Effect of Broken Time-Reversal Symmetry on the Interaction Between Two Localized Magnetic Moments in a Host Solid
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Rotation of the plane of polarization of reflected light (Kerr effect) is a direct manifestation of broken time reversal symmetry and is generally associated with the appearance of a ferromagnetic moment. Here I identify magnetic structures that may arise within the unit cell of cuprate superconductors that generate polarization rotation despite the absence of a net moment. For these magnetic symmetries the Kerr effect is mediated by magnetoelectric coupling, which can arise when antiferromagnetic order breaks inversion symmetry. The structures identifed are candidates for a time-reversal breaking phase in the pseudogap regime of the cuprates.
Pseudogap
Point reflection
Reciprocity
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We elucidate the close relationship between spontaneous time-reversal symmetry breaking and the physics of excitonic instabilities in strongly correlated multiband systems. The underlying mechanism responsible for the spontaneous breaking of time-reversal symmetry in a many-body system is closely related to the Cooper-like pairing instability of interband particle-hole pairs involving higher order symmetries. Studies of such pairing instabilites have, however, mainly focused on the mean-field aspects of the virtual exciton condensate, which ignores the presence of the underlying collective Fermi liquid excitations. We show that this relationship can be exploited to systematically derive the coupling of the condensate order-parameter to the intraband Fermi liquid particle-hole excitations. Surprisingly, we find that the static susceptibility is negative in the ordered phase when the coupling to the Fermi liquid collective excitations are included, suggesting that a uniform condensate of virtual excitons, with or without time reversal breaking, is an unstable phase at T=0.
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We show that singlet superconductivity in the Abrikosov vortex phase is absolutely unstable with respect to the appearance of a chiral triplet component of a superconducting order parameter. This chiral component ${p}_{x}+i{p}_{y}$ breaks time-reversal, parity, and spin-rotational symmetries of the internal order parameter responsible for a relative motion of two electrons in the Cooper pair. We demonstrate that the symmetry-breaking Pauli paramagnetic effects can be tuned by a magnetic-field strength and direction and can be made of the order of unity in organic and high-temperature layered superconductors.
Cooper pair
Parity (physics)
Pauli exclusion principle
T-symmetry
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We show that an isolated impurity in a spin singlet d_{x2-y2} superconductor generates a d_{xy} order parameter with locally broken time-reversal symmetry. The origin of this effect is a coupling between the d_{x2-y2} and the d_{xy} order parameter induced by spin-orbit scattering off the impurity. The signature of locally broken time-reversal symmetry is an induced orbital charge current near the impurity, which generates a localized magnetic field in the vicinity of the impurity. We present a microscopic theory for the impurity induced d_{xy} component, discuss its spatial structure as well as the pattern of induced current and local magnetic field near the localized impurity spin.
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Intermediate spin, which occurs in the theory of anyons, can also be exhibited by mesoscopic magnetic particles. The necessary broken time reversal symmetry is due to a suitably directed magnetic field. As a function of this field a system passes periodically through points which correspond to whole or half-integer spin. Intermediate spin is defined by fields which lie between these points. Since the tunnel splitting in the ground doublet vanishes for half-integer spin, this splitting becomes periodic. The doubly periodic oscillations observed in the magnetic molecular cluster Fe$_{8}$ represent the first unequivocal observation of this phenomena. Here the whole or half-integer nature of the system, i.e., the parity, is periodic for a field which is along either the easy or hard axis or a suitable combination of the two. A detailed theory is presented.
Mesoscopic physics
Parity (physics)
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Invariably, time-reversal symmetry (TRS) violation in a state of matter is identified with static magnetism in it. Here, a directional scalar spin chiral order (DSSCO) phase is introduced that disobeys this basic principle: it breaks TRS but has no density of static moments. It can be obtained by melting the spin moments in a magnetically ordered phase but retaining residual broken TRS. Orbital moments are then precluded by the spatial symmetries of the spin rotation symmetric state. It is allowed in one, two and three dimensions under different conditions of temperature and disorder. Recently, polar Kerr effect experiments in the mysterious pseudogap phase of the underdoped cuprates hinted at a strange form of broken TRS below a temperature T K, that exhibits a hysteretic 'memory effect' above T K and begs reconciliation with nuclear magnetic resonance (which sees no moments), x-ray diffraction (which finds charge ordering tendencies) and the Nernst effect (which detects nematicity). Remarkably, the DSSCO provides a phenomenological route for reconciling all these observations, and it is conceivable that it onsets at the pseudogap temperature ∼T*. A six-spin interaction mediated by enhanced fluctuations of velocity asymmetry between left- and right-movers above the onset of charge ordering in the cuprates is proposed as the driving force behind DSSCO formation. A testable prediction of the existence of the DSSCO in the cuprates is a Kerr signal above T K triggered and trainable by a current driven along one of the in-plane axes, but not by a current along the other.
Pseudogap
Nernst effect
T-symmetry
Charge ordering
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We consider the interaction of a ferromagnetic spinor Bose-Einstein condensate with a magnetic field gradient. The magnetic field gradient realizes a spin-position coupling that explicitly breaks time-reversal symmetry T and space parity P, but preserves the combined PT symmetry. We observe using numerical simulations, a first-order phase transition spontaneously breaking this re-maining symmetry. The transition to a low-gradient phase, in which gradient effects are frozen out by the ferromagnetic interaction, suggests the possibility of high-coherence magnetic sensors unaffected by gradient dephasing.
Dephasing
T-symmetry
Diamagnetism
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We present a theory of orbital magnetic dynamics for a chiral p-wave superconductor with broken time-reversal symmetry. In contrast to the common Landau-Lifshitz theory for spin ferromagnets, the case of orbital magnetism cannot be described in terms of local magnetization density. Hence it is impossible to define unambiguously the spontaneous magnetic moment: the latter would depend on conditions of its experimental investigation. As an example of this we consider orbital magnetization waves and the domain structure energy.
Magnetism
Orbital magnetization
Spin wave
T-symmetry
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We study the boundary Majorana modes for the single component p-wave weak topological superconductors or superfluids, which form zero energy flat bands protected by time-reversal symmetry in the orbital channel. However, due to the divergence of density of states, the band flatness of the edge Majorana modes is unstable under spontaneously generated spatial variations of Cooper pairing phases. Staggered current loops appear near the boundary and thus time-reversal symmetry is spontaneously broken in the orbital channel. This effect can appear in both condensed matter and ultra-cold atom systems.
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Phase transitions involving spontaneous time-reversal symmetry breaking are studied on the honeycomb lattice at finite hole doping with next-nearest-neighbor repulsion. We derive an exact expression for the mean-field equation of state in closed form, valid at temperatures much less than the Fermi energy. Contrary to standard expectations, we find that thermally induced intraband particle-hole excitations can create and stabilize a uniform metallic phase with broken time-reversal symmetry as the temperature is raised in a region where the ground state is a trivial metal.
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Honeycomb
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