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Metal-Insulator Transition in 2D Electron Systems: Recent Progress

Metal-Insulator Transition in 2D Electron Systems: Recent Progress. L.D. Landau Institute, Chernogolovka. P.N. Lebedev Physical Institute , Moscow . Experiment: Dima Knyazev, Oleg Omel’yanovskii Vladimir Pudalov. Theory: Igor Burmistrov, Nickolai Chtchelkatchev.

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Metal-Insulator Transition in 2D Electron Systems: Recent Progress

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  1. Metal-Insulator Transition in 2D Electron Systems: Recent Progress L.D.Landau Institute, Chernogolovka P.N. Lebedev Physical Institute, Moscow Experiment: Dima Knyazev, Oleg Omel’yanovskii Vladimir Pudalov Theory: Igor Burmistrov, Nickolai Chtchelkatchev Schegolev memorial conference. Oct. 11-16, 2009

  2. Major question to be addressed: Groundstate(s) of the 2D electron liquid (T 0) • Outline • Historical intro: classical, semiclassical, quantum transport and 1-parameter scaling • MIT in high mobility 2D systems • The puzzle of the metallic-like conduction • Quantifying e-e interaction in 2D • Transport in the critical regime: 2 parameter RG theory • Data analysis in the vicinity of the fixed point • Data analysis in the vicinity of the fixed point

  3. 1.1.Classicalcharge transport • 1. T >>hwD. Phonon scatterings1/T • 2. T << hwD. Phonon scatterings1/T5 • T << TF. e-e scattering s1/T 2 • 4. T << TF. Impurity scatteringsConst + Umklapp Note (a): There is no σ(T) dependence in the T=0 limit ! (within the classical approximation, for non-interacting electrons )

  4. 1.2.Semiclassical concept of transport (1960) Ioffe-Regel criterion A.F. Ioffe and A.R. Regel, Prog. Semicond. 4, 237 (1960). Abram F. Ioffe “minimummetallic conductivity” Anatoly R. Regel Nevil Mott (1905-96)

  5. s Semiclassical picture: MIT at T = 0 (1970’s) Possiblebehavior of resistivity (dimensionality is irrelevant):

  6. 1.3. Quantum concept of transport(1979): Competition between dimensionality and interefrence Interference of electron waves causes localization B E.Abrahams A Note (b) T.V. Ramakrishnan All electrons in2D become localized at T  0 D.Khmelnitskii for ln(1/T)  P.W. Anderson L.P.Gorkov

  7. 1.4. Scalingideas in the quantum transport picture: Thouless(1974, 77); Abrahams, Anderson, Licciardello, Ramakrishnan (’79); Wegner (’79). Renormalization Grouptransformation: The block sizeis increased from ltr to L g(L) – dimensionless conductance for a sample (size L) in units of e2/h 1-Parameter scaling equation At the MIT: For 2D system: β is always <0; there is no metallic state and no MIT

  8. One-parameter scalingand experiment Low-mobility sample (μ=1.5103cm2/Vs) n Note (c): The sign of dρ/dTat finite T is not indicative of the metallic or insulating state

  9. 2.Metal-insulator transition inhigh mobility 2D system =4,5m2/Vs density N ~1011cm-2 S.Kravchenko, VP, et al., PRB50, 8039 (1994)

  10. Similar r(T) behavior was found in many other2D systems: p-GaAs, n-GaAs, p-Si/SiGe, n-Si/SiGe, n-SOI, p-AlAs/GaAs, etc. n-AlAs-GaAs p-GaAs/AlAs  (/)  (/) Y.Hanein et al. PRL (1998) Papadakis, Shayegan, PRB (1998)

  11. There is no metallic state and no MIT - in the noninteracting 2D systems • Spin-orbitinteraction? Not renormalized • Electron-phononinteraction? Toolowtemperature and too weak e-ph coupling Electron-electron interaction

  12. High mobility =4,5m2/Vs density Eee/EF= rs~10

  13. e-e interaction in Si-MOS structures Note1: Within the concept of the e-e correlations, the role of high mobility in the 2D MIT becomes transparent • The high mobility: • Increases tand, hence, the amplitude of interaction corrections ( Tt); • Translates down the critical density range (decreases the density of impurities ni) • Increases the magnitude of interaction effects (F0s(n) Tt).

  14. 2.1.Signatures of the critical phenomenon - QPT •Mirrorreflection symmetry: (Dn,T)/c = c/(-Dn,T) •data scaling r/rc= f [T/T0(n)] •Critical behavior T0|n-nc|-z Symmetry:holds here and ismissing outside S.V.Kravchenko, W.E.Mason, G.E.Bowker, J.E.Furneaux, V.M.Pudalov, M.D'Iorio, PRB 1995

  15. MIT in 2D system (1994) =35,000cm2/Vs

  16. MIT in 2D system (1994) =35,000cm2/Vs

  17. 2.2. Problems of the data (mis)interpretation In analogy with the 1-parameter scaling: • If “MIT” is a QPT, it is expected: • • rc to be universal, • scaling persists to the lowest T • horizontal “separatrix”rc f(T) • z,  are universal • Experimentally, however, • • rc=0.55 is sample dependent, • • z =0.9  2 is sample dependent, • reflection symmetry fails at low T • and at high T>2K • rins =cexp(T0/T)p1 (p1=0.5 1) • rmet=cexp(-T0/T)p2+r0 (p2=0.5 1) • • separatrix is T-dependent The failure of the OPST approach is not surprising: interactions How to proceed in the 2-parameter problem ? Which parameters should be universal ? Definitions of the critical density, critical resistivity etc. ?

  18. 3. Solving the puzzle of the metallic-like conduction atg >>e2/h (2000-2004) Ballisticinteraction regime Tt>>1

  19. Quantifyinge-einteraction in2D (2000-2004) Fia,s – FL-constants (harmonics) of the e-e interaction

  20. Strong growthin *  m*g*, m*andg* as n decreases V.M.Pudalov, M.E.Gershenson, H.Kojima, Phys.Rev.Lett.88, 196404 (2002)

  21. Fermi-liquidparameter F0s N.Klimov, M.Gershenson, VP, et al. PRB 78, 195308 (2008)

  22. No parameter comparisonof the data and theory in the ballistic regimeT >>1 (2002-2004): Theory: Zala, Narozhny, Aleiner, PRB (2001-2002) Exper.: VP, Gershenson, Kojima, et al. PRL93 (2004)

  23. 4. Transport in the critical regime motivatedus to apply the sameideas to the regime of low density/strong disorder (r ~1) Successful description of the transport in terms of e-e interaction effects in the“high density/low disorder (r <<1) regime VPet al. JETP Lett. (1998)

  24. Theory: Two- parameter renorm. group equations s is in units of e2/h Interplay of disorder and interaction

  25. Exact RG results forB=0 nv=2 One-loop, rmax A.A.Finkelstein, Punnoose, Phys.Rev.Lett. (2005)

  26. Transport data in the critical regime

  27. Magnetotransport in the criticalregime Quantitative agreement of thedata with theory Knyazev, Omelyanovskii, Burmistrov, Pudalov, JETP Lett. (2006) Anissimova, Kravchenko, Punnoose, Finkel'stein, Klapwijk, Nature Phys. 3, 707 (2007) RG equation in B|| field: Burmistrov, Chtchelkatchev, JETP Lett. (2006)

  28. g2(T) – comparison with theory Quantitative agreement with theory for both,r(T) and g2(T)

  29. Anissimova, Kravchenko, Punnoose, Finkel'stein, Klapwijk, Nature Phys. 3, 707 (2007)

  30. Interplayof disorderandinteraction RG-resultinthe two-loopapproximation Finkelstein, Punnoose, Science (2005) No crossover“2D metal”–localized state

  31. 6. Fixedpoint (QCP) Two-loopapproximation, nv= r/rc g2

  32. Data analysis in the vicinity of the fixed point Linearising RG equations close to the fixed point bs = bg2 = 0: k = p/(2n) z = -py/2 p– forheat capacity, n – for correlation length Knyazev, Omelyanovskii, Pudalov, Burmistrov, PRL 100, 046405 (2008)

  33. Scaling of the r/rc(T) data separatrix Note: The quality of the data scaling relative the tilted separatrix rc(T) Separatrix – is a power low function, with no maxima and inflection. Exponentzmust be< 1.

  34. R(T) data scalingin a wide range of(X,Y >1) Fits 64000 data pointsto within 4% over the range |X|<5, Y<3 f1= -X+0.07X2+0.01X3 (1-Y+1.48Y2) (1+1.9Y2+1.7Y3) f2= Reflection symmetry holds within (0.8%) for |X|<0.5, Y<0.7 separatrix

  35. Empiricscalingfunction R(X,Y) – datasplinefor 5 samples Knyazev, Omelyanovskii, Pudalov, Burmistrov, PRL100, 046405 (2008)

  36. Current understanding of the 2D systems Summary • “Metallic”conduction in 2D systems for  >> e2/h-the result of e-e interactions • Interplayof disorder and e-e interaction radically changesthe common believethat the metallic statecan not exist in 2D • Agreement of the data with RG theory andthe 2-parameter data scaling • InRG theory,the 2Dmetal always existfornv=2(or at large g2for nv=1), whereas M-I-T is a quantum phase transition More realistic RG calculations are needed (finite nv, two-loop)

  37. Thankyou for attention! Theory: SashaFinkelstein- Texas U. BorisAl’tshuler - Columbia U. IgorAleiner- Columbia U. DmitriiMaslov - U.of Florida Valentin Kachorovskii- Ioffe Inst. NikitaAverkiev- Ioffe Inst. Alex Punnoose - Lucent Experiment Dima Rinberg - Harvard Univ. SergeiKravchenko - SEU, Boston, Mary D’Iorio - NRC, Canada John Campbell - NRC, Canada Robert Fletcher - Queens Univ. Gerhard Brunthaler - JKU, Linz Adrian Prinz - JKU, Linz Misha Reznikov - Technion, Haifa Kolya Klimov - Rutgers Univ. Misha Gershenson - Rutgers Univ. Harry Kojima - Rutgers Univ. Nick Busch - Rutgers Univ. Sasha Kuntsevich -Lebedev Inst.

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