The QHE as laboratory system to study quantum phase transitions
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1 The QHE as laboratory system to study quantum phase transitions Anne de Visser, WZI-UvA Quantum Hall effect Critical behavior and scaling Magnetotransport at the plateau-insulator transition Scaling functions and RG flow diagram A. de Visser 5 FOM Veldhoven 3 Dec 5
2 Thanks to... Dennis de Lang Leonid Ponomarenko Gianni Galistu Aad Pruisken (ITFA Ulrich Zeitler Further reading: De Lang et al., Physica E ( 666. Ponomarenko et al., Physica E (4 36. Pruisken et al., cond-mat/943 De Lang, Ph.D. thesis, 3 June 5 Ponomarenko, Ph.D. thesis, Sept. 5 A. de Visser 5 FOM Veldhoven 3 Dec 5
3 The quantum Hall effect Magnetotransport DEG (kω InGaAs/AlGaAs T 3 mk n.8x 5 m - µ3.4 m /Vs h/ie R i (kω i h e (T A. de Visser 5 FOM Veldhoven 3 Dec 5 3
4 Simple explanation QHE DOS Landau level c N Slope Width Extended states Localised N N plateau insulator Landau quantization e E n ( n h + m* Disorder metal-insulator transitions at ν n+/ filling fraction ν hn e e A. de Visser 5 FOM Veldhoven 3 Dec 5 4
5 Critical behavior & length scales localization length ξ -c χ sample length L L ϕ T p / ξ L ϕ metal ξ << L ϕ insulator A. de Visser 5 FOM Veldhoven 3 Dec 5 5
6 Scaling of conductivity ij ( T, g ij ([ L ϕ ξ ] / χ Pruisken, PRL 988 g ij ( T p / χ ( c ij ( X scaling variable X ν ν ( T ν ν ν c ν ( T T T κ κ p / χ A. de Visser 5 FOM Veldhoven 3 Dec 5 6
7 The - plane Ponomarenko, Thesis UvA A. de Visser 5 FOM Veldhoven 3 Dec 5 7
8 RG flow diagram (e /h L, c, c n Pruisken, PRL transitions at unstable fixed points θ n scaling fields / n n+ (e /h A. de Visser 5 FOM Veldhoven 3 Dec 5 8
9 Magnetotransport at the plateau-insulator transition At PI transition R H quantization separate scaling behavior from effects of sample imperfections Transport tensor with isotropic, H ( S ( + ε ( ij ij ij H variations of carrier density contact misalignment A. de Visser 5 FOM Veldhoven 3 Dec 5 9
10 Experimental results (h/e (h/e 4 3 InGaAs/InP heterostructure n.x 5 m - µ.6 m /Vs.37K 5 5 (T up down c.37k.6k.k.6k.37k A. de Visser 5 FOM Veldhoven 3 Dec 5.K 4.K Plateau-insulator transition at c 7. T Quantized Hall insulator T. K H ( ( ( + ( ( ( de Lang et al., Physica E
11 Longitudinal resistivity (h/e. I QH /ν T.6 K T 4. K ν c.55 ν 3 κ T (K ν ν c ~ c Scaling yields κ ( X X v ν / v ( T ( T e X O( X c ( T / T h / e κ κ.57 ±. T 88 ± K 3 A. de Visser 5 FOM Veldhoven 3 Dec 5
12 Hall resistivity H Corrections to scaling nd critical exponent y ( X +η( T ( X H η( T T T y H (h/e...8 T 4. K T. K i ν η (T (h/e.5..5 δν c /ν. y.5 ±.. T 9.8 ±.3K. 3 4 X T (K.6 I QH ν T (K A. de Visser 5 FOM Veldhoven 3 Dec 5
13 Renormalization Group flow diagram Universal scaling functions H + + η + η + + η beta functions κ.57 y.5 T 88 K T 9.8 K ( X e ν ( T / T κ T η( T T y d d ln L d d ln L β β ( (,, A. de Visser 5 FOM Veldhoven 3 Dec 5 3
14 Comparing PI and PP raw data isotropic data Particle hole symmetry for PI transition only ( X ( X ( X ( X H H A. de Visser 5 FOM Veldhoven 3 Dec 5 4
15 Summary QHE is a quantum critical phenomenon PI transition: disentwine macroscopic sample inhomogeneities and intrinsic universal aspects Magnetotransport at PI transition - proper scaling - H quantized, deviations corrections to scaling Flow lines ( H at the PI transition have been extracted from the experiment universal scaling functions A. de Visser 5 FOM Veldhoven 3 Dec 5 5
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