After the thanks for Doreen and the bloggers.
Paul Canfield stands up to make a point. In general there seem to be two classes of material.
(1) The old style: MgB2, RNi2B2C, Nb3Ge
They are relatively easy to make and doing stuff to them makes them worse superconductors. They are ordered and reveal their superconducting state easily.
(2) New style: FeAs CuO
These are harder to make and generally need to be doped from a parent (host state) to make them superconductors to remove some other state.
Paul says we know so little that it does not matter what the rational is, as long as we are looking we will find stuff. But, what would be useful to the experimentalists ("animals invited to this paradise") from the theorists is what sort of host materials should we be looking at to reduce the size of the phase space. The hosts will probably be non superconducting.
Laura Greene: well Philip^2 and Si have pointed to Mott insulators as being a good starting point. Also, theorists don't always help because they don't understand stuff that we do about the compounds and so have a simplistic view of the changes that really take place on doping.
Piers Coleman: this is just the start of a better collaboration between the materials and the theorists. It was great to have Juri. But here is an issue: theorists live mainly in momentum space but the chemistry lies in real space. Here perhaps heavy fermions have something to offer.
Andrey Chubukov: Plot Tc against Hubbard U/W then "obviously Tc goes up from the small U/W limit, it must also go down at large U/W. What seems surprising is that Tc is rather flat in the intermediate region with Tc ~ 0.02E_F (Piers says it is not true in heavy fermions). This means Tc ~200K max.
And at this point your blogger must leave for his flight...so over to Sam.
Rick Green: Question to Andrey: what about pressure, which seems to increase superconductivity?
Andrey: Well, the top won't be perfectly flat, and this is a very schematic picture.
Andrey: This was about Tc in the absence of competing orders. Of course, when there is competing order the picture changes. But just to emphasize again, the numbers are quite interesting - that Tc always comes out about 2% of the Fermi energy.
Question: What about dimensionality? Should we stick to 2D systems, or maybe try and move elsewhere?
Andrey: In fact, this picture is quite general in the generic shape; but the more dimensions, the more factors of 2pi and the more small pieces of BZ you have to worry about, so the numbers come out smaller.
Piers: What about condensation entropy? Never seen it go about about 1/3 log 2. That's another way of thinking of these limits.
---
Piers: Now that we've finished scientific questions, what about organization issues. Should we have less talks (seems to be a general consensus that the number of talks is actually quite good). What about more people - many more people could fit in this lecture theatre.
Laura Greene: I'd like to see many more young people.
Piers + Andrey: A lot of this is a question of money - we have to look into getting more funding.
Andriy: What about holding it in the Adriatico lecture hall, rather than this one in the main building? Seems to be general consensus that main building is better.
Well, that's the end!!! Two weeks have gone by very quickly. Ciao tutti.
Physicists met at the International Center for Theoretical Physics to discuss the challenges of understanding and designing strongly correlated electron materials - novel kinds of order, magnetism and superconductivity. The meeting was funded by the ICTP, the NSF, the ESF, ICAM and RIKEN.
Friday, August 13, 2010
Pascoal Pagliuso (Campinas, Brazil): Low symmetry structures and strong f-s(d-s) hybridization as key ingredients to find new unconventional superconductors
Outline
1. Review of structurally related physical properites of HFS families - the role fo CEF tetragonal symmetry
2. CeRhIn5 doped with La and Sn
3. Cd-doped Ce2(RH,Ir) In8
4. Possible relationship with the Fe-based Sc
5. New ideas for new materials.
Next he introduced the family of compounds - from cubic CeIn3, to CeMIn5 to Ce2MIn8. There are several sc in this families (six) - what makes them special? If you consider related materials, including Ce2PdIn8, CePt2In7 and Pu(Co,Rh)Ga5 you have even more sc, but Pascual will keep with the simple
structures of this family.
When you apply pressure you suppress AF and then get sc in CeRhIrIn5 and CeRhIn5.
CeRhIn5 orders AFM with Ce moments in the plane and spiral order along c-axis. Pressure suppresses TN and induces SC. Ce2RhIn8 also orders, but with a commensurate structure.
Next he showed the susceptibility of CeMIn5 - with the anisotropy - c-axis is the magnetic easy axis. Another interesting feature of the data, is that Tc is a linear function of c/a. The evolution of the c-axis susceptibility and Tc struck his group as interesting.
There are three interactions to consider - RKKY, crystal field and the Kondo scale. This is what he is now going to discuss, showing a detailed series of experiments designed to explore the link between each of these variables and the crystal field structure of these compounds.
Ce S=1/2, L=3, J=5/2
Pd, S=1, L = 5, J = 5 Non Kramers ion. No spin, but sometimes non-Kramers doublets.
Gd L=0, J= 7/2 pure spin ion: ideal for a control atom with minimal crystal field effects - this will be important later.
He introduced crystal symmetries for these systems.
Why are Ce and Yb special? Becuase Ce is f1, wherea.s Yb is f13 with one hole. Those states are close to the fermi energy so that fs hybridization is strong. They are different from the other rare earths in this regard, he said.
But they also have a competition between RKKY and Kondo. Showed the Doniach scenario, so that when J is small, RKKY dominates, but once TK becomes larger, Kondo
compensated state develops with a large FS. SC often develops at the transition from the magnet to the heavy fermi liquid.
Gamma 6 - +-1/2
Gamma 7 +- mixture between
a|5/2> + b |3/2> and by tuning the admixture you can tune the anisotropy.
Separating out the interactions
So how can we separate all the interactions using material science? If I track the magnetic properties of all the Gd I am probing the dependence of exchange with M. Gd Rh-Ir all have the same Neel temperature (TN) - this is not affected by either M or going from 115 to 218. This tells you that RKKY is determined by the nearest neighbor interactions - and this is important.
(a) Tuning RKKY without Xtal fields or Kondo: the case of Gd
How do we tune JRRKY? As we go from 218, 115 103 Gd systems, same TN and same magnetic structures (1/2, 0, 1/2) and spins in the ab-plane -> same JRKKY.
Q Canfield asks clarification - usually in a magnetically ordered state you have some magnetostriction.
A Pascoal says yes there is, but it does not reduce the symmetry. Grenado, Serrano PRB (2004), PRB (2006).
(b) Turning on Xtal fields, but without Kondo: the case of Nd.
Now lets turn on the xtal fields by going to the Nd compounds. As you go from Nd In3, Nd2RhIn8, Nd RhIn4, Nd2IrIn8, Nd IrIn8, there is a reduction of the amount of entropy associated with the transition (did I get this right?) - and the TN goes up - larger Gamma 8 CEF splitting leads to a larger TN.
Paul Canfield points out that the Gd TN does actually go down weakly.
PP says yes, but only by 10%.
Now summarizing the magnetic order, Nd spins lie along the c-axis, Tb along c-axis also, but Gd and Ce order in plane (as does Sm). When the moment is along c-axis, TN increases with tetragonal asymmetry, but when the moments lie in the ab plane, TN decreases with tetragonal asymmetry.
H=B20 O20 +B40 O40 + B44 O44.
As you turn on B20, for Ce, moment goes to plane, Nd tends to go along the c-axis. No Kondo in the model.
Rafael Fernandes - what is the difference between the two cases?
PP - you just change the J.
Piers Coleman asks - is there a simple way to understand this?
PP: - for Ce, Gamma 7 has a higher tendancy to have g-anisotropy in the plane. Nd tends to have c-axis Ising anisotropy in this structure.
Going on he shows TN versus the Jz^2 in this model. You do this for 5/2 and 9/2, as a function of Jz^2 anisotropy. For J= 5/2, TN goes down as the Jz^2 goes up, whereas for 9/2 and 6, TN goes up. Ce has the frustrated property that it has a larger C-axis susceptibility, but this suppresses TN.
You may remember this is exactly what you saw experimentally. TN went down with Ising symmetry, but an increase in TN for the large J systems.
But to be sure, the group used neutron scattering to track the evolution of the xtal ield ground-state. As you go from In to 115 Rh - Ir - Co you are increasing the 3/2 part of the xtal fields. Recently confirmed by Severing. Co is more Ising like - Rh is less Ising like and has larger TN.
Rh - Ir - Co Ising symmetry increasing, TN going down.
All of this is going on without any effect of Kondo.
 |
| Increasing the xy anisotropy drives TN below the Kondo temperature, leading to SC. |
2. CeRhIn5 doped with La and Sn
OK. Lets now consider the Kondo effect influence. For this, the group used dilution expts. They choose samples with the same TN=2.8K. One is CeRhIn-Sn, one is Ce-LaRhIn5. Now apply pressure and for the Sn and La one, you get SC, but the critical pressures are different. For La need higher pressure to find superconductivity. From that data, you construct a phase diagram . Can clearly see that the Sn occurs at lower pressure, whereas La shifts SC to a higher pressure. Yet they started at the same TN, so it must be the tuning of something else.
Canfield says equating this with pressure "is a sin in of itself". Because the lattice pressure effects from physical pressure and substitution are different. But blogger did not follow the intricate discussion.Canfield - when you are trying to compare with chemical pressure there are many parameters - it becomes ambiguous. La - changes size of Unit cell, hybridization - magnetic zero La will suppress TN also. Pascoal replied that they certainly accounted for this. He used Gd similar - same La Yt concentration - La distorts, Gd does not, so can show there is no affect of distortion in the TN.
PP says mainly in the plane.
Monika Gazma- this will change hybridization a lot no?
PP - yes.
Monika Gazma- no change of lattice parameters with Sn
PP - no.
Main points again:
1 Ising like doublet.
2 Some sort of hybridization.
3. Cd-doped Ce2(RH,Ir) In8
Now to the Yb systems - why no SC? YbRh2Si2 has a doublet in the plane from the anisotropy in the g-factor - - tends to favor AFM and this is why for PP, this compound will never be superconducting.
Now for YbAlB4, this is Ising like, but has larger susceptibility along c-axis. This system has a very curious ESR signal - with a g that is larger along the c-axis. Confirms this trend.
Meigan Aronson - But the Np compound is different - this is xy
PP -Np - probably 5f2 - different situation.
Paul Canfield - CeCu2si2?
PP - Ising like.
Ising doublets are good for SC.
4/5. Possible relationship with the Fe-based Sc and New ideas for new materials.
Andriy Nevidomskyy - could you please repeat conclusion for YAlB4.
PP - just because it has a larger g out of plane from ESR - small - complication here - we are not directly probing the f-resonance, so we're not capturing all of the anisotropy.
Andriy Nevidomskyy - how would you compare with alpha case?
PP - dont have any coupling to the f-electron - doesn't
Paul Canfield - the unspoken difficulty of a plot with this, is all the compounds that have Tc=0! It is a very highly selective data set.
PP - I don't want the ones with zero Tc, I want guidance about those
T. Hanaguri (RIKEN) : Landau level spectroscopy of helical Dirac fermions in a topological insulator Bi2Se3
--Why are we doing STM?
--Some technical aspects of STS/STM
--Why STM/STS on topological insulator
--Landau level spectroscopy on topological insulator
Strategy to find exotic phenomena
One way we search for exotic phenomena is to build up "boring" electrons to find new emergent macroscopic phenomena.
Alternatively, lets break down "boring" materials, analyze them thoroughly to find quantum structure and interference around impurities and otherwise microscopic properties that show it wasn't as "boring" as we thought.
Background to STM
- STM is a tool to explore the electronic states - measures the local density of states (LDOS), and can make topographical scans of material surfaces.
- At any certain point, can measure current as function of bias, and to a good approximation, the LDOS of the material is given by dI/dV.
- At any fixed bias, can then scan the surface, to get a "topograph conductance" map - this is spectroscopic imaging STM (SI-STM). Then can obtain these images at different biases, V (or in other words, energy, epsilon). Putting these together and taking a Fourier transform gives momentum space information.
Why is STM so powerful?
--Atomic spatial resolution: 0.1nm laterally and ~pm vertically giving very precise local information
--Momentum space accessible, from FT SI-STM (Fourier-Transform Spectroscopic Imaging Scanning Tunneling Microscopy)
--Very high energy resolution, as high as micro-eV
--can do experiments under a wide range of external conditions.
To get good results, one needs a few target specifications of the SI-STM machine:
--Ultra-high vacum (of order 10^-10 Torr), as the surface must be kept clean for a long time.
--High magnetic field >10T to control the spin and Landau orbits
--very low temperature <1k in order to reduce the thermal broadening [ Typical energy scales in materials we want to see: Mott gap ~ eV, Thermal 1K~0.1meV, SC gap (HTC) ~ 10meV, impurity resonances ~ 1meV, Zeeman energy ~ 0.06meV/T ] --variable temperature (in order to study phase transitions) Typical scans (of space and energy) will take of order 36 hours, and require even nm drift forbidden during this timescale. In RIKEN, have a multi-extreme STM, satisfying all of these requirements, including sub-pm noise. How small is sub-pm noise? 0.5pm/2cm = 0.1 micro meter / 4000m (height of Mt. Fuji) [bloggers note: wow! this is serious resolution!]
Now onto main topic of talk
published recently in: Hanaguri et al PRB 82, 081305(R) (2010)
Also see similar recent work in: Cheng et al PRL 105, 076801 (2010)
Introduction to Topological insulators: Topological insulators are (band) insulators with a robust gapless edge or surface state. How can this be true? Need a band structure with a specific "topology".
What about 3D case? [see e.g. Fu, Kane and Mele PRL 98, 106803 (2007)] In 2D, we have gapless edge states with linear dispersion. In 3D, this will map into gapless surface states with a linear dispersion - i.e. Dirac Fermions (with an added helical structure).
In fact, in solid state, one finds that Dirac cones are everywhere!
--Graphene [ see e.g. Castro Neto et al, RMP (2009) ]
--Organic conductors
--d-wave SC
--Surface states of 3D topological insulators (TI).
Usually, the Dirac cones come in pairs. However, in the TI, find an odd number of cones centered at time-reversal invariant momenta. This is due to the TR invariance, one of the conditions of a topological insulator. We also find that in the TI (unlike other cases) there is no spin degeneracy in the surface states. This is related to the spin-orbit coupling necessary to make this state.
Experimental verifications of 3D TI: First, Bi-Sb -- ARPES revealed an odd number of Dirac cones [ Hsieh et al, Nature 452, 970 (2008) ]
Since then, we have found some other cases:
--Bi2Se3 - single isotropic Dirac cone [Zhang et al, Nat. Phys. 5, 438 (2009) ]
--Bi2Te3 - which is anisotropic [ Chen et al, Science, 178 (2009) ]
An odd number of Dirac cones is good evidence for TI states. But what more can we do?
Next, spin-resolved ARPES revealed the helical spin structure.
So ARPES is great! There is a helical Dirac cone in these materials no doubt.
But what else can we do?
Let's look a little close at the helical spin-structure: one of the properties is that it gives suppressed back scattering. Now, scattering interference may generate electronic standing waves (QPI), which should detect this interesting scattering properties of the helical Dirac fermions.
The helical structure can be modeled by a multi-band model with spin-selection rules. Can also include certain FS distortions -- many of these have been calculated, and give nice agreement with QPI patterns.
What about Landau levels?
First, take some lessons from Graphene, [Castro Neto et al, RMP 81, 109 (2009) ]
--Find that the LL (Landau level) energies E_n are proportional to \sqrt{nB}
--Also find a B-independent LL with n=0. This gives a half-integer QHE, and furthermore the large gap due to this n=0 state means that the QHE can even be observed at room temperature. [Novoselov et al, Science 315, 1379 (2007)]
We should compare this to the conventional 2D electron gas where E_n proportional to (n+1/2)B.
In a topological insulator: this should be easier to look at than graphene as you see the Dirac fermions at the surface of a large bulk material. Furthermore, in graphene, you get factors of 4 (from 2 Dirac cones, and 2-fold spin degeneracy). But in a TI, there is a single Dirac cone may give rise to true half-integer QHE. In other words, the TI should be great to look at the ususual QHE properties of the Dirac cone.
But there is a little problem - an unavoidable bulk contribution in Bi2Se3. For example, compare band calculations [Zhang et al, Nat. Phys. 5, 438 (2009)] to ARPES data [Xia et al, Nat. Phys. 5, 398 (2009)] and find that the experimental system looks e-doped. This bulk contribution dominates for example magneto-transport. A surface probe is necessary to study the Dirac cone; but ARPES is not magnetic-field compatible. So lets do STM.
Experiment on Bi2Se3, crystals grown by Igarashi and Sasagawa (TIT). Bulk electron density in range 10^18 to 10^20 for two different samples.
Basic tunneling conductance against sample bias agrees nicely with ARPES results (including e-doping level).
Question: Why is there a sharp kink seen at 0 sample bias?
Answer: Don't know (although I didn't quite catch the slightly more extended answer)
Search for QPI : see almost nothing!!! QPI is very weak in single, isotropic and helical Dirac cone, as compatible with the theory of forbidden backscattering.
Now, LL spectroscopy: Increase B, and measure tunneling conductance against sample bias. We see clearly the development of the Landau levels, including the n=0 level at the Dirac point. E_n is definitely sub-linear in n, and is furthermore consistent with square root behavior of LL of single helical Dirac cone. [T. Hanaguri et al, PRB 82, 081305(R) (2010)].
However, as compared to the perfectly square root behavior seen in Graphene, we find in Bi2Se3 slight deviations from this. A short analysis shows us that in fact plotting E_n against sqrt(nB) is in fact an energy/momentum like relation - showing the slight bending away from linear behavior in the Dirac cones of Bi2Se3. This can be nicely compared to the dispersion seen in ARPES. This is new momentum-resolved spectroscopy using STM!
--missing n<0 LLs - maybe due to coupling with bulk band. --Enhanced amplitude of LL oscillations near E_F. This can be interpreted as an E-dependent QP lifetime. --Also find anomalous fine features near E_F. The fine structures shift in the same manner as LL's. --There is also an extra amplitude enhancement suddenly at |E|<~20meV. This is a new energy scale in the problem. [What is this energy scale?]
Summary
--Studied Helical Dirac fermions at surface of topological insulator.
--Clearly identified unusual LL structure expected for Dirac fermions
--Anomalous fine structures identified near E_F.
--Spectroscopic STM is now ready to explore exotic electronic phenomena.
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