Joining the group
Please contact me (B. Braunecker) if you're are interested to work on challenging theoretical physics projects on the forefront of condensed matter physics, nanostructures, and correlated particles.
I select group members only on the criterion of excellence, but the field of condensed matter theory has still an unexcusable gender imbalance. Therefore I wish to encourage specifically women to apply.
PhD students
PhD programmes in St Andrews start in September, and interviews are typically held in February and March. By March and April all positions are usually filled, but since there may be still some funding available do not hesitate to ask me at any time.
With our research programme and quality in St Andrews we belong to the best research centres worldwide. Therefore we impose the highest standards on our team members, and we wish to encourage the best of you to apply for joining us as PhD students.
The next PhDs will start in September 2018. If you are interested, I recommend you to make first contact with me between November and January. For the CM-CDT programme an official application should be submitted by the end of January, but other sponsors have different deadlines (see below).
The regular PhD programmes in condensed matter physics are sponsored through the CM-CTD or the doctoral training grant. With these grants, a PhD starts in September and lasts between 3.5 to 4 years. The selection of candidates is highly competitive and, as outlined above, you should apply early enough, making first contact with me. If you could access different funding sources, please feel free to discuss them with me.
For students from the mainland China, a number of PhD fellowships is available through the China Scholarship Council, and details can be found here. The call is currently open and you must apply by Jan 19th 2018. Observe that a proof of fluency in English must be obtained before applying. For this application contact us well before the deadline.
Scholarships for applicants from Commonwealth countries are available through the international Commonwealth Scholarship and Fellowship Plan (for a full list see here). Applications can only be done through your home institution, but contact with St Andrews and an agreement to accept you will be required before. The submission deadline is usually in November, therefore make sure you make contact with us long before.
Further information about PhD funding can be found here, and it is definitely worth to check if you could apply for one of the funding opportunities listed at the Postgraduate Scholarships page.
Some potential PhD projects are described below and can further be found on the project lists of the School of Physics and Astronomy and of SUPA. However, the field of research is evolving rapidly and these projects will be adjusted and updated as required. I'm also open to discuss something even completely different with you.
Postdocs
If you wish to join as a postdoc, please contact me directly. I currently don't have direct funding, but I'm open to discuss with you further funding opportunities.Potential PhD projects
Self-sustained topological phases in quasi-1D and 2D structures
Topological quantum phases have risen to a very active field of research recently, triggered mostly by the realisation that "ordinary" semiconductor nanostructures could be fine tuned to exhibit topological properties which are very attractive for quantum information storing and processing. With the link to semiconductors a major step forward has been taken towards a quantum technological implementation of such states, yet to obtain robust and scalable quantum systems the requirement of fine tuning has to be dropped.Self-sustained topological phases provide such stable and robust systems, and exhibit a multitude of fascinating new physical properties that emerge as an effect of strongly interacting particles in a condensed matter system. We have already demonstrated that such phases spontaneously appear in hybrid magneto-electronic systems in one dimension [1-4]. Yet in 1D the number of topological states is restricted, and to obtain more exotic topological states extensions to higher dimensions must be made. It is, however, mandatory to maintain then the 1D self-sustaining mechanisms to avoid producing only conventional phases [5].
In this PhD project, we will take a systematic approach towards such self-sustained topological phases by enhancing the complexity of the systems step by step while maintaining full control over the strongly correlated electron state. We will investigate the influence of the lattice structure (square, honeycomb, kagome), anisotropies and frustration, as well as the crucial renormalisation of the system properties by electron interactions.
See also the next project.
- [1] B. Braunecker, P. Simon, and D. Loss, Phys. Rev. Lett. 102, 116403 (2009) [arXiv:0808.1685] [PDF].
- [2] B. Braunecker, P. Simon, and D. Loss, Phys. Rev. B 80, 165119 (2009) [arXiv:0908.0904] [PDF].
- [3] B. Braunecker and P. Simon, Phys. Rev. Lett. 111, 147202 (2013) [arXiv:1307.2431] [PDF] [Supplement].
- [4] B. Braunecker and P. Simon, Phys. Rev. B 92, 241410(R) (2015) [arXiv:1510.06339] [PDF]
- [5] P. Simon, B. Braunecker, and D. Loss, Phys. Rev. B 77, 045108 (2008) [arXiv:0709.0164] [PDF].
Topological physics beneath magnetic structures and interfaces on superconductors
It has been known for a long time that magnetic impurities induce bound states in superconductors [1] but only in recent years it was realised that lining up such states [2] can lead to a twist in the resulting wave function that is known as a changed topological index. The study of such topological states has by now become a highly active field of research. A strong promotor is the rather recent insight that any quantum technology will have to rely on some form of topological states. In this PhD project we will investigate how topological properties appear at interfaces or magnetic structures embedded on superconductors, in a set-up where a strict dimensional decoupling as considered by most approaches is not possible. This will build on our recent work [3]. A particular emphasis will be given to interactions between the states generated by the interaction between the magnetic scatterers and the superconductor, and to particular instabilities that can lead to novel quantum phases.See also the previous project.
- [1] L. Yu, Acta Phys. Sin. 21, 75 (1965); H. Shiba, Prog. Theor. Phys. 40, 435 (1968); A. I. Rusinov, JETP Lett. 9, 85 (1969).
- [2] F. Pientka, L. I. Glazman, and F. von Oppen, Phys. Rev. B 88, 155420 (2013); S. Nadj-Perge, I. K. Drozdov, J. Li, H. Chen, S. Jeon, J. Seo, A. H. MacDonald, B. A. Bernevig, and A. Yazdani, Science 346, 6209 (2014).
- [3] C. J. F. Carroll and B. Braunecker, arXiv:1709.06093.
Dynamical Coulomb blockade in arbitrary environments with backaction
The electron transport through nanostructures is always exposed to the electromagnetic fluctuations of the environment. This is a notable and measurable effect in quantum-coherent conductors, in which the motion of a single electron excites nearby electromagnetic modes which in turn act back on the electrons and cause a nonlinear reduction of the conductance. For weakly transmitting conductors this physics is known as environmental Coulomb blockade and well explained by the "P(E) theory" [1]. But this theory does not extend to highly transmitting conductors in which the transmission time becomes comparable with the environment's reaction time. This regime, the dynamical Coulomb blockade regime, requires to model the environment as a quantum object. For specific conditions important advances have been made over the last few years [2]. But recent experimental work has shown that there is still much unknown in the regime of strong backaction of an arbitrary environment [3]. In this PhD project we will access this physics head-on and derive a modelling of the full counting statistics, which gives access to all current correlators, of a mesoscopic electron system coupled to an arbitrary dynamical quantum enviroment. We will focus on an analytical, non-perturbative many-body modelling of the phenomenon, involving bosonisation similar to [4] and further mappings on scattering type boundary value problems that can be solved with recently developed techniques [5].- [1] G.-L. Ingold and Y. Nazarov, in Single Charge Tunneling ed. by H. Grabert and M. H. Devoret, Ch. 2 (Plenum, 1992).
- [2] K. A. Matveev, D. Yue and L. I. Glazman, Phys. Rev. Lett. 71, 3351 (1993); L. W. K. Molenkamp, Flensberg and M. Kemerink, Phys. Rev. Lett. 75, 4282 (1995). Y. V. Nazarov, Phys. Rev. Lett. 82, 1245 (1999); M. Kindermann and Y. V. Nazarov, Phys. Rev. Lett. 91, 136802 (2003); I. Safi and H. Saleur, Phys. Rev. Lett. 93, 126602 (2004); D. S. Golubev, A. V., Galaktionov and A. D. Zaikin, Phys. Rev. B 72, 205417 (2005).
- [3] F. D. Parmentier, A. Anthore, S. Jezouin, H. le Sueur, U. Gennser, A. Cavanna, D. Mailly and F. Pierre, Nat. Phys. 7, 935 (2011).
- [4] J.-R. Souquet, I. Safi, and P. Simon, Phys. Rev. B 88, 205419 (2013).
- [5] B. A. Muzykantskii and Y. Adamov, Phys. Rev. B 68, 155304 (2003); B. Muzykantskii, N. d'Ambrumenil, and B. Braunecker, Phys. Rev. Lett. 91, 266602 (2003); J. Zhang, Y. Sherkunov, N. d'Ambrumenil, and B. Muzykantskii, Phys. Rev. B 80, 245308 (2009); B. Braunecker, Phys. Rev. B. 73, 075122 (2006).
Emergent Order in Hybrid Photon-Atom Systems
Novel self-ordered phases can emerge in a conductor with interacting electrons and embedded magnetic moments [1,2]. This is quite surprising because the energy and time scales of the considered magnetic moments (e.g., nuclear spins) differ by orders of magnitude from those of electrons. Yet, within this decoupling of scales, the ordering mechanism is general and not bound to specific materials. Quite remarkably such self-ordered phases have made recently a strong link with the currently much discussed physics of topological superconductors and Majorana bound states [3].In this PhD project, we shall explore systems in which the time and energy scales are turned upside down, notably, in which the effective interaction that triggers the order travels at a turtle's pace. This is an extreme limit in which this slow dynamics will play a further important role. For a definite example we will focus on cavity photons that are coupled through an interacting atomic gas, which is of the type of systems that are under investigation, for instance, in the group of Prof Jon Simon at the University of Chicago.
- [1] B. Braunecker, P. Simon, and D. Loss, Phys. Rev. Lett. 102, 116403 (2009) [arXiv:0808.1685] [PDF].
- [2] B. Braunecker, P. Simon, and D. Loss, Phys. Rev. B 80, 165119 (2009) [arXiv:0908.0904] [PDF].
- [3] B. Braunecker and P. Simon, Phys. Rev. Lett. 111, 147202 (2013) [arXiv:1307.2431] [PDF] [Supplement].