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Axion Quasiparticles for Axion Dark Matter Detection

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Axion Quasiparticles for Axion Dark Matter Detection Prepared for submission to JCAP Axion Quasiparticles for Axion Dark Matter Detection Jan Sch¨utte-Engel,a,b,c David J. E. Marsh,d Alexander J. Millar,e,f Akihiko Sekine,g Francesca Chadha-Day,h Sebastian Hoof,d Mazhar N. Ali,i,j Kin Chung Fong,k Edward Hardy,l and Libor Smejkalˇ m,n aDepartment of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.A. bIllinois Center for Advanced Studies of the Universe,University of Illinois at Urbana- Champaign, Urbana, IL 61801, U.S.A. cHamburg University, 22761 Hamburg, Germany dInstitut f¨urAstrophysik, Georg-August-Universit¨atG¨ottingen,Friedrich-Hund-Platz 1, 37077 G¨ottingen,Germany eThe Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, AlbaNova, 10691 Stockholm, Sweden f Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstulls- backen 23, 10691 Stockholm, Sweden gRIKEN Center for Emergent Matter Science, Wako, Saitama 351-0198, Japan hDepartment of Physics, University of Durham, South Rd, Durham DH1 3LE, United Kingdom iMax Planck Institute of Microstructure Physics, Weinberg 2, 06120 Halle — Germany jKavli Institute of Nanoscience, Delft University of Technology, Delft, Netherlands kRaytheon BBN Technologies, Quantum Engineering and Computing, arXiv:2102.05366v2 [hep-ph] 6 Sep 2021 Cambridge, Massachusetts 02138, USA lMathematical Sciences, The University of Liverpool, Liverpool, L69 7ZL, United Kingdom mInstitut f¨urPhysik, Johannes Gutenberg Universit¨atMainz, 55128 Mainz, Germany nInstitute of Physics, Czech Academy of Sciences, Cukrovarnick´a10, 162 00, Praha 6, Czech Republic E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Abstract. It has been suggested that certain antiferromagnetic topological insulators contain axion quasiparticles (AQs), and that such materials could be used to detect axion dark matter (DM). The AQ is a longitudinal antiferromagnetic spin fluctuation coupled to the electromagnetic Chern-Simons term, which, in the presence of an applied magnetic field, leads to mass mixing between the AQ and the electric field. The electro- magnetic boundary conditions and transmission and reflection coefficients are computed. A model for including losses into this system is presented, and the resulting linewidth is computed. It is shown how transmission spectroscopy can be used to measure the resonant frequencies and damping coefficients of the material, and demonstrate conclu- sively the existence of the AQ. The dispersion relation and boundary conditions permit resonant conversion of axion DM into THz photons in a material volume that is inde- pendent of the resonant frequency, which is tuneable via an applied magnetic field. A parameter study for axion DM detection is performed, computing boost amplitudes and bandwidths using realistic material properties including loss. The proposal could allow for detection of axion DM in the mass range between 1 and 10 meV using current and near future technology. Preprints: IPPP/20/78, NORDITA-2021-007 Contents 1 Introduction1 2 Axion Quasiparticle Materials4 2.1 General Remarks4 2.2 Realisation in Dirac Quasiparticle Antiferromagnets4 2.2.1 Symmetry criteria for static and dynamical magnetic axion insulators5 2.2.2 Material candidates9 2.2.3 Dirac model of axion quasiparticles 11 2.3 AQ as Longitudinal Magnon 15 2.4 Parameter Estimation 17 2.5 Damping and Losses 20 2.5.1 Resistivity and the Dielectric Function 20 2.5.2 Magnon Losses 22 3 Discovering the Axion Quasiparticle 28 3.1 Axion Electrodynamics and Boundary Conditions 28 3.1.1 General formulation 29 3.1.2 One dimensional model 31 3.1.3 Linearization 31 3.1.4 Losses 33 3.2 Transmission and Reflection Coefficients 33 3.2.1 Solution of linearized equations 34 3.2.2 Matrix formalism for many interfaces 39 3.2.3 Layer of topological magnetic insulator 40 4 Axion Dark Matter and Axion Quasiparticles 47 4.1 Dark axion, axion quasiparticle and photon mixing 47 4.1.1 General formulation 47 4.1.2 Linearized one-dimensional model 48 4.2 Dark matter signal calculation 49 4.2.1 Solution of the one-dimensional model 50 4.2.2 Matrix formalism 51 4.2.3 Layer of topological insulator 52 5 Dark Matter Discovery Potential 61 5.1 Scanning range 61 5.2 Detectors for THz Radiation 62 5.3 Experimental Sensitivity and Forecasts 65 5.3.1 Sensitivity 66 5.3.2 Scanning Strategies 68 5.4 Parameter Study 71 – i – 6 Discussion and Conclusions 73 6.1 Summary of Results 73 6.2 Discussion 76 A Antiferromagnetic Resonance and Magnons for Particle Physicists 78 A.1 Effective Field Theory of AFMR 78 A.1.1 AFMR in Cartesian Coordinates 79 A.1.2 AFMR in Polar Coordinates 82 A.1.3 Longitudinal Spin Waves in the Heisenberg Model 83 A.2 The Landau-Lifshitz Equations 85 B Axion Dark Matter and the Millielectronvolt Range 87 C Comparison to earlier results 89 1 Introduction The quantum chromodynamics (QCD) axion [1–3] solves the charge-parity (CP) problem of the strong nuclear force [4–6], and is a plausible candidate [7–9] to compose the dark matter (DM) in the cosmos [10]. The axion mass is bounded from above [11– 13] and below [14, 15] by astrophysical constraints (for reviews, see Refs. [16–19], and AppendixB), placing it in the range 1 peV . ma . 20 meV . (1.1) The local DM density is known from stellar motions in the Milky Way [20]. As- suming axions comprise all the (local) DM, the axion number density is given by na = ρloc/ma. Due to the very small axion mass, the number density is very large and axions can be modelled as a coherent classical field, φ. The field value is: φ = Φ cos(mat) , (1.2) √ where Φ is Rayleigh-distributed [21, 22] with mean 2ρloc/ma and linewidth ∆ω/ω ∼ 6 10− given by the Maxwell-Boltzmann distribution of axion velocities around the local galactic circular speed, vloc ≈ 200 km/s (see e.g. refs. [21, 23]). Axions couple to electromagnetism via the interaction L = gaγφE · B. Thus, in the presence of an applied magnetic field, B0, the DM axion field in Eq. (1.2) acts as a source for the electric field, E. This is the inverse Primakoff process for axions, and leads to axion-photon conversion in a magnetic field. The rate of axion-photon conversion de- pends on the unknown value of the coupling gaγ and happens at an unknown frequency ω = ma ± ∆ω. For the QCD axion (as opposed to a generic “axion like particle” [16]) the mass and coupling are linearly related, gaγ ∝ ma, although different models for the Peccei-Quinn [1] charges of fundamental fermions predict different values for the con- stant of proportionality. The two historical reference models of Kim-Shifman-Vainshtein- Zhakarov (KSVZ) [24, 25] and Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) [26, 27] span – 1 – a narrow range, while more recent generalisations with non-minimal particle content allow for more variation [19, 28, 29]. The axion-photon coupling gaγ is constrained by a large number of null-results from experimental searches and astrophysical considerations [20]. For experimentally allowed values of (ma, gaγ), and accessible magnetic field strengths, the photon production rate in vacuum is unobservably small. The power can be increased in two basic ways. If the conversion happens along the surface of a magnetized mirror, then the produced photons can be focused onto a detector [30]. This approach is broadband, and does not depend on the axion mass. Reaching sensitivity to the QCD axion requires very large mirrors, very sensitive detectors, and control over environmental noise. Alternatively, the signal can be resonantly or coherently enhanced (e.g. Refs. [31, 31–40]). These approaches are narrow band, and require tuning to the unknown DM axion frequency. Depending on the model of early Universe cosmology, and the evolution of the ax- ion field at high temperatures T 1 MeV, the entire allowed mass range Eq. (1.1) can plausibly explain the observed DM abundance. The mass range near 1 meV (correspond- ing to frequencies in the low THz) is favoured in some models of axion cosmology (see AppendixB), but is challenging experimentally due to the lack of large volume, tuneable THz resonators, and efficient, low-noise, large bandwidth THz detectors. In Ref. [41] (Paper I) we proposed an experimental scheme to detect axion DM using axion-quasiparticle (AQ) materials based on topological magnetic insulators (TMIs) [42], a proposal we called “TOORAD” for “TOpolOgical Resonant Axion Detection”. Since Li et al. [42] first proposed to realise axion quasiparticles in the antiferromagnetic topolog- ical insulator (AF-TI) Fe-doped Bismuth Selenide, (Bi1 xFex)2Se3, the quest to realise − related materials in the lab has picked up incredible pace. A currently favoured candi- date Mn2Bi2Te5 [43], is, however, yet to be fabricated successfully. AQ materials allow the possibility to explore aspects of axion physics in the laboratory [44]. The AQ res- onance hyrbidises with the electric field forming an axion-polariton [42]. The polariton frequency is of order the AF anisotropy field, with typical values O(1 meV), and is tune- able with applied static field B [41]. This proposal opens the possibility for large volume THz resonance, easily tuneable with an applied magnetic field, thus overcoming the first hurdle to detection of meV axions. The proposal makes use of the current interest in manufacture of low noise, high efficiency single photon detectors (SPDs) in THz [45]. The development of such detectors has benefits for sub mm astronomy and cosmology, as well as application to other DM direct detection experiments [30].
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