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.