View source for Mesoscopic physics

{{short description|Subdiscipline of condensed matter physics that deals with materials of an intermediate size}}
{{about|the sub-discipline of condensed matter physics|the branch of meteorology|mesoscale meteorology}}
{{condensed matter physics}}

'''Mesoscopic physics''' is a subdiscipline of [[condensed matter physics]] that deals with materials of an intermediate size. These materials range in size between the [[nanoscopic scale|nanoscale]] for a quantity of [[atom]]s (such as a [[molecule]]) and of materials measuring [[micrometre]]s.<ref>{{cite journal |last1=Muller|first1=M. |last2=Katsov|first2=K. |last3=Schick|first3=M. |date=November 2006 |title=Biological and synthetic membranes: What can be learned from a coarse-grained description? |url=http://dx.doi.org/10.1016/j.physrep.2006.08.003 |journal=[[Physics Reports]] |volume=434 |issue=5–6 |pages=113–176 |doi=10.1016/j.physrep.2006.08.003 |issn=0370-1573 |arxiv=cond-mat/0609295 |bibcode=2006PhR...434..113M |s2cid=16012275}}</ref> The lower limit can also be defined as being the size of individual atoms. At the [[microscopic scale]] are bulk materials. Both mesoscopic and [[macroscopic scale|macroscopic]] objects contain many atoms. Whereas average properties derived from constituent materials describe macroscopic objects, as they usually obey the laws of [[classical mechanics]], a mesoscopic object, by contrast, is affected by thermal fluctuations around the average, and its electronic behavior may require modeling at the level of [[quantum mechanics]].<ref name=Meso-1>{{cite encyclopedia |title=Sci-Tech Dictionary |encyclopedia=McGraw-Hill Dictionary of Scientific and Technical Terms |year=2003 |publisher=[[S&P Global|McGraw-Hill Companies, Inc.]]}}</ref><ref name=Meso-2/>

A macroscopic electronic device, when scaled down to a meso-size, starts revealing quantum mechanical properties. For example, at the macroscopic level the [[electrical conductance|conductance]] of a wire increases continuously with its diameter. However, at the mesoscopic level, the wire's conductance is [[quantization (physics)|quantized]]: the increases occur in discrete, or individual, whole steps. During research, mesoscopic devices are constructed, measured and observed [[experiment]]ally and [[theoretical]]ly in order to advance understanding of the [[physics]] of [[insulator (electrical)|insulators]], [[semiconductor]]s, [[metal]]s, and [[superconductor]]s. The applied science of mesoscopic physics deals with the potential of building nanodevices.

Mesoscopic physics also addresses fundamental practical problems which occur when a macroscopic object is miniaturized, as with the miniaturization of [[transistor]]s in semiconductor electronics. The mechanical, chemical, and electronic properties of materials change as their size approaches the nanoscale, where the percentage of atoms at the surface of the material becomes significant. For bulk materials larger than one micrometre, the percentage of atoms at the surface is insignificant in relation to the number of atoms in the entire material. The subdiscipline has dealt primarily with artificial structures of metal or semiconducting material which have been fabricated by the techniques employed for producing [[microelectronic]] circuits.<ref name=Meso-1/><ref name=Meso-2/>

There is no rigid definition for ''mesoscopic physics'' but the systems studied are normally in the range of 100&nbsp;nm (the size of a typical [[virus]]) to 1&nbsp;000&nbsp;nm (the size of a typical bacterium): 100 nanometers is the approximate upper limit for a [[nanoparticle]]. Thus, mesoscopic physics has a close connection to the fields of [[nanofabrication]] and [[nanotechnology]]. Devices used in nanotechnology are examples of mesoscopic systems. Three categories of new electronic phenomena in such systems are interference effects, quantum confinement effects and charging effects.<ref name=Meso-1/><ref name=Meso-2>"Mesoscopic physics." McGraw-Hill Encyclopedia of Science and Technology. The McGraw-Hill Companies, Inc., 2005. Answers.com 25 Jan 2010. http://www.answers.com/topic/mesoscopic-physics-1</ref>

==Quantum confinement effects==
[[Quantum confinement]] effects describe electrons in terms of energy levels, [[potential well]]s, [[valence band]]s, [[conduction band]]s, and electron energy [[band gap]]s.

Electrons in bulk [[dielectric]] materials (larger than 10&nbsp;nm) can be described by energy bands or electron energy levels. [[Electron]]s exist at different energy levels or bands. In bulk materials these energy levels are described as continuous because the difference in energy is negligible. As electrons stabilize at various energy levels, most vibrate in [[valence band]]s below a forbidden energy level, named the [[band gap]]. This region is an energy range in which no electron states exist. A smaller amount have energy levels above the forbidden gap, and this is the conduction band.

The quantum confinement effect can be observed once the diameter of the particle is of the same magnitude as the [[wavelength]] of the electron's [[wave function]].<ref>{{Cite book|title=Quantum confinement VI : nanostructured materials and devices : proceedings of the international symposium|last=Cahay|first=M|publisher=Electrochemical Society|others=Cahay, M., Electrochemical Society.|year=2001|isbn=978-1566773522|location=Pennington, N.J.|oclc=49051457}}</ref> When materials are this small, their electronic and optical properties deviate substantially from those of bulk materials.<ref>{{Cite book|title=Quantum theory of the optical and electronic properties of semiconductors|last1=Hartmut|first1=Haug|last2=Koch|first2=Stephan W.|date=1994|publisher=World Scientific|isbn=978-9810220020|edition= 3rd|location=Singapore|oclc=32264947}}</ref>
As the material is miniaturized towards nano-scale the confining dimension naturally decreases. The characteristics are no longer averaged by bulk, and hence continuous, but are at the level of quanta and thus discrete. In other words, the energy [[spectrum]] becomes discrete, measured as quanta, rather than continuous as in bulk materials. As a result, the [[bandgap]] asserts itself: there is a small and finite separation between energy levels. This situation of discrete energy levels is called ''quantum confinement''.

In addition, quantum confinement effects consist of isolated islands of electrons that may be formed at the patterned interface between two different semiconducting materials. The electrons typically are confined to disk-shaped regions termed [[quantum dots]]. The confinement of the electrons in these systems changes their interaction with electromagnetic radiation significantly, as noted above.<ref name=Qdots/><ref>{{cite journal |author=Sánchez D, Büttiker M |title=Magnetic-field asymmetry of nonlinear mesoscopic transport |journal=Phys. Rev. Lett. |volume=93 |issue=10 |pages=106802 |year=2004 |pmid=15447435 |doi=10.1103/PhysRevLett.93.106802 |bibcode=2004PhRvL..93j6802S|arxiv = cond-mat/0404387 |s2cid=11686506 }}</ref>

Because the electron energy levels of quantum dots are discrete rather than continuous, the addition or subtraction of just a few atoms to the quantum dot has the effect of altering the boundaries of the bandgap. Changing the geometry of the surface of the quantum dot also changes the bandgap energy, owing again to the small size of the dot, and the effects of quantum confinement.<ref name=Qdots>[http://www.evidenttech.com/quantum-dots-explained/how-quantum-dots-work.html Quantum dots] {{webarchive|url=https://web.archive.org/web/20100201142348/http://www.evidenttech.com/quantum-dots-explained/how-quantum-dots-work.html |date=2010-02-01 }}. 2008 Evident Technologies, Inc.</ref>

==Interference effects==
In the mesoscopic regime, scattering from defects – such as impurities – induces interference effects which modulate the flow of electrons. The experimental signature of mesoscopic interference effects is the appearance of reproducible fluctuations in physical quantities. For example, the conductance of a given specimen oscillates in an apparently random manner as a function of fluctuations in experimental parameters. However, the same pattern may be retraced if the experimental parameters are cycled back to their original values; in fact, the patterns observed are reproducible over a period of days. These are known as [[universal conductance fluctuations]].

==Time-resolved mesoscopic dynamics==
Time-resolved experiments in mesoscopic dynamics: the observation and study, at nanoscales, of [[Physics#Condensed matter|condensed phase dynamics]] such as crack formation in solids, phase separation, and rapid fluctuations in the liquid state or in biologically relevant environments; and the observation and study, at nanoscales, of the ultrafast dynamics of non-crystalline materials.<ref name=Barty-Nature-Photonics-2-415-08>
{{Cite journal
  | last = Barty| first =Anton| title =Ultrafast single-shot diffraction imaging of nanoscale dynamics| journal =[[Nature Photonics]]| volume =2| pages =415–419 (2008) 
  | date =2008-06-22| doi = 10.1038/nphoton.2008.128| issue=7|display-authors=etal| citeseerx =10.1.1.712.8451}}</ref><ref name=Mesoscopic-dynamics>
{{Cite news |title = Study gains images at ultra-fast timescale  |url=http://www.fofweb.com/Science/default.asp?ItemID=WE40 |format=The research appears in the online edition of the journal Nature Photonics |pages=01| publisher =United Press International | date =2008-06-25| work= Science Online. Facts On File, Inc | access-date =2010-01-25 }}</ref>

== Related ==
{{Div col}}
* {{annotated link|Aharonov–Bohm nano rings}}
* {{annotated link|Branched flow}}
* {{annotated link|Ballistic conduction}}
* {{annotated link|Coulomb blockade}}
* {{annotated link|Nanomaterials}}
* {{annotated link|Nanophysics}}
* {{annotated link|Nanotechnology}}
* {{annotated link|Persistent current}}s
* {{annotated link|Quantum chaos}}
* {{annotated link|Quantum Hall effect}}
* {{annotated link|Quantum wire}}
* {{annotated link|Random matrix}}
* {{annotated link|Semiclassical physics}}
* {{annotated link|Spin–orbit interaction}}
* {{annotated link|Weak localization}}
{{Div col end}}

==References==
{{Reflist}}

== External links ==
* {{Cite web|url=https://www.lorentz.leidenuniv.nl/beenakkr/mesoscopics/topics/chaos/frontiers.pdf|title=Chaos in Quantum Billiards|last=Beenakker|first=Carlo|author-link=Carlo Beenakker|date=1995|website=[[Universiteit Leiden]]|access-date=14 June 2018}}
*{{Cite web|url=https://ocw.tudelft.nl/wp-content/uploads/CollegedictaatMesoscopicPhysicsReader.pdf|title=Mesoscopic physics: an introduction|last=Harmans|first=C.|date=2003|website=OpenCourseWare [[TU Delft]]|access-date=14 June 2018}}
*{{Cite journal|last=Jalabert|first=Rodolfo A. |date=2016|title=Mesoscopic transport and quantum chaos|journal=[[Scholarpedia]]|volume=11 |issue=1 |page=30946|doi=10.4249/scholarpedia.30946|arxiv=1601.02237|bibcode=2016SchpJ..1130946J|s2cid=26633032 |doi-access=free }}

{{Branches of physics}}
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[[Category:Mesoscopic physics| ]]
[[Category:Condensed matter physics]]
[[Category:Quantum mechanics]]