Mesoscopic Physics (TMP-TA6),
SoSe-2013
Lecturers: Prof. Dr. Jan von Delft, Dr. Oleg Yevtushenko
Working language: English
6 hrs. per week (lectures and student seminars) on Tuesday,
Thursday, and Friday 14-16, room 449
1. 2nd
Quantization
(1 lecture on April 18), lecture notes can be found here
2. Superconductivity: the BCS
theory, thermodynamics of SupCond, tunnelling - 6
lectures on
May 31 (Fri.) – notes can be found here
·
Introduction:
a failure of the classical Drude model for some
metals at T < Tc, basic properties of SupCond, a brief historical review of the study of SupCond;
·
SupCond as a new
state of matter: H-T phase diagram for type I SupCond,
the principal difference between SupCond and ideal
normal metals;
·
Failure
of the naïve approach to explain superconductivity: a contradiction
between the Landau criterion for superfluidity and
the spectrum of excitation in Fermi systems.
June 4 (Tue.) – notes
can be found here
·
the
Fröhlich polaron:
phonon-mediated attraction of two electrons with opposite spins, the
competition of attraction and repulsion;
·
the
hierarchy of energy scales and the effective model of interactions;
·
Cooper
pairs: the toy model which explains an origin of the bound state in 3d.
June 7 (Fri.) – notes can be found here
·
the
gap in the energy of the Cooper pairs;
·
the
many-body-physics approach to describe the superconductivity, the coherent
state with a single phase;
·
the BCS
ground-state wave function: trial BCS wave-function, minimization of the
ground-state energy (the “u-v” method),
the gap equation for T=0.
June 11 (Tue.) – notes can be
found here
·
the
BCS theory as a MFA: basic ideas, anomalous expectation values, expanding the
reduced Hamiltonian in small fluctuations;
·
diagonalization of the MF
Hamiltonian, the Bololubov transformation, the
spectrum of excitation in new basis and the DoS of Bogolubov quasiparticles;
·
thermodynamics of SupCond: the gap equation at finite T, the gap as the order parameter, the equation for Tc.
June 14 (Fri.) – notes can be found here
·
single
particle- and Cooper pair- tunnelling in NIS and SIS junctions, experimental
observations of the gap;
·
dc-
/ ac- Josephson’s effect, two-level model, effective resistive circuit, the
Josephson generation of ac signals;
·
thermodynamics of SupCond (continuation, if time permits).
June 18 (Tue.)
·
SupCond qubits (by Jan von Delft)
3. Theory of
disordered systems, 6 lectures on
June 25 (Tue.) – notes can be found here
·
Introduction:
Disordered systems, classical diffusion of particles in a disordered potential,
the Einstein relation;
·
Beyond
the classical picture: interference corrections, self-intersecting
trajectories, enhanced return probability in disordered samples;
·
Weak
localization correction to the Drude conductivity: a simple estimate, dephasing time as the IR cut-off.
July 2 (Tue.) – notes can be found here
·
Discrete
models of disorder: random systems on a lattice, fluctuating parameters and
their probability distribution function;
·
The
Anderson model and the localization transition; RMT models for quantum dots and
quantum wires;
·
The
Edwards model of disorder in the thermodynamic limit, its generating
functional, correlation functions and cumulants; the
model of the (weak) Gaussian white-noise disorder.
July 5 (Fri) – notes can be found here
·
Self-averaging
quantities, disorder averaging;
·
Retarded/advanced
Green’s functions (GF), their basic properties, DoS
and LDoS expressed in terms of the GFs;
·
Perturbation
theory in the impurity potential for the GFs, disorder averaging for the
white-noise Gaussian disorder, ir-/reducible
diagrams;
·
Disorder-induced
self-energy and the Dyson equation, the leading contribution to the
self-energy, the disorder-averaged GFs, the elastic scattering time.
July
9 (Tue.) – notes can be found here
·
Disorder
averaged DoS in 3d;
·
Sub-leading
contributions to the disorder-induced self-energy, estimating a phase-space for
different classes of the diagrams, the first selection rule of the diagrammatic
technique;
·
Quantum
propagator of a wave-packet, basics definitions, the expression in terms of the
Green’s functions, simplifications due to the energy scale separation.
July
12 (Fri.) – notes can be found here
·
Normalization
of the diffusive propagator, its short- and long-range classical parts;
·
The
ladder (diffusion) approximation, the Diffuson, the
diffusion equation;
·
Conductivity
of a disordered metal, basics definitions and the expression in terms of the
Green’s functions.
July
16 (Tue.) – notes can be found here
·
Calculating
the classical conductivity by using the Drude/Boltzmann
approximation;
·
Weak
localization corrections, the Cooperon ladder
diagrams;
·
The
second selection rule, mesoscopic diagrammatic
techniques as a loop expansion in Diffusons/Cooperons.
Optional: universal
conductance fluctuations, notes can be found here
July 18 (Thu.) - Weak localization (from the theory of dephasing to the
experimental study of the WL)
July 19 (Fri.)
- Majorana fermions (from basic definitions and
Kitaev’s model to modern experiments)
Recommended literature
1. A.A. Abrikosov,
“Fundamentals of the theory of metals” [general reading]
2. M. Tinkham, “Introduction to
superconductivity” [superconductivity]
3. E. Akkermans and G. Montambaux, “Mesoscopic physics
of electrons and photons” [disordered systems]
4. A. Altland and B.D. Simons
“Condensed matter field theory” [advanced reading]
Last update: 19.07.2013