Sammon, Michael2019-12-112019-12-112019-08https://hdl.handle.net/11299/208993University of Minnesota Ph.D. dissertation. August 2019. Major: Physics. Advisor: Boris Shklovskii. 1 computer file (PDF); x, 130 pages.The modern world's dependency on electronics provides a constant need to discover new materials and devices. A promising technique to fabricate a new device is to create a heterostructure; a device consisting of two bulk crystals joined at an interface. These materials often support a low dimensional electron gas confined to the interface, which exhibits properties different than both the parent materials. These materials have led to the creation of MOSfets, the discovery of the quantum Hall effect, and in recent years the discovery of Majorana edge modes in nanowires. In this thesis, we study several different heterostructures. We begin with one of the most famous heterostructures, AlGaAs/GaAs. Modern AlGaAs/GaAs heterostructures support a high mobility two-dimensional electron gas (2DEG) in a quantum well. The 2DEG is provided by two remote donor $\delta$-layers placed on both sides of the well. Each $\delta$-layer is located in the midplane of a narrow GaAs well, flanked by narrow AlAs layers which capture excess electrons from donors. We show that each excess electron is localized in a compact dipole atom with the nearest donor. The excess electrons screen both the remote donors and background impurities, and are responsible for the observed high mobility. Still, we find that the mobility is substantially lower than theoretical estimates, which may be due to significant disorder in the donor layers, most likely roughness of the interfaces or spreading of the donors out of the midplane of the layer. Thus one should take care to make sure that the donor layers are as ideal as possible. We next move on to oxide heterostructures involving SrTiO$_3$ (STO). More specifically, we study the electron gas in accumulation layers of these heterostructures characterized by a density profile $n(x)$, where $x$ is the distance from the STO surface. SrTiO$_3$ at liquid helium temperatures has the highest dielectric constant which strongly enhances the role of nonlinear dielectric effects. It was recently shown that the nonlinear dielectric response results in an electron density profile $n(x)$ that slowly decays as $1/x^{12/7}$. We show that such a long tail of $n(x)$ causes the magnetization and the specific heat of the accumulation layer to diverge at large $x$. We explore the truncation of the tail by the finite sample width $W$, the transition from the nonlinear to linear dielectric response with dielectric constant $\kappa$, and the use of a back gate with a negative voltage $-\abs{V}$. We find that as a result both the magnetization and specific heat are anomalously large and obey nontrivial power law dependences on $W$, $\kappa$, or $\abs{V}$. In the linear dielectric regime under a strong magnetic field, the large dielectric constant of STO makes it easy to reach a quasi-one-dimensional state known as the extreme quantum limit (EQL) in which all electrons occupy the lowest Landau level. We present a theory of the EQL phase in STO accumulation layers. We find a phase diagram of the electron gas in the plane of the magnetic field strength and the electron surface concentration for different orientations of the magnetic field. In addition to the quasi-classical metallic phase (M), there is a metallic EQL phase, as well as an insulating Wigner crystal state (WC). Remarkably, the insulating Wigner crystal phase depends on the orientation of the magnetic field. We show that these effects can be measured through quantum capacitance measurements of the STO accumulation layer. The third material we study is semiconducting quantum wires. Though it is not a heterostructure, it supports a low dimensional electron gas which is often tuned with an external gate, making it similar to many of the devices we have studied. We have theoretically investigated the influence of interface roughness scattering on the low temperature mobility of electrons in quantum wires when electrons fill one or many subbands. We find the Drude conductance of the wire as a function of the linear concentration $\eta$ has a sharp peak. The height of this peak grows as a large power of the wire radius $R$, so that at large $R$ the conductance $G_{max}$ exceeds $e^2/h$ and a window of concentrations with delocalized states (which we call the metallic window) opens around the peak. Thus, we predict an insulator-metal-insulator transition with increasing concentration for large enough $R$. Furthermore, we show that the metallic domain can be sub-divided into three smaller domains: 1) single-subband ballistic conductor, 2) many-subband ballistic conductor 3) diffusive metal, and use our results to estimate the conductance in these domains. Finally we estimate the critical value of $R_c(\mathcal{L})$ at which the metallic window opens for a given length $\mathcal{L}$. We conclude the thesis with a discussion of a newer class of materials known as transition metal dichalcogenides (TMDs). We study a capacitor made of three monolayers TMD separated by hexagonal boron nitride (hBN). We assume that the structure is symmetric with respect to the central layer plane. The symmetry includes the contacts: if the central layer is contacted by the negative electrode, both external layers are contacted by the positive one. As a result a strong enough voltage $V$ induces electron-hole dipoles (indirect excitons) pointing towards one of the external layers. Antiparallel dipoles attract each other at large distances. Thus, the dipoles alternate in the central plane forming a 2D antiferroelectric with negative binding energy per dipole. The charging of a three-layer device is a first order transition, and we show that if $V_1$ is the critical voltage required to create a single electron-hole pair and charge this capacitor by $e$, the macroscopic charge $Q_c = eSn_c$ ($S$ is the device area) enters the three-layer capacitor at a smaller critical voltage $V_{c} < V_{1}$. In other words, the differential capacitance $C(V)$ is infinite at $V = V_{c}$. We also show that in a contact-less three-layer device, where the chemically different central layer has lower conduction and valence bands, optical excitation creates indirect excitons which attract each other, and therefore form antiferroelectric exciton droplets. Thus, the indirect exciton luminescence is red shifted compared to a two-layer device.enCapacitanceHeterostructuresSemiconductorsTransportThesis or Dissertation