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Graphene physics
Graphene, an isolated single atomic layer of graphite has proven to be an
ideal two-dimensional system which was theoretically predicted to exhibit
many unique electronic properties. The band structure of graphite was
calculated as early as in 1947 which, near the Fermi level at half-filling,
consists of two linearly dispersing Dirac cones. As a result, the
low-energy excitations behave effectively relativistic like, where the
electron dynamics is governed not by the Schrödinger equation, but
by a Dirac equation. In a magnetic field the spectrum develops into the
Landau levels that are four-fold degenerate (two from the spins and the
other two from the two inequivalent Dirac cones). The wave functions for
the electrons in this system shows chiral behaviour. Experimental
observation of the quantum Hall effect in graphene has confirmed many of
these predictions. There are, however, many unanswered questions that
rose from these observations and many other predictions have been
reported regularly. The field is progressing very rapidly and most
of the developments have taken place in 2006 alone.
 V. Apalkov and T. Chakraborty,
Phys. Rev. Lett. 97, 126801 (2006).
H.-Y. Chen, V. Apalkov, and
T. Chakraborty, Phys. Rev. Lett. 98, 186803 (2007).
X.F. Wang and T. Chakraborty,
Phys. Rev. B75, 041404 (R) (2007).
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Electrons in DNA
DNA is the molecule responsible for storage of genetic information in the
cells of all living organisms. Charge migration in natural DNA is linked
to early stage of cancer while it can also serve as the foundation for future
nanoscale devices. Until recently, it was believed that charge migration
occurs primarily between the guanine (G) and adenine (A) bases and DNA as a
current carrier is a polymer chain. There are two established mechanisms of
charge transfer between the DNA bases: tunneling or thermal hopping. The
current decays exponentially in the former case while it remains insensitive
to the length of DNA in the latter case. This picture was largely based on
various experiments reported in the literature. However, Prof. Chakraborty
and his associates realized that these experiments in fact demonstrated a
geometrical effect of DNA: The bases of DNA have a ladder structure instead
of the presumed chain structure, and the experimental observation can be
accounted for by intra- and inter-strand tunneling without invoking the
thermal hopping. With this alternative theory, the experiments could be
explained perfectly.
In another DNA project, Prof. Chakraborty and his collaborators investigated
the transverse charge transport through DNA which is potentially important
for rapid DNA sequencing.
T. Chakraborty, (Ed.),
Charge Migration in DNA: Perspectives
from Physics, Chemistry, and Biology
(Springer, First Edition 2007).
X.F. Wang and T. Chakraborty, Phys. Rev. Lett. 97,
106602 (2006).
V. Apalkov and T. Chakraborty, Phys. Rev. B72, 161102 (R)
(2006).
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Spin-orbit coupling in
nanostructures
It has long been recognized that a two-dimensional
electron gas (2DEG) in narrow-gap semiconductors,
particularly in InAs-based systems with its high values
of the g-factor, exhibit zero-field splitting
due to the spin-orbit (SO) coupling.
This coupling is also the driving mechanism for making
futuristic devices based on controlled spin transport,
such as a spin transistor, where the
electron spins would precess (due to the SO coupling)
while being transported through the 2DEG
channel. Tuning of this precession in the proposed
spin transistor would provide an additional control
that is not available in conventional devices, but may
be crucial for the rapidly emerging field of semiconductor
spintronics.
M. Califano, T. Chakraborty, and P. Pietiläinen, Phys. Rev.
Lett. 94, 246801 (2005).
T. Chakraborty and P. Pietiläinen, Phys. Rev. Lett. 95,
136603 (2005).
V. Apalkov, A. Bagga, and T. Chakraborty, Phys. Rev. B73,
161304 (R) (2006).
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Quantum Hall Effects
Despite a span of more than two decades since the
discovery of this effect, with a truly large number of
people from various sub-fields doing intensive research, and
after two Nobel prizes,
[See additional materials
at the Nobel Foundation site).]
the quantum Hall effects (QHE) still
remain a major topic of interest in condensed matter physics.
Electrons moving on a plane at extremely low
temperatures and under the influence of a strong
perpendicular magnetic field are known to exhibit
very curious behavior. The most famous one is the
fractional quantum Hall effect at 1/3 filled
lowest Landau level discovered by A.C. Gossard, H. Störmer,
and D. Tsui in 1982. The theory of Robert Laughlin described
in 1983 the "1/3-state" where electrons condense into a
ground state which is a charge-neutral liquid.
The low-lying excitations
in the liquid behave
like particles that carry fractions (e/3 for the
1/3 state) of electron charge. The liquid in this state
is famously known to be incompressible
. Störmer, Tsui and Laughlin shared the Nobel prize
in 1998 for initiating a revolution that is yet to subside.
As a result of intense investigations
of the quantum Hall effect over the past two decades,
a lot is known theoretically about the 1/3 state,
but very little in terms of direct information of
the electronic properties of the incompressible state.
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The diagonal line (dashed) represents the "classical" Hall resistance and the
full line with the steps are the observed quantum Hall effects. Magnetic
fields at which the steps appear are marked with arrows. The step first
discovered by Störmer, Tsui and Gossard was at 1/3. The integer steps
were earlier discovered by K. von Klitzing at a weaker magnetic field
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Electron spin: Electron spin played no significant role in the
earliest understanding of the fractional quantum Hall effect, where a
large Zeeman energy was thought to create only fully spin-polarized quantum
Hall states. However, just one year after the discovery of the effect,
Prof. Chakraborty's theoretical work made it clear that electron-electron
interactions could actually lead to quantum Hall states with non-trivial
spin configurations. Subsequently, he made several important predictions
about the properties of various spin-reversed excitations. Such work
motivated several experimental groups, e.g., Bell laboratories [Phys. Rev.
Lett. 62, 1540 (1989)], University of Oxford [Phys. Rev. Lett.
62, 1536 (1989)], Princeton University [Phys. Rev. B45,
3418 (1992)], Cambridge University [Phys. Rev. B44, 13128
(1991)], Yale University [Phys. Rev. Lett. 74, 5112 (1995)],
Max-Planck-Institute, Stuttgart [Phys. Rev. Lett. 81, 2526
(1998)], University of California, Santa Barbara [Phys. Rev. Lett.
81, 2522 (1998)], Grenoble, France [Phys. Rev. Lett.
87, 136801 (2001)], and many others to investigate spin effects and
confirm the predictions by Prof. Chakraborty. The importance of Prof.
Chakraborty's predictions here is that they have improved significantly
the overall understanding of these unique phenomena in correlated two-dimensional
electron liquids. The field is exciting and well-recognized by the award
of two Nobel prizes. Prof. Chakraborty's work has been termed pioneering
in the literature [see, for example, Physics World (September 1989, p. 39].
T. Chakraborty and P. Pietiläinen, The Quantum Hall Effects,
Springer-Verlag, 1st edition (1988), 2nd edition (1995). This monograph has
received, as yet, more than 500 citations, and several excellent reviews:
- "... The book is intended for
nonexpert researchers who want to begin investigating the fractional
QHE. For these people, I believe the book will prove invaluable and I
strongly recommend it. The book can also serve as a useful reference
for active researchers in either theory or experiment. I believe that
this book will succeed in opening up the fractional QHE theory to a
larger community. In writing it, the authors have done a service to the
subject, for there is much left to do." Physics Today, A.H. MacDonald (March 1990).
- American Journal of Physics: D. Thouless
(September 1989).
- Science: R. Joynt (September 1989).
T. Chakraborty, Advances in Physics 49, 959 (2000) (a high-ranking
review journal in physics).
T. Chakraborty and F.C. Zhang, Phys. Rev. B29, 7032 (R)
(1984).
T. Chakraborty, et al., Phys. Rev. Lett. 57, 130 (1985).
Bilayer QHE: Double layer electron-electron electron-hole systems are
known to exhibit interesting and often unexpected physical phenomena.
It was realized early on, primarily through Prof. Chakraborty's work, that a bilayer
quantum Hall system has a much broader scope than that allowed by the standard model.
A double-layer two-dimensioanl electron system carries an extra degree of freedom,
the layer index, which is expected to open up additional possibilities
for new quantum Hall states that have no counterpart in the standard single-layer
quantum Hall systems. That effect is understood to be entirely due to
interlayer Coulomb interaction. This significant prediction was later confirmed
in experiments by several groups, most notably at Bell labs. [Phys. Rev. Lett.
72, 728 (1994)], Princeton [Phys. Rev. Lett. 69, 3553
(1992)], among others. As a result of Chakraborty's pioneering woek, new directions
of exploration have opened up in the field.
T. Chakraborty and P. Pietiläinen, Phys. Rev. Lett. 59,, 2784
(1987).
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Quantum Dots
Quantum dots (QDs), a quasi-zero-dimensional electron system have been
one of the most extensively studied quantum structures in recent
years. They represent the ultimate reduction in the dimensionality of
a semiconductor device. In these systems, electrons are confined
in all directions, and occupy spectrally-sharp energy levels similar
to those found in atoms. They are popularly called artificial
atoms, a term first introduced in my paper [1]. Quantum dots
have a wide range of application potentials, ranging from biology, quantum
cryptography to versatile lasers. My papers on the electronic
properties of QDs in a magnetic field [1-3] were the first such work
reported. The field since then has grown enormously [4] and I have made
many original contributions to it. My works on on the role of
electron-electron interaction on the energy spectrum and in particular,
the finding that for a parabolic QD, optical spectroscopy only excites
the center-of-mass motion, were widely considered as novel and
exciting. Many other contributions, such as those on the properties of
elliptical dots, impurity effects, etc. have also helped to gain major
insights into this fascinating system and make further progress in
theoretical and experimental explorations of the properties of QDs
that is going on today.
P. Maksym and T. Chakraborty, Phys. Rev. Lett. 65, 108 (1990).
The impact of this work on the subsequent quantum dot research is evident
from its citation index of 660!
P. Maksym and T. Chakraborty, Phys. Rev. B45, 1947 (R) (1992)
(Times cited 180).
T. Chakraborty, Comments Condens. Matter Phys. 16, 35 (1992)
(Times cited 150).
T. Chakraborty, Quantum Dots (Elsevier, 1999) (Times cited 100).
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Quantum Rings
Semiconductor nanostructures have witnessed phenomenal
developments in recent years due to their promising potential
applications in optical and electronic devices. They
are also ideal for exploration of fundamental physics at
the nanoscale. A few-electron quantum ring with its unique
optical and electronic properties is a brilliant example of
such a structure. Recent important advances in fabricating
nanoscale quantum rings where the topology and geometrical
properties can be externally controlled have generated a
lot of attention on the studies of electronic states in a ring
geometry. A metallic ring of mesoscopic dimension subjected to
an external magnetic field exhibits periodic oscillations in
thermodynamic quantities such as magnetization and magnetic
susceptibility, reflecting the behavior of the ground state
energy. Reported experiments that directly probe the low-lying
energy spectra and associated physical properties were motivated
by a theoretical model [1] developed by me a few years prior
to those experimental reports. That model allowed me to evaluate
the energy spectra of quantum rings verya ccurately and from these
I deduced several interesting results related to the electron
spin, optical absorption spectra, etc. that are now confirmed
experimentally [2].
T. Chakraborty and P. Pietiläinen, Phys. Rev. B50, 8460 (1994)
(Times cited 112);
V. Halonen, P. Pietiläinen and T. Chakraborty,
Europhys. Lett. 33, 377 (1996) (Times cited 51).
A. Lorke et al., Phys. Rev. Lett. 84, 2223 (2003); U.F. Keyser,
et al., ibid. 90, 196601 (2003).
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Quantum Cascade Structures
The unipolar quantum cascade laser (QCL) is a product of ingenious quantum
engineering that exploits the properties of electrons confined in
semiconductor nanostructures. Intense interest in this system derives
from its technological importance in trace-gas analysis. I investigated
the physical properties of this device in various novel situations,
such as the presence of an external magnetic field [1] or when the
quantum well in the active regions of this device are replaced by
quantum dots [2]. Similarly, my work on the role of disorder in a
parallel magnetic field [3] explained a puzzling experimental
observation of rapid disappearence and a slight blue shift of the
observed luminescence peak. Research on the QCL is progressing
rapidly and my work has played an important role in gaining
valuable insights into the properties of this nanostructure. I wrote
a review article on this fascinating topic in a prestigious
journal [4].
V. Apalkov and T. Chakraborty, Appl. Phys. Lett. 78, 1973 (2001);
D. Smirnov, O. Drachenko, J. Leotin, H. Page, C. becker, C. Sirtori,
V. Apalkov, and T. Chakraborty, Phys. Rev. B 66, 125317 (2002).
V. Apalkov and T. Chakraborty, Appl. Phys. Lett. 78, 1820 (2001).
V. Apalkov and T. Chakraborty, Appl. Phys. Lett. 78, 697 (2001).
T. Chakraborty and V. Apalkov, Advances in Physics 52, 455 (2003).
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