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Accueil > Zone Pages > Pages Personnelles > Denis Basko > Personal page of Denis Basko

Personal page of Denis Basko

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My research activities
- Anderson localization with interactions
- Optical properties of graphene and graphite
- Energy transfer in hybrid nanostructures

Teaching

My CV

 

 

Research activities

Anderson localization in the presence of interactions or nonlinearities

What is it ?

In a perfect crystal, electronic wave functions are the Bloch waves. The electron freely propagates through the crystal, and each wave function extends over the whole crystal. In a disordered crystal (e.g., due to impurities), it is natural to assume that random scattering on the impurities leads to the diffusive character of the electron motion, the disorder strength determining the diffusion coefficient. The wave functions are then randomly oscillating, but they still extend over the whole crystal. However, sometimes this picture turns out to be totally wrong, and one faces the absence of diffusion in certain random lattices. The electron, injected on one end of the sample, never reaches the other end ; the diffusion coefficient is exactly zero, and all transport is stopped. Everywhere in the crystal, the wave functions are localized with an exponentially decreasing envelope. This is called Anderson localization. It is an effect of quantum interference : the propagation is stopped even in the classically allowed region. In three dimensions it occurs at sufficiently strong disorder or near the band edges. In one dimension, all states are localized by an arbitrarily weak disorder.


Anderson localization is a universal phenomenon, not specific to electrons in disorder. It has been observed for microwaves, light, acoustic waves, and ultracold atoms. It may occur for any wave trying to propagate through a disordered medium. Quantum mechanics is only needed to make particles behave like waves. Formally, one always studies eigenfunctions of a linear operator which contains Laplacian of some sort (differential or discrete), as well as some kind of disordered potential.


Anderson localization is reasonably well understood for non-interacting particles or linear waves. For nonlinear waves the superposition principle breaks down completely ; for interacting quantum particles it holds, but only in the many-body Hilbert space whose dimensionality is exponentially large compared to that of the single-particle problem. Thus, the formal set-up of the problem is completely different from the non-interacting/linear case. Moreover, it depends on the specific system. A relatively simple case is when the system is coupled to an external thermal bath (e. g., electrons coupled to phonons). The bath provides noise which destroys coherence, necessary for Anderson localization. Then the localization is destroyed, and transport is allowed. But what happens if there is no external bath, just intrinsic interaction between particles or nonlinearity present in the medium ? Will the particles be able to propagate ?

Why is it interesting ?

My fascination with the subject comes from the very basic question, underlying the whole statistical physics : how does a system, governed by the reversible Hamiltonian dynamics (whether classical or quantum), irreversibly reach the thermal equilibrium ? Indeed, a localized non-interacting/linear system never equilibrates : the particles will simply sit in their localized states forever. It is only interaction/non-linearity that may (or still may not) lead to non-trivial kinetics, which results in equilibration and transport. Besides this fundamental interest, the problem s quite challenging from the technical point of view, and requires development of new theoretical tools.

Why is it useful ?

In spite of numerous experiments where people have worked very hard to observe Anderson localization, from the simple practical point of view localization looks rather harmful than useful. Indeed, it inhibits conduction and transport. Thus, it is useful to study when the localization persists and when it is destroyed.

My selected publications on this topic :

D. M. Basko, "Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schroedinger chain in the regime of homogeneous chaos", Physical Review E 89, 022921 (2014).

D. M. Basko, "Weak chaos in the disordered nonlinear Schrödinger chain : destruction of Anderson localization by Arnold diffusion", Annals of Physics 326, 1577–1655 (2011).

D. M. Basko, I. L. Aleiner, and B. L. Altshuler, "Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states ", Annals of Physics 321, 1126–1205 (2006).

Some other reading on this topic :

S. Fishman, Y. Krivolapov and A. Soffer, "The nonlinear Schrödinger equation with a random potential : results and puzzles", Nonlinearity 25, R53–R72 (2012).

I. L. Aleiner, B. L. Altshuler, and G. V. Shlyapnikov, "A finite-temperature phase transition for disordered weakly interacting bosons in one dimension", Nature Physics 6, 900–904 (2010).

V. Oganesyan, A. Pal, and D. A. Huse, "Energy transport in disordered classical spin chains", Physical Review B 80, 115104 (2009).

Theory of optical properties of graphene and graphite

What is it ?

Graphene is a two-dimensional layer of tightly bound carbon atoms arranged in a honeycomb lattice. Graphite is what pensils are made of. It consists of parallel graphene layers, which are weakly bound together (this is why pencils write).

Electrons in graphene/graphite are most often probed either by transport measurements (i.e., one attaches contacts to the sample and measures current), or by optical spectroscopy (one shines light on the sample and analyzes the light that comes out). Absorption spectroscopy (meausrement of how much light is lost in the sample) probes excitations of the crystal with energies corresponding to that of the incident photons. typically, electron-hole pairs. Raman spectroscopy (measurement of how much light comes out at frequencies different from the incident frequency) probes excitations at lower energies, and can detect electronic excitations, as well as phonons. Raman spectroscopy can also give information on electron-phonon coupling.

Application of a magnetic field to the sample provides an additional degree of freedom for probing electronic properties. Indeed, instead of the continuous band, electronic spectrum in two-dimensional systems shrinks into a sequence of discrete Landau levels, so all optical transitions are modified. Magneto-absorption and magneto-Raman measurements detect how exactly they are modified, and provide additional information on electrons, phonons, and their interactions.

Why is it interesting ?

Many people are excited about the Dirac form of the low-energy part of the electronic dispersion in the monolayer graphene. On the one hand, this is just one out of many kinds of dispersion which can occur in the good old solid state physics. On the other, this special case has some rather funny consequences. For example, a single graphene layer absorbs a fraction of πα=2.3% of the incident light, which is independent of any material parameters (π=3.14..., α≈1/137). Another example, in a magnetic field, Landau level energies scale as ∝√n instead of ∝n, so that the quantum Hall effect can be observed at room temperature.

What I like about graphene and graphite is their quite simple structure with high symmetry, so that many phenomena can be described by simple models whose parameters are well known and calculations can often be done all the way to final numbers which can be compared to experiments. Indeed, I have benefited a lot from collaborations with experimental groups of Marek Potemski at the Laboratoire National des Champs Magnétiques Intenses in Grenoble and of Andrea Ferrari at the Department of Engineering in Cambridge University.

Why is it useful ?

So much has been said on this subject, that I would rather cite TechEYE, or BBC news, or Physics World.

My selected publications on this topic :

M. Orlita, P. Neugebauer, C. Faugeras, A.-L. Barra, M. Potemski, F. M. D. Pellegrino, and D. M. Basko, "Cyclotron Motion in the Vicinity of a Lifshitz Transition in Graphite", Physical Review Letters 108, 017602 (2012).

D. M. Basko, S. Piscanec, and A. C. Ferrari, "Electron-electron interactions and doping dependence of the two-phonon Raman intensity in graphene", Physical Review B 80, 165413 (2009).

D. M. Basko, "Calculation of the Raman G peak intensity in monolayer graphene : role of Ward identities", New Journal of Physics 11, 095011 (2009).

D. M. Basko, "Theory of resonant multiphonon Raman scattering in graphene", Physical Review B 78, 125418 (2008).

Some general reading on this topic :

K. S. Novoselov, "Nobel Lecture : Graphene : Materials in the Flatland, Reviews of Modern Physics 83, 837–849(2011).

A. C. Ferrari and D. M. Basko, "Raman spectroscopy as a versatile tool for studying the properties of graphene", Nature Nanotechnology 8, 235 (2013).

Energy transfer in hybrid nanostructures

My selected publications on this topic :

V. M. Agranovich, D. M. Basko, and G. C. La Rocca, "Efficient optical pumping of organic-inorganic heterostructures for nonlinear optics", Physical Review B 86, 165204 (2012).

D. M. Basko, F. Bassani, G. C. La Rocca, and V. M. Agranovich, "Electronic energy transfer in a microcavity", Physical Review B 62, 15962–15977 (2000).

D. Basko, G. C. La Rocca, F. Bassani and V. M. Agranovich, "Förster energy transfer from a semiconductor quantum well to an organic material overlayer", European Physical Journal B 8, 353–362 (1999).

Some other reading on this topic :

V. M. Agranovich, Yu. N. Gartstein, and M. Litinskaya, "Hybrid Resonant Organic–Inorganic Nanostructures for Optoelectronic Applications", Chemical Reviews 111, 5179–5214 (2011).

Teaching

Kinetic theory and its applications to electron transport in metals
Electronic transport in disordered systems

Short CV

1991–1997 : Московский физико-технический институт (Moscow Institute for physics and technology), факультет общей и прикладной физики, 126 группа, undergraduate student
1998–2000 : Scuola Normale Superiore di Pisa, Classe di Scienze, Ph.D. student
2001–2002 : University of Rochester, Chemistry Department, post-doc
2002–2004 : International Centre for Theoretical Physics, Condensed Matter and Statistical Physics Section, postdoc
2004–2005 : Princeton University, Physics Department, postdoc
2005–2007 : Columbia University, Department of Physics, postdoc
2007–2008 : Scuola Internazionale Superiore di Studi Avanzati, Condensed Matter Theory Sector, researcher
2008–present : Centre National de la Recherche Scientifique, Laboratoire de Physique et Modélisation des Milieux Condensés, researcher


My full list of publications