198
J.-P. Brison
6.10 UTe 2
The last discovered p-wave superconductor is again an uranium-based system, also
orthorhombic, and again close to a ferromagnetic instability but not ferromagnetic:
UTe 2 . This time, the T SC is even more accessible: between 1.4 and 1.6 K from bulk
measurements depending on the samples [23, 24]! Moreover, it presents similar
astonishing field-reinforced superconductivity [23, 25, 26], with an absolute record
(for such a low-T SC system) of an upper critical field higher than 60 T [26]! An
interesting point concerning the possible d-vector for such a paramagnetic system
is the observation, on all samples, of a finite residual term of about half the normal
state value of the specific heat C/T . The origin of this term is still unsettled, but an
interesting proposal was that it would arise from a state similar to the A 1 state of
superfluid
3 He (see Sect. 6.8.1.3).
Naturally, this can only happen if spin–orbit coupling is weak enough (otherwise,
it would not be possible to form Cooper pairs on one Fermi surface and not on the
other), and in this case, indeed, group theory classification leads to the possibility of
such states (see Table 1 in [27])
d(k) = (1, i, 0)ϕ(k) .
(6.62)
Moreover, because this is for a weak spin–orbit case, any rotation of the d-vector is
a possible order parameter. According to (6.17), this means that the order parameter
would be simply (k) =
↑
ϕ(k), with no other component. In the case of UTe 2 , the
largest susceptibility axis is the a-axis, so the quantization axis should be along a.
In such a case, the Fermi surface with down-spin would remain unpaired, explaining
the residual specific heat term.
Another consequence of such an order parameter is that it is non-unitary, with a
finite spin for the Cooper pairs (along the a-axis). For the total system, this spin of the
Cooper pairs would be compensated by that of the unpaired electrons (from the downspin Fermi surface). This might lead to a total null magnetization. Nevertheless, in
such a case, there is no reason that the state with such a d-vector would be stabilized,
as half the condensation energy is lost compared to any other state, where pairing
occurs on Fermi sheets of each spin direction. For such a state to be favoured, one
needs some advantage of having this spin polarization in the superconducting state,
so, for example, a form of coupling between the spin Cooper pairs and the normal state
magnetization [27]. Then, this would also induce, like for superfluid
3 He in the A 1
state [28], a finite magnetization when entering the superconducting phase; globally,
it is as if the system would become ferromagnetic on entering the superconducting
state, with a (weak?) magnetization increasing linearly with temperature below T SC
[27]. Up to now, this has not been detected, and it remains to be settled if this (rather
improbable) hypothesis is valid or not.
In any case, this last system beautifully confirms that p-wave superconductors
are an incredible playground, where almost every new system brings its own share
of surprise and stimulating challenges.
J.-P. Brison
6.10 UTe 2
The last discovered p-wave superconductor is again an uranium-based system, also
orthorhombic, and again close to a ferromagnetic instability but not ferromagnetic:
UTe 2 . This time, the T SC is even more accessible: between 1.4 and 1.6 K from bulk
measurements depending on the samples [23, 24]! Moreover, it presents similar
astonishing field-reinforced superconductivity [23, 25, 26], with an absolute record
(for such a low-T SC system) of an upper critical field higher than 60 T [26]! An
interesting point concerning the possible d-vector for such a paramagnetic system
is the observation, on all samples, of a finite residual term of about half the normal
state value of the specific heat C/T . The origin of this term is still unsettled, but an
interesting proposal was that it would arise from a state similar to the A 1 state of
superfluid
3 He (see Sect. 6.8.1.3).
Naturally, this can only happen if spin–orbit coupling is weak enough (otherwise,
it would not be possible to form Cooper pairs on one Fermi surface and not on the
other), and in this case, indeed, group theory classification leads to the possibility of
such states (see Table 1 in [27])
d(k) = (1, i, 0)ϕ(k) .
(6.62)
Moreover, because this is for a weak spin–orbit case, any rotation of the d-vector is
a possible order parameter. According to (6.17), this means that the order parameter
would be simply (k) =
↑
ϕ(k), with no other component. In the case of UTe 2 , the
largest susceptibility axis is the a-axis, so the quantization axis should be along a.
In such a case, the Fermi surface with down-spin would remain unpaired, explaining
the residual specific heat term.
Another consequence of such an order parameter is that it is non-unitary, with a
finite spin for the Cooper pairs (along the a-axis). For the total system, this spin of the
Cooper pairs would be compensated by that of the unpaired electrons (from the downspin Fermi surface). This might lead to a total null magnetization. Nevertheless, in
such a case, there is no reason that the state with such a d-vector would be stabilized,
as half the condensation energy is lost compared to any other state, where pairing
occurs on Fermi sheets of each spin direction. For such a state to be favoured, one
needs some advantage of having this spin polarization in the superconducting state,
so, for example, a form of coupling between the spin Cooper pairs and the normal state
magnetization [27]. Then, this would also induce, like for superfluid
3 He in the A 1
state [28], a finite magnetization when entering the superconducting phase; globally,
it is as if the system would become ferromagnetic on entering the superconducting
state, with a (weak?) magnetization increasing linearly with temperature below T SC
[27]. Up to now, this has not been detected, and it remains to be settled if this (rather
improbable) hypothesis is valid or not.
In any case, this last system beautifully confirms that p-wave superconductors
are an incredible playground, where almost every new system brings its own share
of surprise and stimulating challenges.