HEAVY FERMION PHYSICS (BOREAS)
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Researchers
Dr. Freek Massee, Peter Sprau


Recent Research Achievements

Publications

[1] Schmidt A.R., et al. "Imaging the Fano lattice to 'hidden order' transition in URu2Si2"
(full text : Nature, 465, 570)
[2] Hamidian, M.H., et al. "How Kondo-holes create intense nanoscale heavy fermion hybridization disorder"
(full text : PNAS, 108, 18233)
[3] Allan, M. P. et al. "Imaging Cooper pairing of heavy Fermions in CeCoIn5"
(full text : Nature Physics, 9, 468)
[4] Dyke, J. S. v. D. et al. "Direct evidence for a magnetic f‐electron mediated Cooper pairing mechanism of
heavy fermion superconductivity in CeCoIn5"
(full text : PNAS Early, Jul 2014)


Visualizing Heavy Fermion Formation

Heavy fermion compounds constitute a large class of strongly correlated materials that exhibit a variety of behavior including magnetic ordering, density waves, unconventional superconductivity, and possibly quantum criticality. Their branding as 'heavy' is due to the hybridization between the localized f-electrons and delocalized electrons of other bands. The basic implications of such hybridization for the microscopic electronic structure have long been known within the context of the Anderson Lattice lattice model, and experiments over the past 30 years have been consistent with those predictions. However, a direct observation of the hybridization process and the resulting heavy band formation (the central result of the theoretical framework) was not achieved until the introduction of spectroscopic imaging STM (SI-STM) techniques to heavy fermion materials.

Using the Fourier transform SI-STM approach developed earlier, we recently began studies of the 'heavy fermion' problem in which hybridization processes between conduction and localized electrons generate the heavy fermion electronic state. The first imaging of the opening of a hybridization gap and of heavy band formation in a heavy fermion system was achieved using the compound URu2Si2 and its alloy Th0.01U0.99Ru2Si2.

Figure: Determining the momentum space electronic structure through Fourier transform heavy quasiparticle interference imaging (lower left panel). The extracted momentum space structure (top panels) show that the low temperature bands are in very good agreement with that of Kondo lattice theory (lower right panel)


Visualizing Individual Kondo Holes and their Destruction of Heavy Fermions

The presence of magnetic interactions in heavy fermion compounds stems from the presence of a lattice of magnetic moment carrying atoms. It is the interaction of high temperature background Fermi sea with this magnetic lattice that generate the new state as the temperature is lowered. Hence, very soon after the discovery of heavy fermion compounds a number of careful experiments focused on better understanding these atomic scale interactions by introducing a small concentration of nonmagnetic impurities, referred to as Kondo Holes, into the magnetic lattices and probing the bulk effects. The observations led to a series of hypotheses regarding how the local microscopic perturbations to the heavy fermion structure were affecting the macroscopic properties. Amongst them were disorder in the interaction strengths between the magnetic lattice and the delocalized electrons, bound states at the defect sites, and a weakening of the heavy fermion effect. Furthermore, motivated by STM advances, recent numerical calculations predicted a spatial oscillation of the heavy fermion hybridization strength around a Kondo Hole, an effect that cannot be studied by bulk probes.

The nonmagnetic Th atoms in the sample Th0.01U0.99Ru2Si2 that replace a very small number of magnetic U atoms are believed to act as Kondo Holes. Being a local probe, the STM is ideally suited to measure the effect of their local perturbations. By developing the 'hybridization gapmap' technique, a completely novel spatial visualization of hybridization strength became possible. The theoretical predictions of disorder could now be explained as resulting from the phase incoherent interference of the hybridization oscillations emanating from each defect site. More importantly, it showed directly how both the real and momentum space electronic structures were altered due to the Kondo Holes. The analysis further revealed the unexpected result that the wavelength of the oscillations was actually set by the high temperature electronic structure, a finding which unmistakably distinguishes it from a Friedel type response. More definitively, the visualization of the hybridization strength made clear that the disorder due to Kondo Hole dilution is in fact not just a local effect but one in which the impurities add texture to the electronic structure across the whole sample.

Figure: (Left) Hybridization gap map showing spatial nanoscale disorder of the heavy fermion hybridization strength. (Middle) Fourier transform of the hybridization gap map demonstrating that within the spatial disorder there exists a highly dominant wavevector. (Right) Hybridization strength oscillations around a single Th atom showing that the nonmagnetic impurities are the source of the hybridization oscillations.


Imaging Cooper Pairing of Heavy Fermions in CeCoIn5

The discovery of superconductivity in heavy-fermion materials marked the birth of unconventional superconductivity. As with the subsequently found cuprates and iron pnictides, the Cooper pairing mechanism of heavy-fermion superconductors, while long hypothesized as due to spin fluctuations, has not been determined. It is the momentum space (k-space) structure of the superconducting energy gap Δ(k) that encodes specifics of this pairing mechanism. However, because the energy scales are so low, it has not been possible to directly measure Δ(k) for any heavy-fermion superconductor. Bogoliubov quasiparticle interference (QPI) imaging, a proven technique for measuring the energy gaps of high-Tc superconductors (see above), has recently been proposed by Akbardi et al. (PRB 84, 134505, 2011) as a new method to measure Δ(k) in heavy-fermion superconductors, specifically CeCoIn5.

By implementing this method, we detect a superconducting energy gap whose nodes are oriented along k||(±1,±1)π/a0 directions. Moreover, for the first time in any heavy-fermion superconductor, we determine the detailed structure of its multiband energy gaps Δi(k). For CeCoIn5, this information includes: the complex band structure and Fermi surface of the hybridized heavy bands, the fact that largest magnitude Δ(k) opens on a high-k band so that the primary gap nodes occur at unforeseen k-space locations, and that the Bogoliubov quasiparticle interference patterns are most consistent with dx2-y2 gap symmetry. Such quantitative knowledge of both the heavy band-structure and superconducting gap-structure will be critical in identifying the microscopic pairing mechanism of heavy fermion superconductivity.

For more information, see M.P. Allan* & F. Massee* et al., Nature Physics 9, 468 (Aug 2013).


Magnetically mediated Cooper pairing in CeCoIn5

Using the experimentally determined band structure of CeCoIn5[3], we reveal quantitatively the momentum space (k-space) structure of the f-electron magnetic interactions. Then, with the assumption that these magnetic interactions are mediating Cooper pairing, the coupled superconducting gap equations are solved on the two heavy-fermion bands Eα,β(k). The resulting calculated momentum space structure of the superconducting gap, Δα,β(k) is in remarkable good agreement with the experimentally determined one. Furthermore, our phase sensitive quasi particle interference scattering measurements are in good agreement with a sign change of the superconducting order parameter, which provides additional strong indications for a d-wave superconducting gap in CeCoIn5.

From the k-space structure of the f-electron magnetic interactions, a variety of characteristics for unconventional superconductivity driven by them can be calculated. We show that the calculated superconducting transitions temperature, the spin resonance seen by neutron scattering, and the spin relaxation rate are all qualitatively in good agreement with experiment, providing direct evidence that the heavy fermion Cooper pairing in this material is indeed mediated by f-electron magnetism.

For more information, see J. van Dyke* & F. Massee* et al., PNAS Early (Jul 2014).

 

Instrument

Experimental Room

Our SI-STM and fridge are held from a vibration-isolation table, which is installed in a radio-frequency (RF) shielded room. We use a gas panel for our vacuum system and a dilution refrigeration unit to reach milliKelvin temperatures. The RF shield room, together with its foundation consisting of 26 tons of concrete, is floated by 6 air springs. Vacuum lines are anchored to the concrete block and wall before going into the RF shield room. All these instruments are installed inside an acoustic shielded room which is isolated from an external control room where the electronics are placed. Vacuum pumps are located underneath the floor of the control room.

RF-shield room Insert, vibration-isolation table, gas panel Gas panel, RF-tight box Gas panels Vacuum lines Control room

Click to enlarge pictures.
See also William Wilson Associated Architects Inc. site.

 

Milli-Kelvin 9-Tesla Spectroscopic Imaging STM (SI-STM)

The system consists of a low circulation Kelvinox 400 dilution refrigerator retrofitted with ultra low vibration 4He-pot and for very high vacuum capabilities, surrounded by a persistent American Magnetics magnet. It is suspended in a very low boilrate Dewar from a massive low vibration cryostat. The cryostat is housed inside an acoustic/RF shield room (shown left), itself supported on a 25 ton inertial block on vibration isolators. This whole assembly is installed in an underground acoustic/vibration isolation vault. The pump set is remote and highly vibration isolated and the control room is remote. The SI-STM head is at the center of the magnet suspended below the refrigerator. We use this system to study Bi2Sr2CuO6+δ, NbSe2, YBa2Cu3O6+δ, Sr2RuO4, GaAs, GaSb, and Ca2-xNaxCuO2Cl2. Sample exchange from room temperature to 4K takes ~6 hours and to 10mK takes ~9 hours.


Dilution Refrigerator

The dilution refrigerator system, shown on the right, was purchased from Oxford Instruments. The highly modified design included decreased circulation rate at the base temperature of 10mK, decreased helium boiloff, and an off-axis top loading port. The refrigerator itself consists of a 1K pot (pumped liquid 4He), a condenser (to liquefy 3He coming from the room temperature pumps), the still (to pump on the dilute 3He-4He mixture), two sets of heat exchangers (one side of each heat exchanger contains 3He from the condenser while the other side has dilute mixture headed toward the still), and the mixing chamber (which contains the phase boundary between the pure 3He coming from the condenser and the 94% 4He - 6% 3He, the "dilute" phase, going to the still).

 

 

 

 

 

 

 

 

 

 

 

The modifications are shown on the right side of the figure. A system for in situ cryo-cleaving of crystalline samples is bolted to the 4K plate. This cleaving stage must also act as a radiation shield to prevent 300K black body radiation (from the room temperature vaccum port) from impinging directly on the dilution refrigerator and SI-STM. [Empirically, if we leave the door to the cleaving system open, the refrigerator warms up to roughly 1K.] The cooling system (rather difficult to see in this photo) consists of an extra pair of stainless steel tubes which are heat sunk to each stage of the refrigerator. Cryogen (either LN2 or LHe) is forced through the tubes from a storage dewar outside the cryostat, returning along the second tube back into the room. This allows us to cool the entire system from room temperature to 4K without using exchange gas. Two sample guides are used to, well, guide the sample from the cleaving stage into the SI-STM receptacle. Finally, the SI-STM is located at the bottom of the cryostat. Thermometers, heaters, and electrical connections are not shown for clarity (or minimal clutter, in this case).


Head Compartment

Top view Side view After assembly
STM diagram -- top view STM diagram -- side view
  1. Sample Receptacle
  2. Sample Holder
  3. Tip
  4. Tube Scanner
  5. Scanner Holder
  6. Sapphire Prism
  7. Shear Piezo Stacks
  8. Macor Body
  9. Spring Plate
  10. Capacitive Sensor


Collaborators
Alexander V. Balatsky - Los Alamos National Lab
Graeme Luke - McMaster University
Dirk Morr - University of Illinois at Chicago
Cedomir Petrovic - Brookhaven National Laboratory