Laser ARPES study on Ba_(1-x)K_xFe2As2 and KFe2As2
Introduction
Brief review of BaK122 phase diagram and previous ARPES results. It's clear that the optimally doped system (x = .4) is fully gapped, while the end member KFe2As2 has nodes. Whether the optimally doped sample is s+- or s++ is still an open question, as is the d-wave vs. s+- nature of KFe2As2. Understanding these gap symmetries is essential for understanding the mechanism.
Most people believe that the mechanism is spin-fluctuations, which comes from intra-orbital nesting. In favor of this, STM in Fe(Te,Se) finds sign reversal. Disfavoring it, the insensitivity to impurities and the ARPES on KFe2Se2 showing that there is no nesting despite the high Tc favor s++.
The multiorbital nature, where DOS(zx) > DOS(yz) below the structure transition indicates orbital ordering, and ARPES on Ba122 sees 2-fold symmetry Fermi surface below Ts. Kontani's theory of orbital fluctuations relies on interorbital pair scattering, which gives s++ superconductivity.
Information about Laser ARPES. Very high resolution (70 mueV), low temperatures T < 1.5K, bulk sensitive (100 Angstrom electron escape depth), and can change polarization easily to differentiate the different orbital contributions. The 7eV laser covers the Gamma surface, and they are developing an 8eV laser that should cover the electon surfaces too.
Laser ARPES results on Ba122 doped with K
Optimally doped: They observe three hole Fermi surfaces around the Z-point (measure kz = Z plane), with the orbital dependences: x/y, xz/yz-z^2,x^2-y^2 (from inside out). For the optimally doped sample, previous ARPES saw a gap around 10meV with a shoulder around 6-10 meV (kz = Gamma plane). They see smaller gap (3meV), and two sharp peak structures (A,B). Identify the lower energy peak, A as the SC peak, as it vanishes above Tc, but the higher energy peak B persists up to 100K, becoming very broad but not dispersing in energy, and thus is not a superconducting peak. The smaller gap magnitude at the Z point is consistent with other measurements finding the smallest gap at the Z point. Borisenko (at Gamma point) sees peak A, but not B. The FS dependence of the gap is not particularly anisotropic (4-fold anisotropy) and is the same for all three bands.
So how does the anisotropy change with doping?
KFe2As2: Transport shows line nodes for the KFe2As2 material, while SANS shows the nodes must be along the c-axis or there must be a full gap. Measuring at the Z-point, they see the three bands as before.After symmetrizing and plotting for different angles around the FS, they see that the inner band is always gapped (2meV), the middle band is sometimes gapped and sometimes not (1meV max), while the outer band is always ungapped (well, .2meV). The nodes on the middle band exist around +- 5 degrees, giving a total of 8 nodal points around the four-fold symmetric points (0,90,...). There is also a gap minima around 45 degrees. Chubukov et al have shown that the gaps can all be fit by the form \Delta_0 (1 + A cos(4 \phi) + B cos(8\phi)) with different A's and B's for each band. This observation of nodes is direct evidence for s+- over s++, and thus evidence for the spin fluctuation mechanism.
Underdoped (x = .2, .3):
They again measure the SC gap on the three surfaces, finding the inner two to be stronger than the outer, again see two peaks on both FS. They also see a kink that may correspond to the non-SC peak. As they get more underdoped, the difference between the gaps increases, the non-SC peak intensity becomes weaker and so does the kink structure. Since the gaps are different in magnitude, this implies the inter-orbital pairing is stronger than in the optimally doped sample.
Overdoped (x=.7):
There is no gap on the outer sheet, while the inner and middle sheets have near the the same gap size, which is only weakly anisotropic.
There is a clear doping dependence of the SC gap size, and a clear difference between different Fermi surfaces. The gap on the inner and middle sheets nearly corresponds to Tc, but outer does not (Inner and middle are active, outer(x2-y2) is passive), and the gap on the outer sheet vanishes abruptly at x=.55. What happens to cause such a drastic change? The electron FS at X-point vanishes. It is also composed of x^2-y^2 orbital, so intra-orbital (spin-fluctuation) pairing is important in the over-doped region.
So the picture is then that spin fluctuations are important at low and high doping, while the orbital fluctuations are important at optimally doping. This can be potentially explained by examining the dependence of the As-Fe-As angle on doping. It passes through the magic tetrahedral angle around optimal doping, which should lead to stronger orbital fluctuations - Kontani also proposes a (s+-)(s++)(s+-) type phase diagram with the angle, so it might be s++ at optimal doping.
Next he discussed the temperature dependence of the non-SC peak. It has the form of the SC gap + a temperature independent constant. Above Tc, they observe a two-kink structure that is T independent. The non-SC peak doping dependence is a dome around .4, with much weaker dependence above x = .6.
The non-SC peak has some similarities to the magnetic resonance, which also has a magnitude of around 15meV, but disappears above Tc. It also gets weaker above x = .7 and is maximal at x = .4. The doping dependence of the magnitude and intensity are similar. Likely also related to the disappearance of the electron FS at the X point. SO the non-SC peak/kink is likely related to the magnetic mode.
Open question: Why does on the the x=1 material have 8-fold symmetry?
Questions:
Fernandes - what about claims by dHvA that KFe2As2 has one band with a mass renormalizaton on the order of 10?
A - question about normal state, while this study was in the SC state.
Shibauchi comment - the heavy mass is seen near the X-point, not the Z-point.
Wen - Maximum gap now appears to be 3-4 meV, making 2\Delta/Tc only 1.3 - less than weak coupling BCS.
A - If electron FS has a larger gap, it could compensate, and most people say that it is sufficiently large.
Borosenko comment - they measure gap in Z-plane only, so limited momentum region. The gamma point is larger, on order of 10 meV.
Maiti - At x = .2, do you see isotropic gaps, even though it's within the coexistence regime?
A - Yes, slight four-fold symmetry.
Chubukov- From data alone, is there anything to distinguish between s++ and s++ at optimal doping?
A - No Fermi surface is special and there are no nodes.
Introduction
Brief review of BaK122 phase diagram and previous ARPES results. It's clear that the optimally doped system (x = .4) is fully gapped, while the end member KFe2As2 has nodes. Whether the optimally doped sample is s+- or s++ is still an open question, as is the d-wave vs. s+- nature of KFe2As2. Understanding these gap symmetries is essential for understanding the mechanism.
Most people believe that the mechanism is spin-fluctuations, which comes from intra-orbital nesting. In favor of this, STM in Fe(Te,Se) finds sign reversal. Disfavoring it, the insensitivity to impurities and the ARPES on KFe2Se2 showing that there is no nesting despite the high Tc favor s++.
The multiorbital nature, where DOS(zx) > DOS(yz) below the structure transition indicates orbital ordering, and ARPES on Ba122 sees 2-fold symmetry Fermi surface below Ts. Kontani's theory of orbital fluctuations relies on interorbital pair scattering, which gives s++ superconductivity.
Information about Laser ARPES. Very high resolution (70 mueV), low temperatures T < 1.5K, bulk sensitive (100 Angstrom electron escape depth), and can change polarization easily to differentiate the different orbital contributions. The 7eV laser covers the Gamma surface, and they are developing an 8eV laser that should cover the electon surfaces too.
Laser ARPES results on Ba122 doped with K
Optimally doped: They observe three hole Fermi surfaces around the Z-point (measure kz = Z plane), with the orbital dependences: x/y, xz/yz-z^2,x^2-y^2 (from inside out). For the optimally doped sample, previous ARPES saw a gap around 10meV with a shoulder around 6-10 meV (kz = Gamma plane). They see smaller gap (3meV), and two sharp peak structures (A,B). Identify the lower energy peak, A as the SC peak, as it vanishes above Tc, but the higher energy peak B persists up to 100K, becoming very broad but not dispersing in energy, and thus is not a superconducting peak. The smaller gap magnitude at the Z point is consistent with other measurements finding the smallest gap at the Z point. Borisenko (at Gamma point) sees peak A, but not B. The FS dependence of the gap is not particularly anisotropic (4-fold anisotropy) and is the same for all three bands.
So how does the anisotropy change with doping?
KFe2As2: Transport shows line nodes for the KFe2As2 material, while SANS shows the nodes must be along the c-axis or there must be a full gap. Measuring at the Z-point, they see the three bands as before.After symmetrizing and plotting for different angles around the FS, they see that the inner band is always gapped (2meV), the middle band is sometimes gapped and sometimes not (1meV max), while the outer band is always ungapped (well, .2meV). The nodes on the middle band exist around +- 5 degrees, giving a total of 8 nodal points around the four-fold symmetric points (0,90,...). There is also a gap minima around 45 degrees. Chubukov et al have shown that the gaps can all be fit by the form \Delta_0 (1 + A cos(4 \phi) + B cos(8\phi)) with different A's and B's for each band. This observation of nodes is direct evidence for s+- over s++, and thus evidence for the spin fluctuation mechanism.
Underdoped (x = .2, .3):
They again measure the SC gap on the three surfaces, finding the inner two to be stronger than the outer, again see two peaks on both FS. They also see a kink that may correspond to the non-SC peak. As they get more underdoped, the difference between the gaps increases, the non-SC peak intensity becomes weaker and so does the kink structure. Since the gaps are different in magnitude, this implies the inter-orbital pairing is stronger than in the optimally doped sample.
Overdoped (x=.7):
There is no gap on the outer sheet, while the inner and middle sheets have near the the same gap size, which is only weakly anisotropic.
There is a clear doping dependence of the SC gap size, and a clear difference between different Fermi surfaces. The gap on the inner and middle sheets nearly corresponds to Tc, but outer does not (Inner and middle are active, outer(x2-y2) is passive), and the gap on the outer sheet vanishes abruptly at x=.55. What happens to cause such a drastic change? The electron FS at X-point vanishes. It is also composed of x^2-y^2 orbital, so intra-orbital (spin-fluctuation) pairing is important in the over-doped region.
So the picture is then that spin fluctuations are important at low and high doping, while the orbital fluctuations are important at optimally doping. This can be potentially explained by examining the dependence of the As-Fe-As angle on doping. It passes through the magic tetrahedral angle around optimal doping, which should lead to stronger orbital fluctuations - Kontani also proposes a (s+-)(s++)(s+-) type phase diagram with the angle, so it might be s++ at optimal doping.
Next he discussed the temperature dependence of the non-SC peak. It has the form of the SC gap + a temperature independent constant. Above Tc, they observe a two-kink structure that is T independent. The non-SC peak doping dependence is a dome around .4, with much weaker dependence above x = .6.
The non-SC peak has some similarities to the magnetic resonance, which also has a magnitude of around 15meV, but disappears above Tc. It also gets weaker above x = .7 and is maximal at x = .4. The doping dependence of the magnitude and intensity are similar. Likely also related to the disappearance of the electron FS at the X point. SO the non-SC peak/kink is likely related to the magnetic mode.
Open question: Why does on the the x=1 material have 8-fold symmetry?
Questions:
Fernandes - what about claims by dHvA that KFe2As2 has one band with a mass renormalizaton on the order of 10?
A - question about normal state, while this study was in the SC state.
Shibauchi comment - the heavy mass is seen near the X-point, not the Z-point.
Wen - Maximum gap now appears to be 3-4 meV, making 2\Delta/Tc only 1.3 - less than weak coupling BCS.
A - If electron FS has a larger gap, it could compensate, and most people say that it is sufficiently large.
Borosenko comment - they measure gap in Z-plane only, so limited momentum region. The gamma point is larger, on order of 10 meV.
Maiti - At x = .2, do you see isotropic gaps, even though it's within the coexistence regime?
A - Yes, slight four-fold symmetry.
Chubukov- From data alone, is there anything to distinguish between s++ and s++ at optimal doping?
A - No Fermi surface is special and there are no nodes.
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