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Sumathi Rao
Research Summary:
I have mainly been working in the area of electronic transport
in quantum wires and quantum dots. The aim is to compute
conductances in these low-dimensional systems. The new approach that
we have taken in the last few years has been to generalise the
standard Landauer-Buttiker approach to include inter-electron
interactions perturbatively. This method reproduces the
results of using Luttinger liquid theory and the
formalism of bosonisation in most cases, and is useful, because it
can directly be related to experiments. But there are certain
kind of tunneling processes, which cannot be completely understood
in terms of this approach and in those cases, we are forced to
use the formalism of bosonisation and Luttinger liquid theory.
Using the generalisation of the two-terminal junction of interacting
quantum wires to N-terminals and
renormalisation group flow
of the S-matrix for N ≥ 3, we study conductances in
different geometries of quantum wires and obtain results for
different temperatures, different lengths of wires and different
magnetic fluxes through rings.
Surprisingly, in some geometries, we find that
the back-scattering decreases and conductance increases
due to interactions, contrary to the experience of
two-terminal junctions.
We also study conductances through
two resonant levels using a mapping to the generalised
Coulomb gas model and show that there exists a non-trivial
fixed point, where conductance is generically different
from that through a single resonant level and the conductance
exhibits a non-linear dependence on the interaction parameter,
again, unlike the case of a single resonant level.
Publications in refereed journals:
- Effective action and interaction energy of coupled quantum
dots (with Sourin Das), Phys. Rev. B68 073301 (2003).
- Transport through multiply connected carbon nano-tubes
(with Sourin Das), to be published in Phys. Rev. B.
- Renormalisation group study of the conductances
of interacting quantum wire systems with different geometries
(with Sourin Das and Diptiman Sen), to be published in Phys. Rev. B.
Publications in Conference Proceedings:
- Transport through quantum dots, to be published
in Proceedings of National Seminar on `Recent Advances in Physics',
19-20 September 2003, Gopalpur-on-sea, organised by Berhampur
University and Institute of Physics, Bhubaneswar.
- Effects of interactions and different geometries on
conductances of quantum wires : the ring and the stub systems,
(with S. Das and D. Sen), to be published in International
Conference on Nanoscience and Technology, Kolkatta, December 2003.
Preprints:
- Tunneling through two resonant levels:
fixed points and conductances (with D. Sen), cond-mat/0404010.
Conference/Workshops Attended:
- National Seminar on `Recent Advances in Physics',
19-20 September 2003, Gopalpur-on-sea, organised by Berhampur
University and Institute of Physics, Bhubaneswar.
- One day conference on theoretical physics,
Jawaharlal Nehru University, 9th March 2003.
Visits to other Institutes:
- Institute of Physics, Bhubaneswar, 16-18 September 2003.
- Indian Institute of Science, Bangalore, Summer 2003.
Invited Lectures/Seminars:
- `Transport in Quantum wires' , 17th September 2003,
Institute of Physics, Bhubaneswar.
- `Transport through quantum dots' 19th september,2003, Gopalpur-on-sea.
- `Transport through coupled quantum wires and dots',
9 March 2004, Jawaharlal Nehru University, New Delhi.
Other Activities:
- Acting director, August 2003 - December 2003.
- Member of National Organising Committee,
Statphys 22, to be held in Bangalore in July 2004.
- Member of the International Union of Pure and
Applied Physics working group on `Women in physics'.
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