Silicon carbide detectors for sub-GeV dark matter

We propose the use of silicon carbide (SiC) for direct detection of sub-GeV dark matter. SiC has properties similar to both silicon and diamond but has two key advantages: (i) it is a polar semiconductor which allows sensitivity to a broader range of dark matter candidates; and (ii) it exists in many stable polymorphs with varying physical properties and hence has tunable sensitivity to various dark matter models. We show that SiC is an excellent target to search for electron, nuclear and phonon excitations from scattering of dark matter down to 10 keV in mass, as well as for absorption processes of dark matter down to 10 meV in mass. Combined with its widespread use as an alternative to silicon in other detector technologies and its availability compared to diamond, our results demonstrate that SiC holds much promise as a novel dark matter detector.

Figure 1

Crystal structures of the polytypes of SiC considered in this work. Si atoms are blue and C atoms are brown.

Figure 2

(a)–(f) Calculated electronic band structures of SiC polytypes, with high-symmetry paths selected using SeeK-path [24], alongside the density of states. Valence band maxima and conduction band minima are highlighted with blue and pink circles, respectively. To show the conduction band valleys in momentum space, (g)–(l) are isosurfaces of the electronic energy bands at 0.2 eV above the conduction band minima, plotted within the first Brillouin zone boundaries of the polytypes. For the positions of the high-symmetry points, see Fig. 11, and for details of calculations, see Appendix pp1.

Figure 3

First-principles calculations of phonon band structures, with high-symmetry paths selected using SeeK-path [24]. For details of calculations, see Appendix pp1.

Figure 4

Left: The dependence of energy resolution on fractional surface area covered by sensors ($f_{\mathrm{abs}}$) is shown for each of the designs from Table 3. Dots indicate the resolutions quoted in the table. For designs C and D, the resolution is the same in the small $f_{\mathrm{abs}}$ limit or where there are five or fewer sensors; in this limit, all sensors are assumed necessary to reconstruct events. Meanwhile, for larger $f_{\mathrm{abs}}$, the improved scaling of design D over design C results from the fixed number of sensors read out (here taken to be five) as the detector bandwidth is increased. Also shown are devices with the current best demonstrated noise power and resolution. The TES and SNSPD benchmarks come from Refs. [14, 73], where the shaded band corresponds to the detectors listed in Ref. [73], and the lines correspond to best DM detector performance from the respective references. We also include two superconducting photon detectors optimized for high detection efficiency for THz photons, where the best demonstrated NEP, roughly ${10}^{-20}\mathrm{W}/\sqrt{\mathrm{Hz}}$ in both cases, is comparable to the NEP assumed for designs C and D. The quantum capacitance detector (QCD) is from Ref. [72], and the SNS junction is from Ref. [71]. Right: The relative change in resolution as polytype and interface transmission are changed for a range of (surface-limited) phonon lifetimes, compared to the nominal, impedance-matched 3C/Al design at the chosen phonon lifetime. The resolutions of these devices are best-case scenarios for perfect phonon detection efficiency and thus represent a lower resolution limit for the given technology.

Figure 5

Reach and daily modulation for DM interactions mediated by a scalar coupling to nucleons, assuming a massive mediator. Left: All reach curves are obtained assuming kg-year exposure and zero background, and we show the 90% C.L. expected limits (corresponding to 2.4 signal events). For single-phonon excitations relevant for $m_{\chi }\lesssim 10\mathrm{MeV}$, we show two representative thresholds of 1 (solid lines) and 80 meV (dotted) for the different SiC polytypes. We also show the reach for a superfluid He target [19]. The dashed lines show sensitivity to nuclear recoils assuming threshold of 0.5 eV. In the shaded region, it is expected that the dominant DM scattering is via multiphonons (see discussion in Refs. [79, 80]). Right: The daily modulation of the DM-phonon scattering rate as a function of DM mass, where the quantity shown corresponds exactly to the modulation amplitude for a purely harmonic oscillation. The modulation is much smaller for scattering into acoustic phonons $\omega >1\mathrm{meV}$, so we only show scattering into optical phonons with $\omega >80\mathrm{meV}$. The modulation amplitude is generally largest for 2H and smallest for 3C. The inset compares the phase of the modulation among the polymorphs for $m_{\chi }=80\mathrm{keV}$.

Figure 6

Similar to Fig. 5, but for DM interactions mediated by a massless scalar coupling to nucleons. In this case, we also compare with the reach of another polar material, GaAs, for acoustic and optical branch thresholds [17].

Figure 7

The 90% C.L. expected limits into DM-electron scattering parameter space for $1\mathrm{kg}\text{−}\mathrm{year}$ of exposure of select polytypes of SiC for heavy (left) and light (right) mediators. For comparison, we also show the reach of Si and diamond, assuming a threshold of one electron or energy sensitivity down to the direct band gap in the given material. The reach of Si given a two-electron threshold is shown for comparison, for the case that charge leakage substantially limits the reach at one electron. Relic density targets from Ref. [1] are shown as thick blue lines for the freeze-in and freeze-out scenarios, respectively. The gray shaded region includes current limits from SENSEI [88], SuperCDMS HVeV [89], DAMIC [49], Xenon10 [90], Darkside [91], and Xenon1T [93].

Figure 8

Reach and daily modulation for DM-phonon interactions mediated by a massless dark photon. Left: The 90% C.L. expected limits assuming kg-year exposure and zero background (corresponding to 2.4 signal events). The reach from single optical phonon excitations in SiC (solid lines) is similar for all the polytypes, while the dotted lines in the same colors are the electron-recoil reach from Fig. 7. The thick solid blue line is the predicted cross sections if all of the DM is produced by freeze-in interactions [3, 96], and the shaded regions are constraints from stellar emission [94, 95] and Xenon10 [90]. We also show the reach from phonon excitations in other polar materials, GaAs and ${\mathrm{Al}}_2{\mathrm{O}}_3$ [16, 17], and from electron excitations in an aluminum superconductor [12] and in Dirac materials, shown here for the examples of ${\mathrm{ZrTe}}_5$ and a material with a gap of $\mathrm{\Delta }=2.5\mathrm{meV}$ [15]. (For clarity, across all materials, all electron-recoil curves are dotted and all phonon excitation curves are solid.) Right: The daily modulation of the DM-phonon scattering rate as a function of DM mass, where the quantity shown corresponds exactly to the modulation amplitude for a purely harmonic oscillation. The modulation is negligible in the 3C polytype due to its high symmetry and is largest in 2H. The inset compares the phase of the modulation among the polytypes for $m_{\chi }=80\mathrm{keV}$.

Figure 9

Absorption of kinetically mixed dark photons (left) and axionlike particles (right). Left: Projected reach at 95% C.L. for absorption of kinetically mixed dark photons. The expected reach for a kg-year exposure of SiC is shown by the solid and dashed black curves (using the data of Ref. [83] and strongest phonon branch, respectively). Projected reach for germanium and silicon [82], diamond [7], Dirac materials [15], polar crystals [17], molecules [100], superconducting aluminum [13] and WSi nanowire [14] targets are indicated by the dotted curves. Constraints from stellar emission [101, 102], DAMIC [103], SuperCDMS [104], Xenon [102] data and a WSi nanowire [14] are shown by the shaded orange, green, purple, light blue and blue regions, respectively. Right: Projected reach at 95% C.L. for absorption of axionlike particles. The reach of a kg-year exposure of SiC is shown by the solid black curve, where only excitations above the band gap are assumed. The reach for semiconductors such as germanium and silicon [82], diamond [7] and superconducting aluminum [13] targets is depicted by the dotted curves. Stellar constraints from Xenon100 [105], LUX [76] and PandaX-II [106] data and white dwarfs [107] are shown by the shaded red and orange regions. Constraints arising from (model-dependent) loop-induced couplings to photons are indicated by the shaded blue regions [108, 109], while the QCD axion region is given in shaded gray.

Figure 10

An incident longitudinal (L) acoustic wave is both reflected and refracted into longitudinal and transverse (SV) modes in the two media. The various angles here satisfy geometric-optical relations such as law of reflection and Snell’s law. Reproduced from [129].

Figure 11

Brillouin zones and high-symmetry points for the polytypes of SiC. (a) Face-centered cubic type for the 3C polytype. (b) Primitive hexagonal type for the 2H, 4H, 6H and 8H polytypes. (c) Rhombohedral hexagonal type for the 15R polytype.