ERC Advanced Grants
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Open questions

The pressing open problems to be addressed include:

  1. Can one determine the analog of Figure 2 (see Background), i.e. highly reliable universal scaling curves for unconventional quantum criticality?
  2. What is the microscopic meaning of the new energy scale in heavy fermion compounds?
  3. Is the appearance of additional energy scales universal for unconventional quantum criticality or are there different kinds hereof?
  4. Can the local quantum criticality scenario be combined with powerful band structure methods to obtain quantitative agreement with experiments?

Figure 2: Universal scaling in the liquid gas transition for eight different liquids. After E. A. Guggenheim, J. Chem. Phys. 13, 253 (1945).

Scientific approach

We will attempt to answer these questions using a multifaceted approach, as illustrated below. The different facets are represented as pieces of a jigsaw “quantum puzzle”. It needs to be fully assembled to find the solutions – a new level of understanding of unconventional quantum criticality in heavy fermion compounds and, more generally, of phase transitions in matter.


Figure 3: QuantumPuzzle: Schematic representation of the tasks as pieces of a jigsaw "quantum puzzle".

Pieces P1 and P2 define the materials basis where highest quality samples are prepared both in “bulk” and thin film form. To push sample quality on the bulk side (P1) to extremes,  the institut's state-of-the-art crystal growth infrastructure will be supplemented with carefully selected new equipment. An important task of P1 is, besides the growth of highest-quality single crystals of  known compounds, to search for new materials which display unconventional quantum criticality. This is very important since to date unconventional quantum criticality has been observed only in a relatively small number of compounds. Also the number of clear-cut SDW transitions is not large.

Thin film techniques (P2) provide additional parameters (e.g. choice of substrate) to deliberately taylor a given compound. This will be exploited in the project to tune the distance of compounds to their
quantum critical point. In addition thin films will, for nothing but their reduced weight and dimension, be needed for some of the experiments described below. Excellent scientific and technical support is provided by the Center for Micro- and Nanostructures (ZMNS) at TU Vienna. A new molecular beam epitaxy (MBE) chamber will shortly be available for QuantumPuzzle at the ZMNS.

A broad physical characterization of the materials produced in P1 and P2 will follow in P3, using state-of-the-art techniques available at the institute and large facilities such as ILL (neutrons) or PSI (muons). The goal is to identify by these experiments the samples most promising for the highly advanced measurements in P4-6.

Experiments to be conducted in P4 go beyond state-of-the-art. While in most heavy fermion compounds the variation of one external “tuning” parameter suffices to drive a material to quantum criticality (e.g. magnetic field in the case of Figure 1), others need to be simultaneously subject to two or more extreme conditions. As an example, in the case of CeRhIn5, one of the most promising candidates for unconventional quantum criticality, these conditions are high pressure, high magnetic field, and low temperatures.

Another experimental jigsaw piece, P5, focusses on key question 2, the nature of the new energy scale. With a radically new approach of ultra low energy spectroscopy, employing technical know-how from the superconducting quantum bits community, we will attempt to “optically” excite the new energy scale. We expect a clear-cut answer on whether or not this scale represents the suspected breakup of the heavy quasiparticles.

While the above pieces mostly focus on key questions 2 and 3, the approach of P6, going to ultra-low temperatures, is at the heart of question 1: To test for universal scaling, accurate temperature dependences of both thermodynamic and transport properties are needed in the widest possible temperature range. By using a nuclear demagnetization cryostat which will be shortly installed at IFP we aim at going 1 to 2 orders of magnitude below the temperatures typically reached to date in investigations of quantum criticality in heavy fermion compounds.

All important advance in the field of quantum criticality have come about by intense collaboration between theoreticians and experimentalists in the field. This successful approach shall also be used in QuantumPuzzle (P7). Focus will be on introducing material specific aspects into the calculations, e.g. by using LDA + DMFT.


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