Yuri Grin: Chemistry of strongly correlated systems

Continuing the discussion on materials design, Yuri Grin gave a chemists perspective on the problem. Yuri argued that design requires an understanding of the chemistry, and that one of the major problems chemists face, is a lack of understanding of the principles that govern the combinations of elements in intermetallics. Normally, one uses the concept of valence to determine the best combinations of elements. But this idea in its simplest form doesn't work in intermetallics. For example, consider combinations of Eu and Ga - you can make

EuGa,         EuGa4,   Eu5Ga9


Another issue that chemists face,  is to understand the bonding of electrons fare from the Fermi surface. One needs to know what combinations work - and he said that these considerations have led him, and his collaborators to develop a new method for calculating oxidation numbers.  These methods have been very successful for developing and discovering a new range of clathrate compounds.


The heart of the problem seems to be that one needs better tools to separate out the ionic and covalent parts of electron bonding. To this end, they have developed a new technique called the "electron localization indicator".

Here's the blogger's understanding of what this means. The point is, that density alone is poor indicator of individual electron localization- a better way is to use a weighted measure of the electron density, given by

                
where the integral is over small regions of space (omega) around the point r, and the denominator is the equal spin pair correlation function.   This is my rendition of the electron localizability indicator.
(See Becke and Edgcombe, J. Chem. Phys. 92, 5397 (1990); doi:10.1063/1.458517 ;Miroslav Kohout, Int J. Mod. Quantum Chemistry, 97, 651 (2004)). In regions of space where electrons are better localized, the pair correlation function will be smaller (lower momentum, higher wavelength, bigger correlation hole), which enhances the above index.  In regions of space where electrons are less well localized, the correlation hole will be much smaller, and zeta will be bigger.  The denominator can be calculated within a Hartree scheme to give a simple formula for zeta(r)>

Yuri showed us how this index gives a very nice indication of electron shells, and can be used to delineate covalent bonds, and well-defined clusters of atoms, behaving effectively as a single ion.
For instance,  in the clathrate compound Na24Si_136, 136 Si atoms form a cluster with charge 24+.

With this scheme, one can show how various clusters of atoms behave as single units , and one can account for the anomalous oxidation numbers of such clusters.    The increase in understanding, he argued is helping his group navigate and synthesize new kinds of clathrates that are of interest for their thermo-electric properties.










The talk aroused a lot of interest, particularly amongst physicists actively involved in materials synthesis.

Eric Bauer (Los Alamos National Laboratory): Understanding anisotropy to develop superconductors by design

In the afternooon session, two of the worlds leading intermetallic synthesis experts: Eric Bauer from the condensed matter group at Los Alamos National Laboratories and Yuri Green from the Max Planck Institute for Chemical Physics, Dresden,  presented two contrasting views of the challenges of material design.

Eric Bauer posed the question - how can you make superconductors by design? One of the strategies adopted by the LANL group is to try to exploit and understand anisotropies of intermetallic crystals. He showed how in the family of heavy electron 115 materials, the superconducting transition temperature Tc scales with the c/a ratio of the tetragonal unit cell - a feature that traditionally was interpreted as a consequence of Tc becoming larger in more 2dimensional metallic environment. He aslo showed  how it Tc scales with the characteristic scale of the spin fluctuations.

As an example, he discussed PuCoGa5.  This system has the highest Tc=18.5K of the 115 superconductors - but how might one make it larger?  He described three possibilities:

• Make the system more two dimensional by trying PuCo2Ga7 (he didn't say what happens).
• Try to increase the spin fluctuations by going to more magnetic PuCo5Ga2
• Seek still higher bandwidth by trying to discover d-electron analogs of this material.

Eric discussed how heavy fermion materials were an ideal platform for studying new kinds of material behavior in metals, because they are

• highly tunable (low energy scales)
• there are a wide variety of ground-states
• they can be made with very high purity.

He showed how one could explore material space - varying the structure with a fixed f-ion and also changing from 4f to 5f.

4f:       CeIn3 -   Ce2MIn8 ->   CeMIn5 ->  CeM2In17    (attempt to make it more 2D)
              |                                                       (eg CePt2In7 - an AFM that becomes SC with pressure)
              |
             \/
5f    NpPd5Al2

He showed us a fascinating new compound CePd1.5Al3.5 with an incredible unit cell that they are studying.

As a last topic, Eric discussed how anisotropies in spin fluctuations appear to be closely correlated with transition temperature.











There followed about 20 minutes of discussion.  One of the topics discussed, was how we might
increase the amount of serendipitious discovery.  Yuri Grin pointed out that in the drugs industry, typically 20,000 people are required to bring one new drug to the point where it can be tested.
Zlatko Tesanovic has pointed out that its not just Tc, but getting a better material for superconductivity thats important - if only we could get the iron-based superconductors up to the same Tc as the cuprate materials - because iron based sc are much more friendly for making contacts and wires. This would be a multi-billion industry if we could only find the material.

A long discussion ensued about how it would certainly be cost-effective to society if we could only encourage funding of materials exploration that would permit us to find these exciting new materials.

Mohammad Hamidian (Seamus Davis group, Cornell U.) : Imaging the Fano lattice to "hidden order" transition in URu2Si2

Mohammad Hamidian linked up to the ICTP by Skype, with his desktop presentation beamed up onto the two ICTP screens. Mohammad spoke from the STM room in Ithaca, and despite the 4000 mile separation, the sound and images were crystal clear.  It was however, difficult for Mohammad to field questions, since the field of reception from the mike was very localized.

Mohammad began with a summary of the basic physics of heavy electron systems. He explained the Kondo effect as a many-body resonance surrounding a singlet - leading to quasiparticles with masses that are up to 1000 me inferred from the specific heat coefficient, susceptibility and optical conductivity. Can one however, image this process directly?  This is a motivation to try STM - and the system they have chosen is URu2Si2 ("uruthi").

See: Imaging the fano-lattice to 'hidden order' transition in URu2Si2

 He began with a brief review of the key features of URS  - showing the specific heat and remarking how the so called "hidden order" in this material gives rise to a huge thermodynamic signal in the specific heat coefficient, showing the development of a gap in the excitation spectrum. Can one examine what is taking place using STM measurements?

Mohammad then turned to the STM/QPI interference information that has been obtained

from the Cornell group's studies of URu2Si2. The surface of this material cleaves nicely, making it possible to obtain single-atom resolution in the STM.  At each point in real space, they see a classic asymmetric "fano resonance", (dip-hump in dI/dV) that is well-described by the Fano formula:

where ε₀ and Γ are the position and width of the resonance respectively while ζ = tf/tc is the ratio of the tunneling coupling to the f-electrons and conduction electrons, respectively. These two quantities vary periodically with position in the lattice, giving rise to what is called a "Fano lattice". This kind of fano resonance is seen in tunneling into individual magnetic atoms on metallic surfaces, and is taken to be a sign of the development of a Friedel resonance associated with the quenching of the local moment (Kondo effect). The observation of similar features, albeit modulated in a lattice, suggest that above the hidden order temperature, coherent scattering has not fully developed, so that the local density of states is that of an impurity fano resonance.

Next Mohammad turned to Th-doped URu2Si2 (TURS). The Cornell group has identified the surface on which they see the fano lattice as the Si layers of URS.  In TURS, they can see the individual Th atoms, and this makes it clear that they are now imaging the U layers.  At this point, the Blogger asked a question.

Q:  The Princeton group has also imaged the Fano Lattice of URS (see Aynajian et al.), but they have reasons to believe they are imaging the U surface.  How would this affect the physics, if this is true?
A:  Mohammad said that the alternative interpretation would not change the physics a lot, but would imply a different interpretation about the shape of the U orbitals.

When they cool down into the hidden order state, the  TURS data displays

• a new low energy feature inside the fano resonance with a spectroscopic gap that is in accord with the one infered from the thermodyanmics
• the development of quasiparticle interference (QPI) from which they can determine the dispersion of the heavy quasiparticles.

This is the first time that the hybridized heavy bands of a Kondo lattice have been directly imaged, (though of course they have been probed by other means, such as dHvA and optics, which do "see" the heavy electrons in other ways). One of the fascinating features of their data, is that they see hybridization: the formation of two distinct bands-  but that it only develops at the hidden order transition.  A similar observation has been made on URS by Santander et al in their optical studies.




Mohammad pointed out two features in the data that are important:

1. that the indirect gap seen in the hybridization is off-centered from the Fermi energy.
2. that there are no fixed Q features in the STM that would appear if there was some kind of density wave.

 Bloggers aside: This suggests one of two possibilities:

• The hybridization "is" the order parameter - in that somehow, the development of a coherent heavy fermion band is associated with a broken symmetry. This is not the case in conventional heavy fermion systems - what broken symmetry could this be?
• That the development of a gap in the excitation spectrum removes the sources of inelastic scattering, making it possible to resolve the hybridization.

 After the talk, there were many questions - folks lined up to put a question to Mohammad over the microphone.  One question, raised by Dirk Morr, was whether in a one-band system one can really say one is measuring the quasiparticle density of states.   Mohammad agreed that this was precisely the point about the Fano lattice, that electrons can enter the heavy fermion state by more than one tunneling path.

Dai Aoki (CEA, Grenoble): Re-entrant superconductivity and the field-induced magnetic instability in uranium compounds

 Dai's talk was a great introduction and summary of the issues around the heavy fermion ferromagnetic superconductors. 

In his introduction, Dai showed a great diagram, attributed to Miyake, which shows the convergence of research into magnetism and superconductivity - these two areas were once viewed as mutually exclusive, but today we know that magnetism is a major driver in unconventional superconductivity.

  

The three actors on the stage are: UGe2, URhGe and UCoGe. Experimentally the fact that these materials are able to exceed the Pauli pair breaking limit for superconductivity is very suggestive that they are triplet superconductors. Dai reminded us of the old Fay and Appel paper which considered how ferromagnetic fluctuations can produce a triplet superconductor whose maximum in Tc is near the FM quantum critical point. Crucially ferromagnetic fluctuations can pair break as well as pair and according to the theory of Fay and Appel, Tc goes to zero at the critical point itself.

Aoki discussed first UGe2, and here, he showed from their experiments, that the sc is occuring in the vicinityof a tri-critical point, where the FM phase boundary switches from 2nd, to 1st order.  The vicinity to a metamagnetic QCP is important for this system, and the daughter compounds URhGe and UCoGe.

UGe2 is the "mother compound" for the other UTGe materials.  As one changes T, one finds a correlation between the linear specific heat and the U-U distance.  Thus for G=Ru, gamma~ 40mJ/mol/K^2 and dUU=3.4A, but for Rh, dUU~ 3.5A shows gamma~ 150mJ/mol/K^2. dUU~3.5A is the "Hill Limit", and beyond this value, U systems become ferromagnetic, thus for T= Ir, Ni and Pd, where dU-U rises above 3.5A, the ground-state is ferromagnetic.   Based on the Hill criterion, URhGe is teetering on the edge of ferromagnetism. This is a bit confusing, because actually, both URhGe and UCoGe are actually ferromagnets, even though dUU < 3.5A. Dai discussed the remarkable example of URhGe, which displays re-entrant superconductivity. This system has Tc~ 0.2K with an anisotropic upper critical field with Hc2 much larger than the value expected for a Pauli-limited superconductor. He argued it must therefore be a spin-triplet sc. Remarkably, if you tune up the field, URhGe becomes sc again above H=8T, and continues to be so all the way up to 12T! Dai explained that this remarkable effect arises because as one tunes the field, the system passes close to a quantum-critical end point somewhere around 10T.  The mass of the quasiparticles rises rapidly around 10T.  Using a model where m*=(1+lambda)mb, the coherence length and hence the upper-critical field of the superconductor is tuned by the field-dependent m^*, as follows:

In the regions where Hc2(H)>H, re-entrant superconductivity develops!

Aoki ended with a mystery. He showed the phase diagram of UCoGe as a function of pressure. In this system, Fm and SC co-exist, and if you tune TCurie to zero with pressure, one finds that contrary to Fay and Appel, the SC Tc is smooth around the FM QCP.  Why is this - what is different about the FM/SC interplay in this fascinating U system?

Stefan Wirth (MPICpFS): Magnetotransport and tunneling investigations on heavy-fermion systems

Stefan Wirth introduced heavy fermion materials, describing them as a "Kondo lattice" of local moments embedded in a sea of conduction electrons. There are two types of interactions, he said - the local "Kondo" or s-d interaction betwen the local moments and conduction electrons

H = J S. s

that is responsible for the famous "resistance minimum", and a non-local "RKKY" interaction

H= J(R_ij) S_i.S_j

where the sign of the interaction oscillates due to Friedel oscillations. The competition between these two interactions in the Kondo lattice gives rise to a quantum critical point between the antiferromagnetic and heavy fermi liquid phases, according to the Doniach Scenario. The point that separates the antiferromagnet from the heavy fermi liquid is a quantum critical point - and it is in the vicinity of this point that new types of phases form - such as anisotropic superconductivity.

Steffan introduced the 115 materials, and discussed the rich interplay of antiferromagnetism and superconductivity in these systems. Of particular interest is Cd doped CeCo(In1-xCdx)5. Cd drives this system antiferromagnetic and leads to a two-stage transition (1) antiferromagnetism and (2) superconductivity. The H-T phase diagram of the SC and AFM are similar, with the sc nested inside the afm phase. The magnetic moment rises below the Neel temperature (4K?) but becomes T-independent in the superconducting phase. This suggests that f-electrons that would normally condense into the AFM order are instead, condensing into the sc condensate. Surely this is an argument for homogenious magnetism and sc?

There was a lot of discussion about whether the sc and magnetism exist homogeniously. Wirth argued that the comparable size of the SC and antiferromagnetic coherence length suggested they were homogenious - but surely NMR data by Curro et al refutes this?

Steffan also showed the global phase diagram including the Fermi liquid behavior. The FL extends out along the high field, low T part of the phase diagram, apparently extending inside the AFM dome.

Next Steffan turned to a discussion of STM data on heavy fermion compounds. He showed two sets of new data -

STM data on CeCoIn5 and STM data on YbRh2Si2.
In the CeCoIn5, which was cleaved at room temperature, the MPICpFS/Los Alamos group has observed a superconducting gap - but remarkably, the gap develops at 3K, while the s.c develops only at lower temperature - at 2.3K.  This raises the question as to whether there is a kind of pseudogap region above the sc transition - a point that was infered from bulk measurements some years ago.

In the YRS, which was cleaved at low temperature, the surface is much cleaner, and single-atom resolution is possible in the STM data.  The group does not know which layer they are cleaving on, but it is either Si or Yb layers.

Steffan discussed the STM curves, which show a kind of
V-shaped feature, with steps at negative bias that he is able to identify with the Crystal fields at 43, 25 and 17meV.  The overall shape of the dI/dV curve is however quite mysterious.  Wirth expressed the concern that they were mainly tunneling into the Si layers, with little direct coupling to the f-electrons


Bloggers aside: Interestingly enough - there is a remarkable similarity between the form of the dI/dV curve seen in this Non-Fermi liquid material, and the calculated density of states presented on tuesday by Massimo Capone, at a three-channel Kondo impurity quantum critical point.

Mainly f-electron Materials

A beautiful day on the Adriatic. The Abdus Salam Institute for Theoretical Physics is set on the Adriatic coast, just outside the old Austrian-Hungarian port-city of Trieste. The central lecture Hall of the ICTP is an impressive room - dating back to the 1960's, this lecture Hall was constructed not long after the United Nations building in Manhattan, and though unused, one can still see the simultaneous translation booths. There is a long black-board for the rpesentation of ideas and calculations, above which there are two large screens for the more modern form of power-point presentation.

The first day of the meeting focussed mainly on f-electron materials. 4f and 5f electron materials provide an exciting platform for research in strongly correlated materials. While the characteristic energy scales of these materials are probably too small for practical room-temperature applications, it is this very feature that makes it possible to tune their properties by pressure and magnetic fields. This, combined with their high purity, makes them an important research platform for studying the physics of strongly correlated electron materials.