FIG. 1. Frustrated magnetism is one major direction within the TOPOLECTRICS project. Shown is a phase diagram analysis for the J1-J2-Jd Heisenberg model on the kagome lattice. In comparison to the upper left classical phase diagram exhibiting different magnetic orders (magnetic ordering peaks such as for cuboc or ferromagnetic order are sketched in grey), a new paramagnetic regime (denoted in red) appears in the quantum phase diagram. The upper right figure displays how pressure modifies the effective Heisenberg parameters for different compounds. Further details can be found in Iqbal et al., Phys. Rev. B 92, 220404(R) (2015).
New insights into topological quantum states Topological quantum states of matter have become a major branch of both theoretical and experimental research, which now demands a new theoretical language. Professor Ronny Thomale, the Principal Investigator of the Topolectrics project, tells us about their work in developing a theoretical framework to unify the appearance of topological quantum states of matter Many advances in
physics have been achieved through scientific experimentation, where researchers observed new and exotic phenomena which they then studied and analysed, gaining new insights. However, theoretical development has also been a central part of the story of scientific development, says Professor Ronny Thomale, the Principal Investigator of the Topolectrics project, an EU-backed initiative investigating the topological quantum states of matter which result from electronic interactions. “We want to develop a theoretical framework, a theoretical language, in which we can unify the different appearances of topological quantum states of matter,” he says.
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Topological quantum states of matter There are many topological quantum states of matter in nature. Now researchers in the Topolectrics project are trying to help experimentalists identify them, using their topological properties. The discovery of the Integer Quantum Hall Effect by German scientist Klaus von Klitzing, work for which he was awarded the Nobel Prize for Physics in 1985, is a central part of the story. “The Integer Quantum Hall Effect is a phenomenon observed in gallium arsenide heterostructures, where electrons are placed in what is effectively a 2-dimensional environment and subjected to a strong magnetic field,”
outlines Professor Thomale. “Klaus von Klitzing found that he could perform a conductivity measurement where the low energy transport behaviour is fully characterized by chiral modes at the boundary of the sample. With some predecessors such as polyacethylene and superfluid Helium-3 not to be forgotten, this truly gave birth to the field of topological quantum states of matter.” This conductivity measurement was found to depend only on topological aspects of the system, implying it to be invariant under local perturbations, such as changing the shape of the sample’s boundary. This is an important insight, which has played a fundamental role in subsequent research. “Von Klitzing’s
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