Evidence of anisotropic Kondo coupling in nanostructured devices

Transcription

1 Evidence of anisotropic Kondo coupling in nanostructured devices Luiz Nunes de Oliveira and Krissia Zawadzki University of São Paulo University of São Paulo Stockholm, 19 September 2012

2 Nanostructured devices Elementary geometries Single electron transistor V G V G controls dot occupation n d Side-coupled device V G

3 Coulomb blockade V G Conduction only when n dot is a half-integer

4 Coulomb blockade V G Conduction only when n dot is a half-integer

5 where TK Coulomb blockade can be lifted at very low 0 T Kondo effect FIG. 3. Conductance versus temperature for various values of e0 on the right side (a) and left side (b) of the left-hand peak in Fig. 2. is taken to equal T p K 2 1s 2 1 so that GT K G 02. For the appropriate choice of s, which determines the steepness of the conductance drop with increasing temperature, this form provides a good fit to numerical renormalization group (NRG) results [13] for the Kondo, mixed-valence, and empty orbital regimes, giving the correct KondoVtemperature G in each case. The parameter s is left unconstrained in the fit to our data, but its fit value is nearly constant at in the Kondo regime, while Goldhaber-Gordon as expected it varies rapidly as wet approach al., the mixed-valence regime [Fig. 3(b)]. The expected value PRL 81, 5225 (1998) a e c d r Odd n dot Dot has magnetic moment Conduction spins screen moment Screening allows conduction FIG. 4. The normalized conductance G GG0 is a universal function of T TTK, independent of both ẽ0 and G, in the Kondo regime, but depends on ẽ0 in the mixed-valence F f e

6 Outline of the talk Introduction More recent experimental results Theory Theory vs. experiment and a puzzle Conclusions

7 Ten years after 1998 V G Grobis et al, PRL 100, (2008).

8 Theory Single-electron transistor Anderson Model H = k ɛ k n k U 2 (n d n d ) 2 + V G n d + V k (c k c d + H. c.) G = G 2 G S ( T T K ) G 2 2e2 h 1.0 FL G G2 0.5 V G = 0 ASYMMETRIC SYMMETRIC V G T/TK 103 LM

9 Theory Side-coupled device Anderson Model H = k ɛ k n k U 2 (n d n d ) 2 + V G n d + V k (c k c d + H. c.) G = G 2 [ 1 G S ( T T K )] 1.0 G G2 V G = G0/G2 (G2 G S )/G2 U =3D Γ =0.1 D V G T/TK

10 Theory Anderson model H = k ɛ k n k U 2 (n d n d ) 2 + V g n d + V k (c k c d + H. c.) V G 0 ( ) ( )] T G = αg S + β [1 G S T K TTK G(T T K ) = α = κg 2 sin 2 ( πn LT 2 ) G FL G(T T K ) = β = κg 2 sin 2 ( πn HT 2 ) G LM V G Seridonio et al., EPL 86, 67006(2009).

11 Theory Anderson model H = k ɛ k n k U 2 (n d n d ) 2 + V g n d + V k (c k c d + H. c.) V G 0 ( ) ( )] T G = αg S + β [1 G S T K TTK G(T T K ) = α = κg 2 sin 2 ( πn LT 2 ) G FL G(T T K ) = β = κg 2 sin 2 ( πn HT 2 ) G LM V G Seridonio et al., EPL 86, 67006(2009).

12 Comparison with experiment ( ) ( ) G T maps linearly onto G T TK S TK (a) GF L G ( T TK ) = G S ( T TK ) G FL ( )] + [1 G T S G TK LM 0.8 VG = 204.5mV ( 2e 2 ) TK = 92mK G h GLM ( 2e 2 ) GS h (b) GF L 0.8 VG = 211mV ( 2e 2 ) TK = 168mK G h GLM ( 2e 2 ) GS h

13 Comparison with experiment ( ) ( ) G T maps linearly onto G T TK S TK (a) GF L G ( T TK ) = G S ( T TK ) G FL ( )] + [1 G T S G TK LM 0.8 VG = 204.5mV ( 2e 2 ) TK = 92mK G h GLM ( 2e 2 ) GS h (b) GF L 0.8 VG = 211mV ( 2e 2 ) TK = 168mK G h GLM ( 2e 2 ) GS h

14 Comparison with experiment High (LM) and low (FL) temperaturas 0.8 G( 2e2 h ) 0.6 G F L 0.4 G LM V G (mv) -200

15 Comparison with experiment High (LM) and low (FL) temperaturas 0.8 G( 2e2 h ) 0.6 G F L 0.4 G LM V G (mv) -200

16 Comparison with experiment Symmetrized conductances at high (LM) and low T (FL) 0.8 Ḡ( 2e2 h ) G ( 2e2 h ) 0.00 G F L G LM V G (mv) V G (mv) 200

17 Comparison with experiment Symmetrized conductances at high (LM) and low T (FL) 0.8 Ḡ( 2e2 h ) G ( 2e2 h ) V G (mv) G F L G LM Anisotropy? V G (mv) 200

18 Comparison with experiment Results for 34 V G s ( ) T Gs TK Gs(1) Gs(0) Gs(1) G G(TK) G(0) G(TK) TK(mK) V G (mv) T /T K 1 1

19 Summary Anderson model describes experimental data very well Thanks to universality There are perturbations outside the scope of the model Must allow for partial screening at high T Anisotropic Kondo coupling?