related