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Computational Condensed Matter Theory Group

Projects for students

Quantum Transport in Weyl Semimetals of Types I and II

(bachelor project)

In the last few years, the concept and experimental discovery of Weyl semimetals has greatly stimulated the research of novel topological phases in condensed matter systems. Namely, unlike other semimetals such as graphene, Weyl semimetals exhibit topologically protected Dirac cones that are not spin degenerate (nodes). They have been predicted to give rise to peculiar electromagnetic responses, such as the chiral magnetic effect in which current flows due to an applied magnetic field.

It has recently been argued that Weyl nodes come in two flavors: type I with broken inversion or time-reversal symmetry but preserved emergent Lorentz invariance; and type II, which breaks Lorentz invariance due to the tilting of the linear dispersion close to the Weyl nodes. It is suspected that magnetically ordered noncentro-symmetric materials can exhibit a transition from type I to type II Weyl nodes or might even exhibit both types of nodes simultaneously in the band structure. In this project, we propose to study these hybrid systems by means of transport simulations within a tight-binding framework with the goal of understanding quantum transport properties in this new class of materials.

If you are interested in this project, please contact Dr. Daniel Hernangómez Pérez.

Further reading: F. Li et al., Phys. Rev. B 94, 121105(R) (2016); M. Park et al., Phys. Rev. B 95 094201 (2017).

Vortex-superlattices in structured organic matter and waveguides

(bachelor project)

When an electron moves through an inhomogeneous piece of matter, e.g. a metal film, almost unavoidably it undergoes a scattering process. Our recent work has shown that due to effects of quantum interference the scattered wave can exhibit a strong tendency to form current vortices (“eddies”). The local current density in these vortices can exceed the average transport current by up to two orders of magnitude.

Ideas have been proposed how to use this effect in order to design a material that supports current vortices on a regular lattice. In this project different designs will be tested via transport simulations within a tight-binding framework. The ultimate goal would be to propose novel materials in which magnetic lattices form on the nano-scale when a current runs through it.

Further reading: E. Dix and J. E. Inglesfield, J. Phys. Condens. Matter 10, 5923 (1998); M. Walz et al., Phys. Rev. Lett 113, 136602 (2014); J. Wilhelm et al. Phys. Rev. B 90, 014405 (2015).

Lotka-Volterra model for simulating aspets of the US elections (2016)

(bachelor project)

In the 2016 presidential elections the US were divided into blue (pro Clinton) and red (pro Trump) states. The difference in percentage pro blue and pro red per state gives rise to a distribution with large tails that allows in 14 states more than 60% per of the popular votes for one candidate.

In this bachelor thesis a hypothesis will be tested according to which the “bimodal” voting behavior can be modeled qualitatively with a generalized Lotka-Volterra model. Lotka-Volterra models are frequently used to simulate a population dynamics in theoretical biology or theoretical ecology, but they also appear in studies of market and customer behavior. In this thesis a new variant is investigated that is designed to simulate decision making with collectively enhanced biasing.

Further reading: US President Election Results Map

 
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