My research lies in the area of condensed matter theory, where the aim is to characterise and understand the physical properties of materials consisting of enormously large numbers of interacting particles. Of particular interest are 'strongly-correlated' systems, in which the interactions between particles are simply too large to ignore or treat using mean-field approaches. One instead develops quantum many-body techniques to determine the underlying physical behaviour.

I am currently interested in many-body effects on the nanoscale, as observed in the electronic conductance of single molecules, carbon nanotubes and other so-called 'quantum dot' devices. These kinds of system present exciting prospects for novel electronic devices, in part due to their innate tunability: the electrons' energy levels and their mutual Coulomb and exchange interactions can all be adjusted, allowing controlled access to a wide range of interesting many-body phenomena.

In the classic example, the quantum dot is set up so that it contains an unpaired electron in its outermost orbital. The large energetic cost to remove this electron, or add another, means that the dot cannot conduct electricity simply by electrons independently tunnelling on and off, one at a time. But -- remarkably -- experiments nonetheless show perfect conductance at low temperatures.

The enhanced conductance is due to the *Kondo effect,* where correlated motion of the electrons allows them to pass through the quantum dot even though sequential, one-at-a-time tunnelling is not energetically feasible. To understand this effect, and more exotic, related phenomena, we analyze the many-body Hamiltonians that describe the key features of the experiment, using a combination of analytical and numerical methods. A selection of recent publications is listed below.

*Tunable Kondo Physics in a Carbon Nanotube Double Quantum Dot*

S. J. Chorley, M. R. Galpin, F. W. Jayatilaka, C. G. Smith, D. E. Logan, and M. R. Buitelaar,

*Phys. Rev. Lett.*

**109**, 156804 (2012)

*Interplay between Kondo physics and spin-orbit coupling in carbon nanotube quantum dots*,

M. R. Galpin, F. W. Jayatilaka, D. E. Logan and F. B. Anders, *Phys. Rev. B ***81**, 075437 (2010).

*Tunneling transport and spectroscopy in carbon nanotube quantum dots*,

D. E. Logan and M. R. Galpin, *J. Chem. Phys. ***130**, 224503 (2009).

*Correlated electrons in two-level quantum dots: Phase transitions, transport, and experiment*,

D. E. Logan, C. J. Wright and M. R. Galpin, *Phys. Rev. B ***80**, 125117 (2009).

*A local moment approach to the degenerate Anderson model*,

M. R. Galpin, A. B. Gilbert and D. E. Logan, *J. Phys.: Condensed Matter ***21**, 375602 (2009).

*Zero-bias conductance in carbon nanotube quantum dots*,

F. B. Anders, D. E. Logan, M. R. Galpin and G. Finkelstein, *Phys. Rev. Lett. ***100**, 086809 (2008).

*Anderson impurity model in a semiconductor*,

M. R. Galpin and D. E. Logan,* Phys. Rev. B* **77**, 195108 (2008).

*A local moment approach to the gapped Anderson model*,

M. R. Galpin and D. E. Logan, *Eur. Phys. J. B.*** 62**, 129 (2008).

*Quantum phase transition in capacitively coupled double quantum dots*,

M. R. Galpin, D. E. Logan and H. R. Krishnamurthy, *Phys. Rev. Lett.* **94**, 186406 (2005).