BECK, C

EPS Conference on High Energy Physics, Venice 2017

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Possible resonance effect of dark matter axions inSNS Josephson junctionsChristian Beck∗School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UKE-mail: c.beck@qmul.ac.ukDark matter axions can generate peculiar effects in special types of Josephson junctions, so-calledSNS junctions. One can show that the axion field equations in a Josephson environment allowfor very small oscillating supercurrents, which manifest themselves as a tiny wiggle in the I-Vcurve, a so-called Shapiro step, which occurs at a frequency given by the axion mass. The effectis very small but perfectly measurable in modern nanotechnological devices. In this paper I willsummarize the theory and then present evidence that candidate Shapiro steps of this type haveindeed been seen in several independent condensed matter experiments. Assuming the observedtiny Shapiro steps are due to axion flow then these data point to an axion mass of (106±6)µeV,consistent with what is expected for the QCD axion. In addition to the above small Shapiroresonance effects at frequencies in the GHz region one also expects to see broad-band noiseeffects at much lower frequencies. Overall this approach provides a novel pathway for the futuredesign of new types of axionic dark matter detectors. The resonant Josephson data summarizedin this paper are consistent with a ’vanilla’ axion with a coupling constant fa =√vEW mPl =5.48 ·1010GeV given by the geometric average of the electroweak symmetry breaking scale vEWand the Planck mass mPl .The European Physical Society Conference on High Energy Physics5-12 July, 2017Venice∗Speaker.c© Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/arXiv:1710.04299v1  [hep-ph]  11 Oct 2017Possible resonance effect of dark matter axions in SNS Josephson junctions Christian Beck1. IntroductionBesides WIMPs, the QCD axion is one of the leading candidates to account for dark matterin the universe [1]–[25]. In recent years some new experimental techniques have been proposed todetect the axion in new types of laboratory experiments on the Earth [1, 2, 14, 16, 17, 18, 20, 21, 22].One of these detection ideas is based on resonance effects in special types of Josephson junctiondevices. In this paper I will summarize the most important results based on the idea that so-calledSNS Josephson junctions could be highly effective axion detectors[1, 2]. I will briefly discuss the’axionic Josephson effect’ that underlies this proposal and then come to experimental consequencesand observations. Remarkably, out of this approach comes a concrete prediction of the axion mass,taking into account observed resonance effects that were seen in experiments done by variouscondensed matter groups in the recent past (and that were re-interpreted in terms of axion physicsin [1, 2]): If these data are produced by axions then the axion mass must be in the region 100...112µeV. This gives future axion haloscope experiments (e.g. [23, 24, 25]) a powerful suggestion ofwhere to start the search and where one might ultimately be successful in finding the QCD axion.The prediction that the QCD axion mass could be in this region was published for the first timein 2013 in [1], at a time where most people thought the axion mass would be smaller (in the rangeof a few µeV as searched for by the ADMX experiment at that time). Later, in 2015 Kawasaki etal. [11] obtained a prediction consistent with the above region (their 2015 paper quotes the result60µeV < mac2 < 150 µeV ). Their numerical method is based on a completely different method,namely estimating the production rate of axions from simulations of domain walls and strings andcomparing with the measured abundance of dark matter, assuming all of dark matter is made up ofaxions. The recent lattice simulations of Borsanyi et al. [9] confirmed this rather large value of theaxion mass (they quote 50...1500µeV), and also theoretical models such as the so-called SMASHmodel [10] advocate an axion mass of around 50...200µeV. On the other hand, axionic string anddomain wall simulations are very complicated and a modified numerical method [13] taking intoaccount large string tensions very recently yielded a somewhat different result than [11], with atendency that axion production from strings and walls is somewhat less efficient, thus in principleallowing for a smaller axion mass, assuming that all of dark matter is axions.In the following we give a brief summary of the most important theoretical results of [1, 2]and then come to experimental predictions, in particular we give an update on the axion massprediction, taking into account further data from other condensed matter experiments in additionto the single experiment discussed in [1]. The prediction we arrive at by taking the average of 5independent condensed matter experiments [1, 2, 26, 27, 28, 29, 30] ismac2 = (106±6)µeV. (1.1)2. The axionic Josephson effectLet us first recall some basic facts about Josephson junctions which are needed in the fol-lowing. A Josephson junction consists of two superconductors separated by a weak-link region.The weak link-region is an insulator for tunnel junctions and a normal metal for so-called SNSjunctions. The distance between the superconducting plates is d ∼ 1nm for tunnel junctions,1Possible resonance effect of dark matter axions in SNS Josephson junctions Christian Beckand about d ∼ 1µm for SNS junctions. If a DC voltage V is applied then a Josephson junctionemits Josephson radiation of frequency h̄ωJ = 2eV . In this case the phase difference δ (t) of themacroscopic wave functions describing the ’left’ and ’right’ superconductor grows linearly in time:δ := ΦL−ΦR ∼ ωJt. A Josephson junction in that state was proposed as an axion detector in [1],provided the Josephson frequency ωJ resonates with the axion mass.The field equations of axions passing through a Josephson environment are [2]θ̈ +Γθ̇ − c2∇2θ + m2ac4h̄2sinθ = −gγ4π21f 2ac3e2~E~B (2.1)∇×~B− 1c2∂~E∂ t= µ0~j+gγπα1c~E×∇θ −gγπα1c~Bθ̇ (2.2)∇~E =ρε0+gγπαc~B∇θ (2.3)δ̈ +1RCδ̇ +2eIch̄Csinδ =2eh̄CI (2.4)Pa→γ =116βa(gγ Bec L)21π3 f 2a1α(sin qL2h̄qL2h̄)2, (2.5)where ma is the axion mass, fa is the axion coupling constant, βa = va/c is the axion velocity, ~E isthe electric field, ~B is the magnetic field, gγ =−0.97 for KSVZ axions, respectively gγ = 0.36 forDFSZ axions, q is the momentum transfer, Pa→γ is the probability of axion decay, Ic is the criticalcurrent of junction, and α ≈ 1/137 is the fine structure constant.These equations were carefully analysed in [2]. Interestingly, they have a nontrivial solution(besides the trivial solution where the axion does not interact with the Josephson environment atall): For the nontrivial solution, inside the weak link area, the Josephson phase angle δ synchro-nizes with the axion misalignment angle θ , self-inducing a formal surface magnetic field whichmakes incoming axions decay (but which can also re-create them when leaving the weak link, i.e.there is a tunneling process). Microscopically, for SNS junctions this can be interpreted in termsof an axion– Andreev pair interaction, as sketched in Fig. 1: Tunneling axions trigger additionalCooper pair transport that would not be there if there were no axions passing through the junction.Much more details on this can be found in [1, 2].Fig. 1. Microscopic model of whathappens in an SNS junction. An axiontunnels through the junction and trig-gers (by multiple Andreev reflections)the transport of n Cooper pairs (heren = 3). Picture from [1].2Possible resonance effect of dark matter axions in SNS Josephson junctions Christian BeckThe result of a longer calculation in [2] based on eqs.(2.1)-(2.5) is that galactic axion flowthrough the junction is expected to induce a small oscillating supercurrent in the junction given byIa(t) =√ρavahαw ·2e · cos(ωat), (2.6)where ρa is the axion energy density surrounding the Earth, va is the axion velocity, w is the widthof the Josephson junction, h = 2π h̄. Note that the final result (2.6) is independent of fa, gγ andΓ, which drop out of the equations when the calculations are done. This axion-induced currentproduces a Shapiro step (a tiny step (or wiggle)) in the I-V curve that occurs at a voltage Va wherethe Josephson frequency ωJ coincides with the axion mass ma:h̄ωJ = 2eVa = mac2 = h̄ωa. (2.7)Observing such a wiggle (and excluding any other cause of it) one can thus determine theaxion mass. And, making further assumptions on the number of Andreev reflections involved inFig. 1, one can conclude from the wiggle intensity onto the product of axion density ρa and axionvelocity va, though there are large theoretical model uncertainties in this last step, depending onthe microscopic model used. Overall, the effect of axion flow is mathematically similar to theexistence of a second Josephson junction in addition to the measuring one, with a formal criticalcurrent Iac =√ρavahα w ·2e, interacting in a SQUID-like configuration. Putting in realistic values forρa, va, and w one notices that the expected effect from galactic axion flow is a small but perfectlymeasurable effect: Iac ∼ 10−8A. In addition, there are also broad-band 1/ f noise effects from axionflow at very low frequencies, see [22] for more details of that aspect.3. Candidate axion signalsA small measured peak of unknown origin observed at voltage Va ≈ 55µV by Hoffmann etal. [26] was used in [1] to conclude onto an axion mass of about mac2 ≈ 110µeV and an axiondensity of the order of magnitude ρa ∼ 10−1GeV/cm3, the latter number being just a rough order-of-magnitude estimate obtained for an assumed velocity of 2.3 ·105 m/s (the velocity of the Earthrelative to the axion background). This was the very first estimate of this kind. In subsequentwork [2] it became clear that several other experiments done with various other types of Josephsonjunctions also saw unexplained anomalies at a similar voltage. These Shapiro-step like featureswere observed at the following voltages (for details, see [2]):• Hoffmann et al. [26] Va = (55±1)µV• Golikova et al. [27] Va = (52±5)µV• He et al. [28] Va = (53±3)µV• Bae et al. [29] Va = (55±1)µVTo this list one could also add a paper by Bretheau et al.[30] who observe an anomalous currentpeak at3Possible resonance effect of dark matter axions in SNS Josephson junctions Christian Beck• Bretheau et al. [30] Va = (50±3)µVThe size of the observed peak (∼ 10−8A) is again consistent with an axion density surroundingthe Earth of about∼ 10−1GeV/cm3 (about a quarter of the expected dark matter density in the halo),again with large theoretical uncertainties. Of course we should mention at this stage that we cannotexclude other causes of the observed anomalies in the above-mentioned Josephson experiments,but assuming they are due to axion flow then the observed peak positions in the 5 independentexperiments point quite robustly to an axion mass ofmac2 = 2eVa = (106±6)µeV. (3.1)The above value is obtained by taking the average over the above 5 condensed matter experiments,with equal weighting to each experimental group, and using a conservative estimate of statisticaland systematic errors that are expected to occur in these types of experiments. Our suggestion isthat future axion haloscope experiments, such as ORPHEUS [23], MADMAX [24] or ORGAN[25], which are of course extremely important since they are not based on the assumption of thevalidity of the axionic Josephson effect, should start their search in the mass region (3.1), which ismost promising. This suggestion has been taken up in [25].4. A theoretical prediction for a ‘vanilla’ axionThe above results leading to Eq. (3.1) are purely experimental. They need to be confirmed infuture experiments that are performed under controlled conditions, i.e. being totally shielded fromany potentially disturbing electromagnetic radiation, and checking for a possible yearly modulationof the signal, as suggested in [1]. But can we give a theoretical prediction of the QCD axion massvalue? Not really, but at least we can be inspired by some numerical observation. The QCD axionmass is given by [8]mac2 = 57.0(7)µeV ·1011GeVfa(4.1)where fa is the symmetry breaking scale of Peccei Quinn symmetry. Now the QCD axion really isrelevant for all types of interactions, it solves the strong CP problem for QCD, it can interact withelectromagnetic fields via the term ~E~B and thus knows electroweak interactions, and it has gravi-tational effects as dark matter. This motivates us to define a ’vanilla’ axion (i.e. a most plausibleaxion) as having a Peccei Quinn symmetry breaking scale fa that is the geometric average of thetwo most important symmetry breaking scales we know about, electroweak symmetry breaking atvEW = 246 GeV and Planck scale symmetry breaking at mPl = 1.221 · 1019 GeV. This means thevanilla axion is defined as having the coupling constantfa =√vEW mPl = 5.48 ·1010GeV (4.2)(based on a seesaw mechanism of the two most important symmetry breaking scales in nature) andconsequently, by combining eq. (4.1) and (4.2), its mass is theoretically predicted asmac2 = (104.0±1.3)µeV. (4.3)The 5 independent measurements of mac2 = 2eVa seen in the Josephson junction experiments aboveseem to indicate that the QCD axion could be of vanilla type.4Possible resonance effect of dark matter axions in SNS Josephson junctions Christian BeckReferences[1] C. Beck, Phys. Rev. Lett. 111, 231801 (2013) [arXiv:1309.3790][2] C. Beck, Phys. Dark Univ. 7-8, 6 (2015) (open access) [arXiv:1403.5676][3] S. Weinberg, Phys. Rev. Lett. 40, 223 (1978)[4] F. Wilczek, Phys. Rev. Lett. 40, 279 (1978)[5] R.D. Peccei, H. Quinn, Phys. Rev. Lett. 38, 1440 (1977)[6] O. Wantz, E.P.S. Shellard, Phys. Rev. D 82, 123508 (2010) [arXiv:0910.1066][7] X. Liang, A. Zhitnitsky, Phys. Rev. D 94, 083502 (2016) [arXiv:1606.00435][8] G. Grilli di Cortona, E. Hardy, J. Pardo Vega and G. Villadoro, JHEP 1601, 034 (2016)[arXiv:1511.02867][9] S. Borsany et al., Nature 539, no. 7627, 69 (2016) [arXiv:1606.07494][10] G. Ballesteros, J. 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Possible resonance effect of dark matter axions in SNS Josephson junctions

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Possible resonance effect of dark matter axions in SNS Josephson junctions

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