Adequacy of Si:P chains as Fermi–Hubbard simulators

Abstract

The challenge of simulating many-body models with analogue physical systems requires both experimental precision and very low operational temperatures. Atomically precise placement of dopants in Si permits the construction of nanowires by design. We investigate the suitability of these interacting electron systems as simulators of a fermionic extended Hubbard model on demand. We describe the single-particle wavefunctions as a linear combination of dopant orbitals (LCDO). The electronic states are calculated within configuration interaction (CI). Due to the peculiar oscillatory behavior of each basis orbital, properties of these chains are strongly affected by the interdonor distance R 0 , in a non-monotonic way. Ground state (T = 0 K) properties such as charge and spin correlations are shown to remain robust under temperatures up to 4 K for specific values of R 0 . The robustness of the model against disorder is also tested, allowing some fluctuation of the placement site around the target position. We suggest that finite donor chains in Si may serve as an analog simulator for strongly correlated model Hamiltonians. This simulator is, in many ways, complementary to those based on cold atoms in optical lattices-the trade-off between the tunability achievable in the latter and the survival of correlation at higher operation temperatures for the former suggests that both technologies are applicable for different regimes.

Topological phases of a dimerized Fermi–Hubbard model for semiconductor nano-lattices

“…The band theory of topological insulators (TI) [18] based on the independent-electron approximation is well developed and has had many successes. However, in many of the possible experimental platforms for quantum simulation of TI using electrons in solids, such as dopant atoms and gate-defined quantum dots in semiconductors [19,20], the electron-electron interaction is much stronger than the hopping amplitude of the electrons [21,22] and therefore the independent-electron approximation is poor. Topological phases of strongly correlated models form a topic of ongoing active research with intense theoretical [23][24][25][26] and experimental effort, including recent implementations in cold atoms [27] and in a real two-dimensional material [28].…”

Disordered Si:P nanostructures as switches and wires for nanodevices

“…In this work we extended the LCDO formalism [8,10] to include Gaussian disorder, a multi-orbital description and technical improvements, specified in the Appendix, which results in a more realistic description of P nanochains and to access nanoribbons of arbitrary widths. Our simulations treat the problem considering realistic system sizes and disorder.…”

“…As demonstrated in Refs. [8,10], the Hilbert space can be effectively represented by a reduced basis formed by a Linear Combination of Donor Orbital (LCDO). In this hybrid method each donor orbital is accounted for by a multi-valley central cell effective mass approach, that incorporates the Si host effects in the donor orbital itself.…”

“…In order to improve the reliability of the electronic calculations at smaler interdornor distances, we extend the treatment presented in Ref. [10] by including multi-orbitals and three-center corrections due to neighboring cores in the hopping energies. A detailed presentation is found in the Appendix.…”

“…As in previous works [8,10] the Hamiltonian terms are calculated by the atomistic HamiltonianĤ =Ĥ i +Ĥ , whereĤ i is the single donor Hamiltonian andĤ is the perturbation due to neighboring donor cores. We project the donor orbital to this atomistic Hamiltonian to extract the onsite and hopping terms.…”