Mass fluctuations and absorption rates in dark-matter sensors based on Dirac materials

We study the mass fluctuations in gapped Dirac materials by treating the mass term as both a continuous and discrete random variable. Gapped Dirac materials were proposed to be used as materials for dark-matter sensors. One thus would need to estimate the role of disorder and fluctuations on the interband absorption of dark matter. We find that both continuous and discrete fluctuations across the sample introduce tails (e.g., Dirac-Lifshitz tails) in the density of states and the interband absorption rate. We estimate the strength of the gap filling and discuss implications of these fluctuations on the performance as sensors for dark matter detection. The approach used in this work provides a basic framework to model the disorder by any arbitrary mechanism on the interband absorption of Dirac material sensors.

Figure 1

Three stages to arrive at mass fluctuations in a Dirac cone. The gap is induced by the ${\sigma }_z$ term and different realizations of $M$ are averaged over.

Figure 2

Density of states for the gapless $\left(M_0=0\right)$ and gapped $\left(2M_0=50\mathrm{meV}\right)$ with standard deviation $\sigma$ in $M$. The tail of DOS near $E=0$ needs to be taken into account in a discussion for realistic Dirac materials for sensor applications.

Figure 3

The effect of randomness in $M$ on the probability of a transition per unit time with a mass term $M_0=25\mathrm{meV}$. Normalized such that $〈\mathcal{R}\left(2M_0\right)〉=1$ for $\sigma =0\mathrm{meV}$.

Figure 4

The probability of a transition per unit time $\mathcal{R}$ is reduced by an increase in temperature $T$ and smeared by the random mass $M$ distribution with standard deviation $\sigma$.

Figure 5

Competing transition rates $〈\mathcal{R}〉=A〈\mathcal{R}\left({\omega }_{\text{DM}}\right)〉-B〈\mathcal{R}\left({\omega }_{\text{th}}\right)〉$ for different ratios $A:B$ and increasing mass fluctuations $\sigma$. The transition rates assuming a mass-term of $M_0=25\mathrm{meV}$ and ${\omega }_{\text{DM}}=55\mathrm{meV}$ are compared to the transition rates due to thermal noise ${\omega }_{\text{th}}=0.4\mathrm{meV}$. The shaded area indicates the range with more transitions due to noise than the photons of interest, i.e., $〈\mathcal{R}\left({\omega }_{\text{th}}\right)\gg 〈\mathcal{R}\left({\omega }_{\text{DM}}\right)〉$.