Magnetic impurities, wave packet dynamics, transport in the...
Transcript of Magnetic impurities, wave packet dynamics, transport in the...
Collaborators: José-Antonio Méndez-Bermúdez (Puebla)Stefan Kettemann (Bremen, Pohang)Eduardo Mucciolo (Orlando)Victor Gopar (Zaragoza)Andrei Jesús Martinez Mendoza (Puebla)
thanks to: V.Kravtsov, B.Shapiro, A.Ossipov, Th.Seligman, A.Mirlin, F.Evers,O.Yevtushenko, E.Cuevas, B.Eckhardt, U.Smilansky, G.Zarand
AvH, OTKA, CiC, Conacyt, DFG, POSTECH etc.
Imre VargaElméleti Fizika TanszékBudapesti Műszaki és Gazdaságtudományi Egyetem, H-1111 Budapest, Magyarország
Imre VargaElméleti Fizika TanszékBudapesti Műszaki és Gazdaságtudományi Egyetem, H-1111 Budapest, Hungary
Magnetic impurities, wave packet dynamics, transportin the presence of multi-fractal states
Imre VargaDepartment of Theoretical PhysicsBudapest University of Technology and Economics, H-1111 Budapest, Hungary
Outline Introduction Anderson transition Random matrix modell of the MIT: PBRM Spectral statistics, multifractal states
New results with PBRM at criticality Scattering, transport Wave packet dynamics Magnetic impurities
Summary and outlook
Hamiltonian:
Energies n are uncorrelated, random numbers from uniform (or bimodal, Gaussian, Cauchy, etc.) distribution W
Nearest-neighbor hopping V
Bloch states for W V, localized states for W V
W V ??
Anderson model (1958)
WV <<WV >> WV ∝
Two energy (time) scales: ETh and (D and H) g = ETh/ = H/D
One-parameter scaling (1979)
Metal – insulator transition (MIT) for d>2.
Gell-Mann – Low function
Spectral statistics (d=3)
MIT
Spectral statistics (d=3)
W < Wc• extended states• RMT-like
W > Wc• localized states• Poisson-like
W = Wc• multifractal states• intermediate
‘mermaid’
Superscaling Dependence on symmetry parameter β
superscaling relationthru parameter g
with andare the RMT limit
Varga, Hofstetter, Pipek ’99
Eigenstates
extended stateweak disorder, band center
localized statestrong disorder, band edge
(L=240) R.A.Römer
Multifractal eigenstate at the MIT
Inverse participation numbers
Box counting technique• fixed L• state-to-state fluctuations
PDF analysis
• higher accuracy• scaling with L
http://en.wikipedia.org/wiki/Metal-insulator_transition (L=240) R.A.Römer
Multifractal statesdetected in reality
Unusual features of the MIT Interplay of eigenvector and spectral
statistics Chalker et al. ‘95
Anomalous diffusion at the MIT Huckestein et al. ‘97
Correlation dimension Kravtsov and Cuevas ‘07
LDOS vs wave function fluctuations Huckestein et al. ‘97
2D
Tested for “weak” multifractality (3dO, 2dU, 2dS), i.e. when D2d.
Scattering at the MIT
Kottos and Weiss ’02; Weiss, et al. ‘06
Detect the MIT using a stopwatch!
PBRM: Power-law Band Random Matrix
Model: matrix with and
asymptotically
parameters: and
Mirlin, et al. ‘96, Mirlin ‘00
PBRM: Power-law Band Random Matrix
for RMT, as if for similar to metal with
d
for BRM Poisson, as if for power law localization with exponent (cf. Yeung-Oono 87)
for criticality (cf. Levitov ‘90)
continuous line of transitions: b
PBRM at criticality ( ) for b non-linear -model RG, SUSY (Mirlin ‘00)
• large conductance: g*=4b for b real-space RG, virial expansion, SUSY
(Levitov 99, Yevtushenko-Kravtsov ‘03, Yevtushenko-Ossipov ‘07)
Mirlin ‘00
Multifractality universal distribution of participation numbers
with
state-to-state fluctuations of correlation dimensions
and
connection between the two: fixed point
so
Cuevas ‘02 and Varga ‘02
β = 1
β = 2
joint distribution state-to-state fluctuation
Varga ‘02
How does multifractality show up?
Scattering, conductance
LDOS vs wave function fluctuations
Anomalous diffusion at the MIT
Screening of magnetic impurities
Scattering: PBRM + 1 lead scattering matrix
Wigner delay time
resonance width, eigenvalues of poles of
Perfect coupling distribution of phases for
b > 1:
with
perfect coupling achieved:
Measure multifractality using a stopwatch!
PBRM + 1 lead
JA Méndez-Bermúdez – Kottos ‘05 Ossipov – Fyodorov ‘05:
b = 0.1 b = 0.1
b = 1.0 b = 1.0
b = 10 b = 10
JAMB and Varga ‘06
b = 0.1b = 0.1
b = 1.0 b = 1.0
b = 10b = 10
JAMB and Varga ‘06
Scaling of typical values
JAMB and Varga ‘06
Scattering, transport geometry
Geometry A
Geometry B
JAMB, Gopar, and Varga ’10, (Monthus and Garel ‘09, ’10)
Scattering matrix elements
A
B
Transport quantities: T, P
Conductance
Shot noise
w(T) for M=1
A B
A Bw(ln T) for small b
w(T) for M=2
A B
AB
universal behavior
ConductanceA B
Shot noiseA B
AConductance and shot noise
Unusual features of the MIT
LDOS vs wave function fluctuations
Anomalous diffusion at the MIT
Tested for weak multifractality (3dO, 2dU, 2dS)
Wave function and LDOS
Wave functions LDOS
JAMB and Varga ’10 (in preparation)
Wave function and LDOS
Wave packet dynamicsasymptotic wave packet profile survival probability
Wave packet dynamics (summary)
effective dimensionality changes with b
JAMB and Varga ’10 (in preparation)
Kondo effect in disordered metals
TK depends on r P(TK) wide, bimodal
Nagaoka – Suhl:
Unscreened (free) magnetic moments exist,
if
Weakly disordered metal: Insulator:
D the bandwidthS. Kettemann, E. Mucciolo and I. Varga ’09
Kondo effect at the critical pointlognormaldistribution ofwave function components
Joined probability of wave functions
enhanced energy correlationof wave functions
Kondo effect around the critical point
Free magnetic moments exist away from the critical point
Symmetry class of the metal-insulator transition
Critical point symmetry dependent:
In case of
Summary and outlook
Summary new details of scattering, transport at criticality; wave packet dynamics understood for weak
multifractality only (b → ∞); new details found about the MIT
as an interplay of Kondo physics and disorder;
Outlook spectral correlation for strong multifractality RKKY + Kondo effect of many body physics other ???
Thank you for your attention