Transport in low-dimensional mesoscopic systems [Elektronische Ressource] / von Sergey Syzranov

Syzranov, Rykovanov Sergey

Sujets

• Physik

Informations

• Publié par: ruhr-universitat_bochum
• Publié le: 01 janvier 2011
• Nombre de lectures: 10
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

derTBoranspvortPhinBoLovw-dimensional2011MesoscopicundSystemsersitDISSERhTSergeyAMoskTIONhzururErlangungysikdesAstronomieGradesRuhr-UnivDoktoratdercNaturwissenscumhaftenonanSyzranoderausFauakultcatumfEremin1.ter:Gutac05.05.2011hDr.ter:derProf.hDr.ProfK.B.I.EfetoDatumvDisputation:2.GutacTransport in Low-Dimensional
Mesoscopic Systems
Sergey Syzranov
Physics Department
Ruhr-Universit¨at Bochum
A thesis submitted for the degree of
PhD
January 20111. Reviewer: Prof. Dr. K.B. Efetov
2. Reviewer: Prof. Dr. I. Eremin
Day of the defense: 05.05.2011
Signature from head of PhD committee:
iiContents
Summary iii
Zusammenfassung vii
List of Figures xi
Glossary xiii
1 Introduction 1
1.1 Graphene: overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Electronic properties of graphene . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Networks of Josephson junctions . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Hamiltonian of junction arrays and granulated superconductors 9
1.5 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Electron dynamics in irradiated graphene sheet 15
2.1 Radiation-induced dynamical gaps . . . . . . . . . . . . . . . . . . . . . 16
2.2 Tunneling through gaps . . . . . . . . . . . . . . . . . . . . . 19
2.2.1 Normal incidence on a potential barrier . . . . . . . . . . . . . . 19
2.2.2 Radiation-induced hops between trajectories . . . . . . . . . . . 24
3 Photocurrent in graphene p-n junctions 27
3.1 Generic formula for the current in irradiated 2D junction . . . . . . . . 27
3.2 Electron trajectories in a ballistic graphene p-n . . . . . . . . . 30
3.2.1 Effectively two-dimensional electron paths . . . . . . . . . . . . . 32
3.2.2 Almost normal incidence on a barrier . . . . . . . . . . . . . . . 35
3.3 Photocurrent in ballistic samples . . . . . . . . . . . . . . . . . . . . . . 36
i3.3.1 Photocurrent due to effectively two-dimensional modes . . . . . . 37
3.3.2 Photocurrent due to normal modes . . . . . . . . . . . . . . . . . 41
3.3.3 Total current vs. radiation intensity . . . . . . . . . . . . . . . . 43
3.3.4 Suppression of the tunneling . . . . . . . . . . . . . . . . . . . . 43
3.4 Photocurrent in disordered samples . . . . . . . . . . . . . . . . . . . . . 44
3.5 Photocurrent in shallow-potential junctions . . . . . . . . . . . . . . . . 51
3.6 Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.6.1 Optimal conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.6.2 Shallow-potential junctions . . . . . . . . . . . . . . . . . . . . . 59
4 Quantum interference in irradiated low-dimensional junctions. 61
5 Discussion of Chapters 2–4 71
6 Granulated superconductors: mean-field approach 73
7 First-order superconductor-insulator transition 77
7.1 Effective field theory in a clean JJA . . . . . . . . . . . . . . . . . . . . 77
7.2 RG analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
7.3 Phase diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
8 Conductivity of a weakly disordered JJA 85
9 Discussion of chapters 6–8 91
Acknowledgements 93
References 95
Brief CV 105
Publications 106Summary
Technological advance of the past couple decades has enabled researches to manipulate
quantumstates of single electrons and few-levelsystems, as well as to observe quantum
interference phenomena on the macroscopic scale aka mesoscopic phenomena.
The achievements in fabricating miniature superconductive devices, elements of
carbon-based electronics, and qubits demand an adequate theoretical description of
respective systems.
The thesis you are holding in your hands deals with two burning topics of the
modern-day mesoscopics: (i) physics of graphene-based optoelectronics and (ii) low-
temperature properties of granulated superconductors and superconductive films.
Radiation-induced phenomena in graphene
The first topic is the subject of Chapters 2–4. First we consider generic illumination
effects on electron dynamics in the bulk of a clean graphene sheet, with no reference
to particular devices or practical applications. We show that monochromatic radiation
opensdynamicalgapsinthequasiparticlespectra, proportionaltotheamplitudeofthe
electromagnetic field and inversely proportional to its frequency. In the spatial regions,
where the Fermi level matches the position of the dynamical gap, the transmission
of quasiparticles is determined by the dynamical Landau-Zener tunneling through the
gap.
In Chapter 3 we consider graphene p-n junctions subject to an illumination by a
monochromatic electromagnetic wave. The dynamical gaps lead to a strong modifica-
tion of the current-voltage characteristics of the junctions. In case of high enough po-
tential barriers the directed current (photocurrent) flows through the junction without
iiianydcbiasvoltageapplied. Wecalculateanalyticallythephotocurrentandcompareits
values to those observed in the recent experiments on graphene-based photodetectors.
Atsmallradiationintensities,thephotocurrent,proportionaltotheradiationpower,
is a result of inelastic quasiparticle tunneling assisted by one-photon absorption. The
photocurrent is maximal for the photon energies~Ω smaller than the height of the
potential barrier U in the junction and quickly decreases with increasing the ratio0
~Ω/U for larger photon energies.0
At large intensities, the photocurrent decreases with radiation power and finally
saturates at some constant value, provided the potential barrier in a junction is high
enough. Otherwise the photocurrent decreases to zero at large radiation intensities,
which can be used to suppress transport in graphene devices by illumination.
Also, we analyse the effect of elastic impurities and electron-electron interaction on
themagnitudeofthephotocurrent, andshowthattheyweaklyaffectthephotocurrent,
if the diffusive resistance of the junction is not too large compared to the ballistic one.
InChapter4wepredictandanalysearadiation-inducedquantuminterferenceeffect
in a clean effectively one-dimensional junction, e.g. based on a carbon nanotube: the
photocurrent oscillates as a function of gate voltages due to the interference between
electron paths accompanied by the resonant photon absorption.
Physics of Josephson networks
Chapters 6–8 deal with low-temperature phase transitions and transport in disordered
arrays of Josephson junctions and granulated superconductors. As we show in the
Introduction, the generic Hamiltonian, that we use to describe the motion of bosons in
such systems, is equivalent to the Hamiltonian of Cooper pairs in uniformly disordered
superconductive films.
First we study in Chapter 6 the phase diagram of the systems under consideration
using the mean-field approach. We recover the previously known results for the critical
parameters, at which the superconductor-insulator transition occurs, and discuss the
applicability of the mean-field method.
It turns out that arbitrarily small intergrain Coulomb interactions, that are al-
ways present in the systems under consideration, lead to divergencies in the effectiveGinzburg-Landau functional and thus void the applicability of the single-parameter
time-independent mean-field approach.
To consider properly the effect of long-range interactions we follow the approach of
Fisher and Grinstein, namely, we introduce a gauge field that comes from the voltage
induced on a grain by the other far-away grains. However, our RG analysis of the
effective Ginzburg-Landau action leads to conclusions qualitatively different from the
previously known results. We show in Chapter 7 that the superconductor-insulator
transition is of the first order in all 3D systems and in most 2D arrays of superconduc-
tive islands. The first-order phase transition may be detected, e.g., by the hysteretic
behaviour of physical quantities when applying magnetic field to the system or by the
ac conductivity that should acquire a finite value immediately at the transition point.
In Chapter 8 we study transport in the insulating phase sufficiently far from the
superconductor-insulator transition, meaning the Josephson couplings between grains
are sufficiently exceeded by the characteristic charging energies.
Theconductivitycomesfromthemotionofchargedmonopole-likeexcitations. They
posses a gap in their spectrum approximately equal to the energy required to bring the
charge of a Cooper pair on a single grain. Because of the gap the conductivity of the
system is exponentially small in the temperature∝exp(−E /T ), whereE is the value0 0
of the gap.
Inabsenceofdisordertheexcitationsfreelypropagateinthesystemwithoutscatter-
ing and thus the conductivity is infinite. A system of finite size, however, is character-
ized by a finite conductance. Because the concentration of excitations is exponentially
small in temperature, so is the conductance.
To arrive at a finite conductivity it is essential to account for disorder represented
by irregularities in the array and offset charges. We develop a diagrammatic technique
to treat the disorder, and, using it, find the Drude-type conductivity and the weak
localization correction to the conductivity. Again, they is exponentially
small in temperature with the activation gap nearly equal to the charging energy of a
boson on a grain.
If the temperature i