Permanent Current now Proven due to noncommutativity! Permanent current from non-commutative spin algebra

 The key here is the non-commutativity of the SU(2) spin algebra, which breaks the time-reversal
symmetry, and leads, in the presence of electron coherence, to a permanent electron current.

https://arxiv.org/pdf/cond-mat/0208377.pdf 

 Due to the non-commutativity of σi, the amplitude depends on the order of the scattering
event; A(n1)A(n2) 6 = A(n2)A(n1) in general. Various features in spin transport, which is
under intensive pursuit recently [9, 10], arise from this non-commutativity. It, however, does
not affect the charge transport, since the charge is given as a sum of the two spin components
(denoted by tr), and tr[A(n1)A(n2)] − tr[A(n2)A(n1)] = 0. Anomaly in the charge transport
arises at the third order. 

the symmetry under time-
reversal (more appropriately, reversal of motion) is generally broken in the charge transport.
In fact, relation (2) indicates that the contribution from one path, x→X1→X2→X3→x
(Fig.1a), and its (time-) reversed one, x→X3→X2→X1→x (Fig.1b), are not equal, and this
difference results in a spontaneous electron motion in a direction specified by the sign of
C123, namely, a permanent current. What is essential here is the non-commutativity of the
SU(2) algebra

 Tatara, G., & Mizukami, S. (2017). Consistent microscopic analysis of spin pumping effects. Physical Review B, 96(6). doi:10.1103/physrevb.96.064423

The spin pumping
effect, spin Berry’s phase, and the spin motive force have the
same physical root, namely, the noncommutative spin algebra.

The essence of the spin pumping effect is therefore the
noncommutativity of spin operators. The above picture in the
perturbative regime naturally leads to the effective gauge field
picture in the strong-coupling limit [6].
The same scenario applies for cases of spatial variation of
spin, and an equilibrium spin current proportional to n × ∇i n
emerges, where i denotes the direction of spatial variation [7].
The spin pumping effect is therefore the time analog of the
equilibrium spin current induced by vector spin chirality.
Moreover, a charge current emerges from the third-order
process from the identity [6]