We propose a device for studying the Fermi-Hubbard model with long-range Coulomb interactions using an array of coupled quantum dots defined in a semiconductor two-dimensional electron-gas system. Bands above the lowest energy band are used to form the Hubbard model, so that a high average electron density may be used to implement the device. We find that depending on the average electron density, the system is well described by a one- or two-band Hubbard model. Our device design enables the control of the ratio of the Coulomb interaction to the kinetic energy of the electrons independently to the filling of the quantum dots, such that a large portion of the Hubbard phase diagram may be probed. Estimates of the Hubbard parameters suggest that a metal-Mott insulator quantum phase transition and a $d$-wave superconducting phase should be observable using current technologies.
We propose a device for studying the Fermi-Hubbard model with long-range Coulomb interactions using an array of coupled quantum dots defined in a semiconductor two-dimensional electron-gas system. Bands above the lowest energy band are used to form the Hubbard model, so that a high average electron density may be used to implement the device. We find that depending on the average electron density, the system is well described by a one- or two-band Hubbard model. Our device design enables the control of the ratio of the Coulomb interaction to the kinetic energy of the electrons independently to the filling of the quantum dots, such that a large portion of the Hubbard phase diagram may be probed. Estimates of the Hubbard parameters suggest that a metal-Mott insulator quantum phase transition and a d-wave superconducting phase should be observable using current technologies.
Strongly interacting electron systems can provide insight into quantum many-body phenomena, such as Mott insulating behavior and spin liquidity, facilitating semiconductor optimization. The Fermi-Hubbard model is the prototypical model used to study such systems. Recent research, however, has shown that the extended Fermi-Hubbard model, which accounts for long-range interactions, is more accurate, especially for systems far from half-filling. In this study, we use the extended Fermi-Hubbard model to mathematically analyze charge transport through a lattice of quantum dots. One-dimensional chains with spinless electrons and source-drain bias are observed, focusing on the transition between the ground state and the first excited state. Level repulsion decreases the expected energy levels of anticrossings as the hopping onto the chain tends to the hopping within the chain. The distribution of charge density along the chain is characterized in terms of the hopping, nuclear, and Coulomb parameters and novel plasmonic behavior is analyzed. Minor perturbations in electron transport are identified, corresponding to the one-dimensional nature of the observed systems. This research will lead to a better understanding of electron behavior in silicon-doped semiconductors, like the formation of correlation-induced band gaps, and open the door to using the extended Fermi-Hubbard model as a more accurate alternative to study quantum many-body systems.
The Hubbard model is an essential tool for understanding many-body physics in condensed matter systems. Artificial lattices of dopants in silicon are a promising method for the analog quantum simulation of extended Fermi-Hubbard Hamiltonians in the strong interaction regime. However, complex atom-based device fabrication requirements have meant emulating a tunable two-dimensional Fermi-Hubbard Hamiltonian in silicon has not been achieved. Here, we fabricate 3 × 3 arrays of single/few-dopant quantum dots with finite disorder and demonstrate tuning of the electron ensemble using gates and probe the many-body states using quantum transport measurements. By controlling the lattice constants, we tune the hopping amplitude and long-range interactions and observe the finite-size analogue of a transition from metallic to Mott insulating behavior. We simulate thermally activated hopping and Hubbard band formation using increased temperatures. As atomically precise fabrication continues to improve, these results enable a new class of engineered artificial lattices to simulate interactive fermionic models.
We are entering the era of the second quantum revolution, where we aim to harness the power of quantum mechanics to create new technologies. Quantum technologies have the potential to revolutionize the fields of simulation, computation, communication, sensing, metrology, and many others. Here we discuss analog quantum simulation, which has attracted a lot of attention in the last few years from several platforms. Although arrays of gate-defined quantum dots exhibit significant potential for analog simulation, example experiments have been few and far between. This thesis focuses on simulating the Fermi-Hubbard model using two dimensional (2d) arrays of quantum dots. The first experiment describes the creation and measurement of a 2x2 quantum dot array. Historically, most experiments with quantum dots have been performed with linear arrays due to the relative ease of fabrication. We introduce a bi-layer gate structure, facilitated by the lift-off of sputtered silicon nitride, to create the 2x2 dot array. This gate design enables us to achieve unprecedented tunability of the tunnel coupling between all nearest-neighbor pairs of dots in 2d arrays. We also demonstrate individual control over the chemical potential and the electron occupation of each dot along with accurate measurement of the on-site and inter-site interaction terms. The use of virtual gates significantly aids in the tuning of tunnel coupling and chemical potential. The demonstrated high degree of control of the system along with fast single-shot spin-readout achieved through Pauli spin blockade establish this dot array as a promising simulator of the Fermi-Hubbard model. The 2x2 dot array is used to simulate Nagaoka ferromagnetism in the next experiment. This form of itinerant ferromagnetism arises from the Fermi-Hubbard model, and was first shown analytically in the limit of infinite interaction strengths and infinite lattices by Nagaoka in 1966. Nagaoka ferromagnetism has been a topic of rigorous theoretical studies ever since, but its experimental signature has eluded us for more than five decades. In this experiment, we load the four dot plaquette with three electrons and demonstrate the emergence of spontaneous ferromagnetism by measuring the spin correlation of two out of the three electrons. Changing the topology of the array to an open chain is shown to destroy the ferromagnetic signature, consistent with the Lieb-Mattis theorem. We also show indications that this ferromagnetic ground state can be destroyed by applying a perpendicular magnetic field, unlike most other forms of ferromagnetism. However, this ground state shows striking robustness to the offset in the local potential of any dot. This is the first experimental verification of Nagaoka’s prediction as well as the first simulation of magnetism using quantumdot arrays. The final experiment takes a different approach to simulate the Fermi-Hubbardmodel with a large 2d array of quantum dots. The dot array is created using only three gates in a top-down approach. This allows for only global control over the electron filling and tunnel coupling of the dots, contrary to the previous experiments. The readout is performed with capacitance spectroscopy, which allows us to directly probe the density of states of the two-dimensional electron systems. We measure the disorder levels and optimize both substrates and gating strategies to induce periodic potential, sufficiently stronger than the disorder level, at the 2d electron gas. Although we demonstrate a novel platformfor the realization of artificial lattices of interacting particles, this effort is currently limited by the substrate inhomogeneity.
The Quantum Monte Carlo simulations of the ionic Hubbard model on a two-dimensional square lattice at half filling were performed. The method based on the direct-space, proposed by Suzuki and al., Hirsch and al., was used. Cycles of increasing and decreasing values of the Coulomb interaction $ U $ were performed for fixed temperature ($ kT=0.01 $). Results indicate that, at low temperature, the two insulator phases are separated by a metallic phase for weak to intermediate values of the staggered potential $ Δ$. For large Coulomb repulsion the system is in a Mott insulator with an antiferromagnetism order. On increasing and decreasing the Coulomb interaction $ U $ the metal-Mott insulator transition shows an hysteresis phenomenon while the metal-band insulator transition is continue. For large $ Δ$ it seems that the metallic region shrinks to a single metallic point. However, the band insulator to the Mott insulator transition is not direct for the studied model. A phase diagram is drawn for the temperature $ kT=0.01 $. For $ Δ=0.5 $ cycles of increasing and decreasing temperature were programmed for different values of the Coulomb interaction $ U $ . A behaviour change appears for $ U\simeq 1.75 $. This suggests that a crossover line divides the metallic region of the phase diagram.
We investigate the role of strong Coulomb interactions beyond the standard Hubbard model in two distinct physical contexts. First, we analyze the superconducting phase transition occurring near the Mott metal-insulator transition. Second, we study transport properties of artificial nano-scale structures containing quantum dots coupled to external electrodes. In both cases, we focus on the impact of the correlated (assisted) hopping (CH) interaction. For superconductors, CH acts as a driving mechanism for the phase transition and modifies the spectral properties of the system. We present the evolution of the spectral function as the system approaches the Mott-type transition under varying model parameters. In quantum-dot-based devices, CH influences the tunneling amplitude between the dot and metallic leads. We demonstrate that the characteristic changes in the conductance of a normal metal-quantum dot-normal metal structure provide a clear signature of the presence and sign of CH interaction.
It has been demonstrated that small plaquettes of quantum dot spin qubits are capable of simulating condensed matter phenomena that arise from the Hubbard model, such as the collective Coulomb blockade and Nagaoka ferromagnetism. Motivated by recent materials developments, we investigate a bilayer arrangement of quantum dots with four dots in each layer which exhibits a complex ground state behavior. We find using a generalized Hubbard model with long-range Coulomb interactions, several distinct magnetic configurations occur as the Coulomb interaction strength is varied, with possible ground states that are ferromagnetic, antiferromagnetic, or having both one antiferromagnetic and one ferromagnetic layer. We map out the full phase diagram of the system as it depends on the inter- and intralayer Coulomb interaction strengths, and find that for a single layer, a similar but simpler effect occurs. We also predict interesting contrasts among electron, hole, and electron-hole bilayer systems arising from complex correlation physics. Observing the predicted magnetic configuration in already-existing few-dot semiconductor bilayer structures could prove to be an important assessment of current experimental quantum dot devices, particularly in the context of spin-qubit-based analog quantum simulations.