Relationship of time-reversal symmetry breaking to optical Kerr rotation

Abstract

We prove an instance of the Reciprocity Theorem that demonstrates that Kerr rotation, also known as the magneto-optical Kerr effect, may only arise in materials that break microscopic time reversal symmetry. This argument applies in the linear response regime, and only fails for nonlinear effects. Recent measurements with a modified Sagnac Interferometer have found finite Kerr rotation in a variety of superconductors. The Sagnac Interferometer is a probe for nonreciprocity, so it must be that time reversal symmetry is broken in these materials.

Necessity of Time-Reversal Symmetry Breaking for the Polar Kerr Effect in Linear Response

“…The significance of Onsager symmetry has been reemphasized in a number of recent papers [25][26][27][28]. This has led to the retraction [29][30][31] of the proposals that various measured Kerr signals are due to optical activity alone.…”

Optical gyrotropy and the nonlocal Hall effect in chiral charge-orderedTiSe2

“…The gyrotropy is evidenced by a nonlocal Hall effect, and gives rise to nonzero optical rotary power (i.e., a Faraday effect at zero magnetic field). Although there cannot be a related nonzero Kerr effect in the presence of time reversal * m.gradhand@bristol.ac.uk † vanwezel@uva.nl symmetry [5][6][7], we argue that the presented results indicate that 1T -TiSe 2 can be used as a model system to investigate the relation between the presence of chiral charge order and the observed optical activity of high-temperature superconductors.…”

“…It was recently pointed out, however, that the expression used to calculate the Kerr response [26] is incomplete, as it ignores the variation of gyrotropy at the sample interface [5][6][7][8]. Taking into account these boundary effects, the linear Kerr effect is always identically zero in time reversal symmetric materials under equilibrium conditions.…”

“…The measurement of a Kerr effect in the pseudogap phase of several high-temperature superconductors constrains the symmetries that this state may exhibit [1][2][3][4]. Although the particular experimental setup used in these studies allows for a nonzero linear response to arise under equilibrium conditions only in the presence of broken time reversal symmetry [5][6][7][8][9], it has been argued that the observed optical activity may nonetheless be fundamentally linked to a breakdown of spatial inversion symmetry, related to the presence of charge order [8]. That it is possible for a chargeordered state to spontaneously break inversion symmetry even in the absence of magnetism or electrostatic polarization, has only recently become clear, with the discovery of chiral charge order in the low-temperature phase of 1T -TiSe 2 [10][11][12][13][14][15].…”

Calculation for polar Kerr effect in high-temperature cuprate superconductors

“…To account for these puzzling experimental observations, time-reversal invariant models with gyrotropic order were employed recently [19][20][21][22] . However, the concept of gyrotropic order as an explanation for non-zero PKE in the cuprates were subsequently retracted [23][24][25] because it does not satisfy Onsager's reciprocity principle in normal reflection that forbids a non-zero PKE in the absence of TRS breaking [26][27][28][29] .…”