Dark matter particles populating our galactic halo could be directly detected by measuring their scattering off target nuclei or electrons in a suitable detector. As this interaction is expected to occur with very low probability and would generate very small energy deposits, the detection is challenging; the possible identification of distinctive signatures (like an annual modulation in the interaction rates or directionality) to assign a dark matter origin to a possible observation is being considered. Here, the physics case of different dark matter direct detection experiments will be presented and the different and complementary techniques which are being applied or considered will be discussed, summarizing their features and latest results obtained. Special focus will be made on TPC-related projects; experiments using noble liquids have presently a leading role to constrain interaction cross sections of a wide range of dark matter candidates and gaseous detectors are very promising to explore specifically low mass dark matter as well as to measure directionality.

https://iopscience.iop.org/article/10.1088/1742-6596/2502/1/012004/pdf

Review on dark matter searches

We develop a tight-binding model based on linear combination of atomic orbitals (LCAO) methods to describe the electronic structure of arrays of acceptors, where the underlying basis states are derived from an effective-mass-theory solution for a single acceptor in either the spherical approximation or the cubic model. Our model allows for arbitrarily strong spin-orbit coupling in the valence band of the semiconductor. We have studied pairs and dimerised linear chains of acceptors in silicon in the `independent-hole' approximation, and investigated the conditions for the existence of topological edge states in the chains. For the finite chain we find a complex interplay between electrostatic effects and the dimerisation, with the long-range Coulomb attraction of the hole to the acceptors splitting off states localised at the end acceptors from the rest of the chain. A further pair of states then splits off from each band, to form a pair localised on the next-to-end acceptors, for one sense of the bond alternation and merges into the bulk bands for the other sense of the alternation. We confirm the topologically non-trivial nature of these next-to-end localised states by calculating the Zak phase. We argue that for the more physically accessible case of one hole per acceptor these long-range electrostatic effects will be screened out; we show this by treating a simple phenomenologically screened model in which electrostatic contributions from beyond the nearest neighbours of acceptor each pair are removed. Topological states are now found on the end acceptors of the chains. In some cases the termination of the chain required to produce topological states is not the one expected on the basis of simple geometry (short versus long bonds); we argue this is because of a non-monotonic relationship between the bond length and the effective Hamiltonian matrix elements between the acceptors.

/pdf/linear-combination-of-atomic-orbitals-model-for-4urfq27gxk.pdf

Linear combination of atomic orbitals model for deterministically placed acceptor arrays in silicon

We consider the interaction between acceptor pairs in doped semiconductors in the limit of large interacceptor separation relevant for low doping densities. Modeling individual acceptors via the spherical model of Baldereschi and Lipari, we calculate matrix elements of the quadrupole tensor between the four degenerate ground states and show that the acceptor has a nonzero quadrupole moment. As a result, the dominant contribution to the large-separation acceptor-acceptor interaction comes from direct (charge-density) terms rather than exchange terms. The quadrupole is the leading nonzero moment, so the electric quadrupole-quadrupole interaction dominates for large separation. We calculate the matrix elements of the quadrupole-quadrupole interaction Hamiltonian in a product-state basis and diagonalize, obtaining a closed-form expression for the energies and degeneracies of the sixteen-state energy spectrum. All dependence on material parameters enters via an overall prefactor, resulting in surprisingly simple and universal results. This simplicity is due, in part, to a mathematical happenstance, the nontrivial vanishing of a particular Wigner 6-$j$ symbol, $\left\{\begin{array}{ccc}2a 2a 2\\ \frac{3}{2}a \frac{3}{2}a \frac{3}{2}\end{array}\right\}=0$. Results are relevant to the control of two-qubit interactions in quantum computing implementations based on acceptor spins, as well as calculations of the thermodynamic properties of insulating $p$-type semiconductors.

Quadrupolar interactions between acceptor pairs in p -doped semiconductors

In this paper, we compute the electronic structure of acceptor clusters in silicon by using three different methods to take into account electron correlations: the full configuration interaction (full CI calculation), the Heitler-London approximation (HL approximation), and the unrestricted Hartree-Fock method (UHF method). We show that both the HL approach and the UHF method are good approximations to the ground state of the full CI calculation for a pair of acceptors and for finite linear chains along [001], [110], and [111]. The total energies for finite linear chains show the formation of a fourfold-degenerate ground state (lying highest in energy), below which there are characteristic low-lying eightfold and fourfold degeneracies, when there is a long (weak) bond at the end of the chain. We present evidence that this is a manifold of topological edge states. We identify a change in the angular momentum composition of the ground state at a critical pattern of bond lengths, and show that it is related to a crossing in the Fock matrix eigenvalues. We also test the symmetry of the self-consistent mean-field UHF solution and compare it to the full CI; the symmetry is broken under almost all the arrangements by the formation of a magnetic state in UHF, and we find further broken symmetries for some particular arrangements related to crossings (or potential crossings) between the Fock-matrix eigenvalues in the [001] direction. We also compute the charge distributions across the acceptors obtained from the eigenvectors of the Fock matrix; we find that, with weak bonds at the chain ends, two holes are localized at either end of the chain while the others have a nearly uniform distribution over the middle; this also implies the existence of the nontrivial edge states. We also apply the UHF method to treat an infinite linear chain with periodic boundary conditions, where the full CI calculation and the HL approximation cannot easily be used. We find the band structures in the UHF approximation, and compute the Zak phases for the occupied Fock-matrix eigenvalues; however, we find they do not correctly predict the topological edge states formed in this interacting system. On the other hand, we find that direct study of the quantum numbers characterizing the edge states, introduced by Turner et al. [Phys. Rev. B 83, 075102 (2011)], provides a better insight into their topological nature.

/pdf/multihole-models-for-deterministically-placed-acceptor-2xl9kpv1oz.pdf

Multihole models for deterministically placed acceptor arrays in silicon

Real semiconductors usually contain both donor and acceptor impurities. A finite compensation degree leads to the possibility of the single carrier to be bounded by two impurity centers. For such an electron complex (near a simple conduction band), the spectral problem resembles the hydrogen molecule ion problem (up to renormalization of the effective mass and dielectric screening). In $p$-type semiconductors, the spectral problem for a single hole in the field of two attracting centers (${A}_{2}^{\ensuremath{-}}$ complex) is more complicated due to the complex structure of the valence band. Here such a problem is presented for the case of the hole bounded at two shallow acceptors close to the ${\mathrm{\ensuremath{\Gamma}}}_{8}$ valence band edge (${\mathrm{A}}^{\mathrm{III}}{\mathrm{B}}^{\mathrm{V}}$ or group $\mathrm{IV}$ semiconductors). The multicomponent envelope functions are used to develop quantum chemistrylike approach (molecular orbital method). The variational approach is applied to calculate the level structure of the complex. The states of the complex are classified by the total angular momentum projection onto the intercenter axis and by the parity with respect to the intercenter permutation. The ground state has a total angular momentum projection of $\ifmmode\pm\else\textpm\fi{}1/2$ and a wave function that is symmetric with respect to the intercenter permutation. The energy levels are found as a function of the intercenter distance. A possible manifestation of ${A}_{2}^{\ensuremath{-}}$ complexes in acceptor-related luminescence is discussed. 

Level structure of hole two-center complex and related luminescence in semiconductors

The interactions between acceptors in semiconductors are often treated in qualitatively the same manner as those between donors. Acceptor wave functions are taken to be approximately hydrogenic and the standard hydrogen molecule Heitler-London model is used to describe acceptor-acceptor interactions. But due to valence band degeneracy and spin-orbit coupling, acceptor states can be far more complex than those of hydrogen atoms, which brings into question the validity of this approximation. To address this issue, we develop an acceptor-acceptor Heitler-London model using single-acceptor wave functions of the form proposed by Baldereschi and Lipari, which more accurately capture the physics of the acceptor states. We calculate the resulting acceptor-pair energy levels and find, in contrast to the two-level singlet-triplet splitting of the hydrogen molecule, a rich ten-level energy spectrum. Our results, computed as a function of interacceptor distance and spin-orbit coupling strength, suggest that acceptor-acceptor interactions can be qualitatively different from donor-donor interactions, and should therefore be relevant to the control of two-qubit interactions in acceptor-based qubit implementations, as well as the magnetic properties of a variety of p-doped semiconductor systems. Further insight is drawn by fitting numerical results to closed-form energy-level expressions obtained via an acceptor-acceptor Hubbard model.

Heitler-London model for acceptor-acceptor interactions in doped semiconductors

Dark matter is five times more abundant than ordinary visible matter in our Universe. While laboratory searches hunting for dark matter have traditionally focused on the electroweak scale, theories of low mass hidden sectors motivate new detection techniques. Extending these searches to lower mass ranges, well below 1 GeV/c$^2$, poses new challenges as rare interactions with standard model matter transfer progressively less energy to electrons and nuclei in detectors. Here, we propose an approach based on phonon-assisted quantum evaporation combined with quantum sensors for detection of desorption events via tracking of spin coherence. The intent of our proposed dark matter sensors is to extend the parameter space to energy transfers in rare interactions to as low as a few meV for detection of dark matter particles in the keV/c$^2$ mass range.

Single Phonon Detection for Dark Matter via Quantum Evaporation and Sensing of $^3$Helium

Dark matter is five times more abundant than ordinary visible matter in our Universe. While laboratory searches hunting for dark matter have traditionally focused on the electroweak scale, theories of low mass hidden sectors motivate new detection techniques. Extending these searches to lower mass ranges, well below $1\text{ }\text{ }\mathrm{GeV}/{c}^{2}$, poses new challenges as rare interactions with standard model matter transfer progressively less energy to electrons and nuclei in detectors. Here, we propose an approach based on phonon-assisted quantum evaporation combined with quantum sensors for detection of desorption events via tracking of spin coherence. The intent of our proposed dark matter sensors is to extend the parameter space to energy transfers in rare interactions to as low as a few meV for detection of dark matter particles in the $\mathrm{keV}/{\mathrm{c}}^{2}$ mass range. 

Single phonon detection for dark matter via quantum evaporation and sensing of 
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We have measured two-dimensional electron systems bound to a thin helium film supported by a metallic substrate. We report on our measurement of electron density obtained via a Kelvin probe technique. The underlying metallic substrate is an amorphous metallic alloy (TaWSi), which can support large uniform densities due to its low surface roughness and homogeneous work function. We find that this substrate is able to support high enough densities that the electrons are expected to be Fermi-degenerate. 

/pdf/measurement-of-high-density-electrons-above-a-helium-film-on-9o9w7cwy.pdf

Measurement of High Density Electrons Above a Helium Film on an Amorphous Metal Substrate

pdf/high-impedance-resonators-for-strong-coupling-to-an-electron-el8on503pnru.pdf

High-impedance resonators for strong coupling to an electron on helium

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Heitler-London model for acceptor-acceptor interactions in doped semiconductors

Single Phonon Detection for Dark Matter via Quantum Evaporation and Sensing of $^3$Helium

Single phonon detection for dark matter via quantum evaporation and sensing of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>He</mml:mi></mml:mrow><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:m

Measurement of High Density Electrons Above a Helium Film on an Amorphous Metal Substrate

High-impedance resonators for strong coupling to an electron on helium