Taka Shibauchi (Department of Physics, Kyoto University)
(Blogged by Tzen Ong)
Good morning everyone, and the next talk is by Taka Shibauchi on nematic transition and AF QCP in P-doped Ba-122 system.
Key Points:
1. AF QCP below the SC dome (K. Hashimoto et. al., Science 336, 1554 (2012))
2. Nematic Transition above the SC dome (S. Kashara et. al., Nature 486, 382 (2012))
3. Summary: A Renewed Phase Diagram
Taka starts by reviewing the phase diagram of the pnictides, specifically the 122 systems.
He introduces a chemical pressure axis with iso-valent doping, where you get very clean and homogenous samples with clear quantum oscillations in dHvA experiments.
He then shows a resistivity (\rho) vs T plot with several kinks, indicating the different phase transitions. There is a kink associated with the nematic phase transition, i.e. tetragonal to orthorhombic, and T_nematic ~ 120 K. There is then the usual resistivity drop at T_c.
Following on from the resistivity plot, Taka shows a \rho vs T above the SC dome, and there is a clear region of T-linear resistivity indicating NFL behaviour. So this raises the possibility of a QCP in the vicinity and perhaps below the SC dome.
Furthermore, from NMR experiments, we see a strong enhancement of 1/T1T due to Curie-Weiss behaviour at low temperatures, and the Curie temperature, \theta changes sign from low to high doping; so by extrapolating, we find a \theta = 0 at x ~ 0.3, implying a AF QCP exists at x ~ 0.3 below the SC dome.
Another piece of evidence if that the effective mass is also strongly enhanced from dHvA measurements, and this is seen in measurements in the normal state, i.e. above T_c.
This then leads to the question: Is there an AF QCP lying below the SC dome, and how does the QCP affect SC below T_c?
Taka then proposes two scenarios:
1. The QCP is avoided by a transition to SC state.
2. An AF QCP lying below the SC dome.
Taka proposes using the superfluid density, n_s, to differentiate between the two scenarios, and he has carried out London penetration depth, \lambda, measurements to measure the superfluid density.
At T = 0, the penetration depth \lambda^2 ~ m*/n_s e^2
He used three different experimental methods to measure \lambda, including Tunnel diode oscillator measurements, Microwave surface impedance, and the T-dependence of Nodal Superconducting gap structure.
He then shows a plot of \lambda^2 vs doping, x, from all 3 methods, and they indicate that there is a sharp peak at x ~ 0.3, approaching from both the low and high doping side. This means that there may strong QC fluctuations of n_s at x= 0.3, i.e, 2nd- order QCP may exist.
Qn: Is this an effective mass effect or is the superfluid density actually decreasing?
Ans: Quantum oscillation measurements show an m* enhancement around the same dopings.
Qn: What is the relation between \rho exponent and NMR results.
Ans: NMR shows monotonic behaviours, i.e. FL behaviour, and does not correspond exactly with the NFL behaviour seen in \rho. Taka said he will return to this point later.
Expt evidence indicates a QCP below the SC dome, meaning there are two different SC phases on both sides of the QCP, i.e. SC1 (pure SC state) and SC2 (co-existing phase of SC + AFM). This then implies a finite-temperature tetra-critical point where SC dome meets SDW state.
Taka therefore puts forth the scenario where the NFL behaviour as seen in \rho measurements and mass enhancement are all associated with the finite-temperature tetra-critical point, which is related to the zero-temperature AF QCP.
Taka also contrasts these results with the cuprates, where divergence or enhancement of \lamba^2 is not seen, e.g. Bi-2212 shows a broad max at p = 0.19, i.e. enhancemnet of n_s/m*, whereas Ba-122 shows a peak in \lambda^2, i.,e suppression of n_s/m* at x = 0.3. This is completely opposite behaviour.
Taka then shows the Uemura plot for the Ba-122 system, i.e T_c vs T_F (Fermi temperature).
The plot of T_c/T_F vs x shows a peak at the QCP - indicating that the strongest pairing occurs at the QCP and the SC may be driven by quantum critical fluctuations.
Taka also compares P-doped and Co-doped Ba-122 systems, and such quantum critical behaviour is not seen in Co-doped system. The reason may be due to disorder in Co-doped system, and STM results shows a large inhomogenity in SC gap for Co-doped systems, whereas P-doped is very clean
In addition, there is also experimental evidence for 4-fold nodes in SC gap for P-doped, but not Co-doped Ba-122 systems.
Nodal SCs in the vicinity of QCPs have been found in many systems, including heavy fermion systems such as CoCoIn_5 and Ce_2PdIn_8. The physics of these SCs is still an open issue, and the effect of the low-energy q.p excitations on the SC state is not well-understood.
He shows that there is a deviation from T-linear behaviour for \rho at x = 0.3 at low T, which is also seen in Ce115 system. It is not likely to be due to disorder because Ce115 is very clean.
Furthermore, a plot of \rho vs T^1.5 shows a good fit, but away from the QCP there are deviations.
Hence it is believed that it is related to the physics of a QCP, and Taka proposes the concept of Nodal Quantum Criticality in Unconventional SCs.
The effect of low energy fermionic quasi-particles may be modeled phenomenologically by a divergence in m* at QCP, which is cut-off at low-energies by deviations from QCP.
v_f ~ Z_k ~ 1/m*(k)~ \Delta^\beta/2
m*^2 ~ (p - p_QCP)^-\beta, and \beta ~ 1 in YbAlB4 and YRS has been observed.
Qn: We have different sheets with different m* in the pnictides.
Ans: There is a large v_F on one of the sheets, and \lambda is governed by this sheet, and all the sheets are coupled, so critical fluctuations must couple to the other sheets.
Qn: Is similar behaviour seen in electron -doped cuprates?
Ans: Taka does not know of any data for \lambda^2 divergence or enhancement in the e-doped cuprates.
Second Key Point: Nematic Transition Above SC Dome
Many experiments have indicated an in-plane anisotropy, in crystals detwinned by uniaxial pressure. However, we have to be careful as uniaxial pressure breaks C_4v and may induce in-plane anistropy.
So we need experiments w/o pressure, so we use magnetic torque measurements which have high sensitivity of 5 * 10 ^-12 emu on small pure crystals, and apply an in plane B field to measure the magnetic susceptibility tensor, \chi.
When there is rotational symmetry, i.e C_4v is preserved, we have \chi_aa = \\chi_bb, \chi_ab = 0
2-fold symmetry.
When there is nematic order, i.e. C_4v broken: \chi_aa \neq \chi_bb and \chi_ab \neq 0
At x = 0.33, and at low-T, there is a 4 \phi component in \chi, i.e. nematic order along Fe-Fe bond. Hence we see evidence for C_4v breaking.
Also synchchroton XRD detected small lattice distortions, with a tiny orthorhombic distortion at T*, i.e. the electronic nematic temperature.
T* changes with doping, and this leads to a new electronic nematic T* line above SC dome, and over a wide doping range.
Nematic and meta-nematic transtions:
Landau free energy = Structural term + electronic term + coupling
\delta = a-ba/+b = structural order
\psi = A_{2\phi} = electronic nematic order
T* : Non-zero \delta and \psi -> Broken C_4v
Suggests a renewed phase diagram:
1. A QCP below the SC dome with SC1 (pure SC) and SC2 (SC + AFM coexist). Nodal quantum criticality
2. Nematicity required for SC and high-T_C associated with AF QCP.
3. A new T* line above the AF state and SC dome.
Qn: Can you differentiate between CDW and nematic order?
Ans; Torque magnetometry cannot differentiate between charge and orbital order.
Qn: Do SC2 and SC1 have the same symmetry?
Ans: Based on the T dependence of \lambda^2 and NMR are similar, so the symmetry seems to the same.
Comment: QC fluctuations + fermions RG machinery shows m* enhances but does not diverge. So there is a peak as seen in the penetration depth measurements.
Comment: In the GL free energy shown, there is a coupling between structural and electronic. However, you can ignore the structural component, and still show that there is a meta-magnetic transition from purely electronic nematic phase transition.
Qn: Have you measured the NFL down to low-T by applying a high B field?
Ans: Not done yet.
Qn: Assume we have a QCP, with q.p. coupled to critical fluctuations, does this imply that the SC gap should be strongly enhanced?
Ans: The QC fluctuations enhances pairing interaction, but also decreases n_s, so it has competing effect.
Qn: What is the meaning of iso-valent doping?
Ans: P is iso-valent to As, so number of electrons and holes are unchanged.
We thank the speaker for a very nice talk!
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