By analyzing the temperature ($T$) and density ($n$) dependence of the measured conductivity ($σ$) of 2D electrons in the low density ($\sim10^{11}$cm$^{-2}$) and temperature (0.02 - 10 K) regime of high-mobility (1.0 and 1.5 $\times 10^4$ cm$^2$/Vs) Si MOSFETs, we establish that the putative 2D metal-insulator transition is a density-inhomogeneity driven percolation transition where the density-dependent conductivity vanishes as $σ(n) \propto (n - n_p)^p$, with the exponent $p \sim 1.2$ being consistent with a percolation transition. The `metallic' behavior of $σ(T)$ for $n > n_p$ is shown to be well-described by a semi-classical Boltzmann theory, and we observe the standard weak localization-induced negative magnetoresistance behavior, as expected in a normal Fermi liquid, in the metallic phase.
Three-dimensional (3-D) topological insulators (TI) are characterized by the presence of metallic surface states and a bulk band gap. Recently theoretical and experimental studies have shown an induced gap in the surface state bands of TI thin films. The gap results from interaction of conduction band (CB) and valence band (VB) surface states from the opposite surfaces of a thin film, and its size is determined by the film thickness. This gap formation could open the possibility of thin-film TI-based metal-oxide-semiconductor field-effect transistors (MOSFETs). Here we explore the performance …
We theoretically investigate the spin injection in different FM/I/n-Si tunnel contacts by using the lattice NEGF method. We find that the tunnel contacts with low barrier materials such as TiO$_2$ and Ta$_{2}$O$_{5}$, have much lower resistances than the conventional barrier materials, resulting in a wider and attainable optimum parameters window for improving the spin injection efficiency and MR ratio of a vertical spin MOSFET. Additionally, we find the spin asymmetry coefficient of TiO$_2$ tunnel contact has a negative value, while that of Ta$_{2}$O$_{5}$ contact can be tuned between positiv…
This letter reports thermopower and conductivity measurements through the metal-insulator transition for 2-dimensional electron gases in high mobility Si-MOSFET's. At low temperatures both thermopower and conductivity show critical behavior as a function of electron density which is very similar to that expected for an Anderson transition. In particular, when approaching the critical density from the metallic side the diffusion thermopower appears to diverge and the conductivity vanishes. On the insulating side the thermopower shows an upturn with decreasing temperature.
We argue that there is a new liquid phase in the two-dimensional electron system in Si MOSFETs at low enough electron densities. The recently observed metal-insulator transition results as a crossover from the percolation transition of the liquid phase through the disorder landscape in the system below the liquid-gas critical temperature. The consequences of our theory are discussed for variety of physical properties relevant to the recent experiments.
The resistance R of the 2DEG on the vicinal Si surface shows an unusual behaviour, which is very different from that in the (100) Si MOSFET where an unconventional metal to insulator transition has been reported. The crossover from the insulator with dR/dT<0 to the metal with dR/dT>0 occurs at a low resistance of R_{\Box}^c \sim 0.04h/e^2. At the low-temperature transition, which we attribute to the existence of a narrow impurity band at the interface, a distinct hysteresis in the resistance is detected. At higher temperatures, another change in the sign of dR/dT is seen and related to the cro…
We report a remarkable symmetry between the resistivity and conductivity on opposite sides of the B=0 metal-insulator transition in a two-dimensional electron gas in high-mobility silicon MOSFET's. This symmetry implies that the transport mechanisms on the two sides are related.
Transport in graphene nanoribbons with an energy gap in the spectrum is considered in the presence of random charged impurity centers. At low carrier density, we predict and establish that the system exhibits a density inhomogeneity driven two dimensional metal-insulator transition that is in the percolation universality class. For very narrow graphene nanoribbons (with widths smaller than the disorder induced length-scale), we predict that there should be a dimensional crossover to the 1D percolation universality class with observable signatures in the transport gap. In addition, there should…
Effective-medium theory is applied to the percolation description of the metal-insulator transition in two dimensions with emphasis on the continuous connection between the zero-magnetic-field transition and the quantum Hall transition. In this model the system consists of puddles connected via saddle points, and there is loss of quantum coherence inside the puddles. The effective conductance of the network is calculated using appropriate integration over the distribution of conductances, leading to a determination of the magnetic field dependence of the critical density. Excellent quantitativ…
We investigate the design of steep-slope metal-oxide-semiconductor field-effect transistors (MOSFETs) exploiting monolayers of transition metal dihalides as channel materials. With respect to other previously proposed steep-slope transistors, these devices require simplified manufacturing processes, as no confinement of the 2D material is needed, nor any tunneling heterojunction or ferroelectric gate insulators, and only n- or p-type contacts are demanded. We demonstrate their operation by studying an implementation based on monolayer CrI$_2$ through quantum transport simulations. We show that…
Polyvinyl-pyrrolidone (PVP) loaded with different fractions of dispersed nano-graphene platelets (NGP) were studied by Broadband Dielectric Spectroscopy in the frequency range from 1 mHz to 1 MHz. Complex permittivity and dynamic ac conductivity as a function of frequency, temperature and composition were explored. The concentration-dependent insulator-to-conductor transition was traced through dependence of the dc conductivity and the onset of the dispersive ac ac conductivity. The temperature evolution of the dielectric spectra, below and above the fractional threshold exhibits different dyn…
In this letter we discuss how the short channel behavior in sub 100 nm channel range can be improved by inducing a step surface potential profile at the back gate of an asymmetrical double gate (DG) Silicon-On-Insulator (SOI) Metal-Oxide-Semiconductor Field-Effect- Transistor (MOSFET) in which the front gate consists of two materials with different work functions.
A new type of a capacitor with a very high volumetric capacitance is proposed. It is based upon the known phenomenon of a sharp increase of the dielectric constant of the metal-insulator composite in the vicinity of the percolation threshold, but still on the insulator side. The optimization suggests that the metallic particles should be of nanoscale and that the distance between planar electrodes should be somewhat larger than the correlation length of the percolation theory and 10 to 20 times larger than the size of the particles while the area of the electrodes might be unlimited. The rando…
A model consisting of a mixture of superconducting and quantum links is proposed to describe the integer quantum Hall transition. The quantum links correspond to tunneling of electrons between trajectories trapped in adjacent potential valleys, while the superconducting links correspond to merging of these trajectories once the Fermi energy crosses the saddle point energy separating the two valleys. The quantum Hall transition in this model corresponds to percolation of the superconducting links. Numerical calculations and scaling analysis using two different approaches yield the critical expo…
According to the scaling theory of localization, all quantum electronic states are localized in two-dimensional (2D) systems. One consequence of the theory is that there is no quantum percolation transition in 2D. However, in a real system at a finite temperature, electron phase coherent length is finite and the system is between quantum and classical. We find, in such a 2D system, a metal-insulator transition (MIT) caused by a novel type of percolation, meta-percolation. The relevance to recently observed 2D MIT is also discussed.
Combining experimental data, numerical transport calculations, and theoretical analysis, we study the temperature-dependent resistivity of high-mobility 2D Si MOSFETs to search for signatures of weak localization induced quantum corrections in the effective metallic regime above the critical density of the so-called two-dimensional metal-insulator transition (2D MIT). The goal is to look for the effect of logarithmic insulating localization correction to the metallic temperature dependence in the 2D conductivity so as to distinguish between the 2D MIT being a true quantum phase transition vers…
Quantum material phases such as the Anderson insulator, diffusive metal, and Weyl/Dirac semimetal as well as topological insulators show specific wave functions both in real and Fourier spaces. These features are well captured by convolutional neural networks, and the phase diagrams have been obtained, where standard methods are not applicable. One of these examples is the cases of random lattices such as quantum percolation. Here, we study the topological insulators with random vacancies, namely, the quantum percolation in topological insulators, by analyzing the wave functions via a convolut…
Recently, a simple non-interacting-electron model, combining local quantum tunneling via quantum point contacts and global classical percolation, has been introduced in order to describe the observed ``metal-insulator transition'' in two dimensions [1]. Here, based upon that model, a two-species-percolation scaling theory is introduced and compared to the experimental data. The two species in this model are, on one hand, the ``metallic'' point contacts, whose critical energy lies below the Fermi energy, and on the other hand, the insulating quantum point contacts. It is shown that many feature…
By carefully analyzing the low temperature density dependence of 2D conductivity in undoped high mobility n-GaAs heterostructures, we conclude that the 2D metal-insulator transition in this system is a density inhomogeneity driven percolation transition due to the breakdown of screening in the random charged impurity disorder background. In particular, our measured conductivity exponent of $\sim 1.4$ approaches the 2D percolation exponent value of 4/3 at low temperatures and our experimental data are inconsistent with there being a zero-temperature quantum critical point in our system.
The existence of a metal-insulator transition at zero magnetic field in two- dimensional electron systems has recently been confirmed in high mobility Si-MOSFETs. In this work, the temperature dependence of the resistivity of gated Si/SiGe/Si quantum well structures has revealed a similar metal- insulator transition as a function of carrier density at zero magnetic field. We also report evidence for a Coulomb gap in the temperature dependence of the resistivity of the dilute 2D hole gas confined in a SiGe quantum well. In addition, the resistivity in the insulating phase scales with a single p…
We show that the unexpected metallic behavior (the so-called two-dimensional metal-insulator transition) observed in low-density Silicon metal-oxide-semiconductor field-effect transistors (Si-MOSFETs) is controlled by a unique characteristic energy scale, the polarization energy. On one hand, we perform Quantum Monte Carlo calculations of the energy needed to polarize the two dimensional electron gas at zero temperature, taking into account Coulomb interactions, valley degeneracy and electronic mobility (disorder). On the other hand, we identify the characteristic energy scale controlling the …
In the standard MOSFET description of the drain current $I_{D}$ as a function of applied gate voltage $V_{GS}$, the subthreshold swing $SS(T)\equiv dV_{GS}/d\log I_{D}$ has a fundamental lower limit as a function of temperature $T$ given by $SS(T) = \ln10~k_BT/e$. However, recent low-temperature studies of different advanced CMOS technologies have reported $SS$(4K or lower) values that are at least an order of magnitude larger. Here, we present and analyze the saturation of $SS(T)$ in 28nm fully-depleted silicon-on-insulator (FD-SOI) devices for both n- and p-type MOSFETs of different gate oxi…
A simple non-interacting-electron model, combining local quantum tunneling and global classical percolation (due to a finite dephasing time at low temperatures), is introduced to describe a metal-insulator transition in two dimensions. It is shown that many features of the experiments, such as the exponential dependence of the resistance on temperature on the metallic side, the linear dependence of the exponent on density, the $e^2/h$ scale of the critical resistance, the quenching of the metallic phase by a parallel magnetic field and the non-monotonic dependence of the critical density on a …
We report on detailed room temperature and low temperature transport properties of double-gate Si MOSFETs with the Si well thickness in the range 7-17 nm. The devices were fabricated on silicon-on-insulator wafers utilizing wafer bonding, which enabled us to use heavily doped metallic back gate. We observe mobility enhancement effects at symmetric gate bias at room temperature, which is the finger print of the volume inversion/accumulation effect. An asymmetry in the mobility is detected at 300 K and at 1.6 K between the top and back interfaces of the Si well, which is interpreted to arise fro…
We report on the first experimental observation of an apparent metal insulator transition in a 2D electron gas confined in an InAs quantum well. At high densities we find that the carrier mobility is limited by background charged impurities and the temperature dependence of the resistivity shows a metallic behavior with resistivity increasing with increasing temperature. At low densities we find an insulating behavior below a critical density of $n_{c} = 5 \times 10^{10}$ cm$^{-2}$ with the resistivity decreasing with increasing temperature. We analyze this transition using a percolation model…
We present the metal - insulator transition study of a quantum site percolation model on simple cubic lattice. Transfer matrix method is used to calculate transport properties - Landauer conductance - for the binary distribution of energies. We calculate the mobility edge in disorder (ratio of insulating sites) - energy plane in detail and we find the extremal critical disorder somewhat closer to the classical percolation threshold, than formerly reported. We calculate the critical exponent $ν$ along the mobility edge and find it constant and equal to the one of 3D Anderson model, confirming c…
An approach is developed for the determination of the current flowing through a nanosize silicon-on-insulator (SOI) metal-oxide-semiconductor field-effect transistors (MOSFET). The quantum mechanical features of the electron transport are extracted from the numerical solution of the quantum Liouville equation in the Wigner function representation. Accounting for electron scattering due to ionized impurities, acoustic phonons and surface roughness at the Si/SiO2 interface, device characteristics are obtained as a function of a channel length. From the Wigner function distributions, the coexiste…
We develop an effective medium model of thermal conductivity that accounts for both percolation and interface scattering. This model accurately explains the measured increase and decrease of thermal conductivity with loading in composites dominated by percolation and interface scattering, respectively. Our model further predicts that strong interface scattering leads to a sharp decrease in thermal conductivity, or an insulator transition, at high loadings when conduction through the matrix is restricted and heat is forced to diffuse through particles with large interface resistance. The accura…
We want to answer the question of whether the divergence in the effective mass in metal-insulator transition (MIT) in 2DEG is in the same universality class as percolation. We use a model to make Percolated state in 2D and then calculate the effective mass in a super-cell and the Bloch Theorem. It is seen that the effective mass, m*, scales as m*~(P-Pc)^a with a=1 and Pc being the (classical) percolation threshold.
Motivated by the recent observation of the metal-insulator transition in Si-MOSFETs we consider the quantum interference correction to the conductivity in the presence of the Rashba spin splitting. For a small splitting, a crossover from the localizing to antilocalizing regime is obtained. The symplectic correction is revealed in the limit of a large separation between the chiral branches. The relevance of the chiral splitting for the 2D electron gas in Si-MOSFETs is discussed.
Positive magnetoresistance (PMR) of a silicon MOSFET in parallel magnetic fields B has been measured at high electron densities n >> n_c where n_c is the critical density of the metal-insulator transition (MIT). It turns out that the normalized PMR curves, R(B)/R(0), merge together when the field is scaled according to B/B_c(n) where B_c is the field in which electrons become fully spin polarized. The values of B_c have been calculated from the simple equality between the Zeeman splitting energy and the Fermi energy taking into account the experimentally measured dependence of the spin suscept…
For the immediate vicinity of the metal-insulator transition (MIT), data on the dependence of the resistivity rho on the charge carrier concentration n from an Si MOSFET experiment by Kravchenko et al. and from an AlAs quantum well study by Papadakis and Shayegan are reanalyzed. In both cases, the rho(T=const.,n) curves for various values of the temperature T seem to exhibit an offset concerning n, where the related resistivity is close to h/e^2. This offset may result from a peculiarity in rho(T=const.,n) indicating the MIT to be present also at finite T. More detailed experiments are imperat…
Two percolation transitions are observed in Ag$_x$(SnO$_2)_{1-x}$ nanogranular films with Ag volume fraction $x$ ranging from $\sim$0.2 to $\sim$0.9. In the vicinity of each percolation threshold $x_{ci}$ ($i$$=$1, 2), the variation in $σ$ with $x$ obeys a power law for $x$$>$$x_{ci}$. The origin of the first percolation transition at $x_{c1}$ ($x_{c1}$$>$$x_{c2}$) is similar to that of the classical one, while the second transition is explained as originating from the tunneling to the second-nearest neighboring Ag particles. These observations provide strong experimental support for the valid…
The performance limits of monolayer transition metal dichalcogenide transistors are examined with a ballistic MOSFET model. Using ab-initio theory, we calculate the band structures of two-dimensional (2D) transition metal dichalco-genide (MX2). We find the lattice structures of monolayer MX2 remain the same as the bulk MX2. Within the ballistic regime, the performances of monolayer MX2 transistors are better compared to the silicon transistors if thin high-κ gate insulator is used. This makes monolayer MX2 promising 2D materials for future nanoelectronic device applications.
The scaling behaviors of graphene nanoribbon (GNR) Schottky barrier field-effect transistors (SBFETs) are studied by solving the non-equilibrium Green's function (NEGF) transport equation in an atomistic basis set self-consistently with a three-dimensional Poisson equation. The armchair edge GNR channel shares similarities with a zigzag CNT, but it has a different geometry and quantum confinement boundary condition in the transverse direction. The results indicate that the I-V characteristics are ambipolar and strongly depend on the GNR width because the bandgap of the GNR is approximately inv…
Scaling theory predicts complete localization in $d=2$ in quantum systems belonging to orthogonal class (i.e. with time-reversal symmetry and spin-rotation symmetry). The conductance $g$ behaves as $g \sim exp(-L/l)$ with system size $L$ and localization length $l$ in the strong disorder limit. However, classical systems can always have metallic states in which Ohm's law shows a constant $g$ in $d=2$. We study a two-dimensional quantum percolation model by controlling dephasing effects. The numerical investigation of $g$ aims at simulating a quantum-to-classical percolation evolution. An unexp…
The 2-D electron system (2DES) in Si metal-oxide field-effect transistors (MOSFETS) consists of two distinct electron fluids interacting with each other. We calculate the total energy as a function of the density $n$, and the spin polarization $ζ$ in the strongly-correlated low-density regime, using a classical mapping to a hypernetted-chain (CHNC) equation inclusive of bridge terms. Here the ten distribution functions, arising from spin and valley indices, are self-consistently calculated to obtain the total free energy, the chemical potential, the compressibility and the spin susceptibility.…
A novel variational method is proposed for calculating the percolation threshold, the real-space structure, and the thermodynamical compressibility of a disordered two-dimensional electron liquid. Its high accuracy is verified against prior numerical results and newly derived exact asymptotics. The inverse compressibility is shown to have a strongly asymmetric minimum at a density that is approximately the triple of the percolation threshold. This implies that the experimentally observed metal-insulator transition takes place well before the percolation point is reached.
The metal insulator transition of nano-scaled $VO_2$ devices is drastically different from the smooth transport curves generally reported. The temperature driven transition occurs through a series of resistance jumps ranging over 2 decades in amplitude, indicating that the transition is caused by avalanches. We find a power law distribution of the jump amplitudes, demonstrating an inherent property of the $VO_2$ films. We report a surprising relation between jump amplitude and device size. A percolation model captures the general transport behavior, but cannot account for the statistical behav…
We argue on the basis of experimental numbers that the B=0 metal-insulator transition in two dimensions, observed in Si-MOSFETs and in other two-dimensional systems, is likely to be due to a few strongly interacting electrons, which also interact strongly with the random positively ionized impurities. At the insulating side the electrons are all bound in pairs to the ions. On the metallic side free electrons exist which are scattered by ions dressed with electron-pairs and therefore alter the bare scattering potential of the ions. The physics at the metallic side of the transition is argued to…
We perform combined resistivity and compressibility studies of two-dimensional hole and electron systems which show the apparent metal-insulator transition - a crossover in the sign of dR/dT with changing density. No thermodynamic anomalies have been detected in the crossover region. Instead, despite a ten-fold difference in r_s, the compressibility of both electrons and holes is well described by the theory of nonlinear screening of the random potential. We show that the resistivity exhibits a scaling behavior near the percolation threshold found from analysis of the compressibility. Notably,…
We study the metal-insulator transition on a three dimensional quantum percolation model by analyzing energy level statistics. The quantum percolation threshold $\pq$, which is larger than the classical percolation threshold $\pc$, becomes smaller when the time reversal symmetry (TRS) is broken, i.e. $\pq({\rm with TRS})>\pq({\rm without TRS})>\pc$. It is shown that critical exponents are consistent with the result of the Anderson transition, suggesting that the quantum percolation problem can be classified into the same universality classes of the Anderson transition. The shape of level stati…
Complementary metal oxide semiconductor (CMOS) logic circuits at the ultimate scaling limit place the utmost demands on the properties of all materials involved. The requirements for semiconductors are well explored and could possibly be satisfied by a number of layered two-dimensional (2D) materials, like for example transition-metal dichalcogenides or black phosphorus. The requirements for the gate insulator are arguably even more challenging and difficult to meet. In particular the combination of insulator to semiconductor which forms the central element of the metal oxide semiconductor fie…
We theoretically consider the carrier density tuned (apparent) two-dimensional (2D) metal-insulator-transition (MIT) in semiconductor heterostructure-based 2D carrier systems as arising from a classical percolation phenomenon in the inhomogeneous density landscape created by the long-range potential fluctuations induced by random quenched charged impurities in the environment. The long-range Coulomb disorder inherent in semiconductors produces strong potential fluctuations in the 2D system where a fraction of the carriers gets trapped or classically localized, leading to a mixed 2-component se…
A relatively simple and physically transparent model based on quantum percolation and dephasing is employed to construct a global phase diagram which encodes and unifies the critical physics of the quantum Hall, "two-dimensional metal-insulator", classical percolation and, to some extent, superconductor-insulator transitions. Using real space renormalization group techniques, crossover functions between critical points are calculated. The critical behavior around each fixed point is analyzed and some experimentally relevant puzzles are addressed.
We investigate transport and magnetotransport properties of binary networks composed of superconducting (MgB2) and ferromagnetic (CrO2 or LSMO) nanoparticles. While for the LSMO/MgB2 system a single percolation threshold is observed, for CrO2/MgB2 binary composites an anomalously high resistance state with two distinct percolation thresholds corresponding to conductor-insulator and superconductor-insulator transitions is found. The existence of this double percolation effect becomes possible when the interface conductance between the two different constituents is suppressed and the condition f…
Using the extensively studied V2O3 as a prototype system, we investigate the role of percolation in metal-insulator transition (MIT). We apply scanning microwave impedance microscopy to directly determine the metallic phase fraction p and relate it to the macroscopic conductance G, which shows a sudden jump when p reaches the percolation threshold. Interestingly, the conductance G exhibits a hysteretic behavior against p, suggesting two different percolating processes upon cooling and warming. Based on our image analysis and model simulation, we ascribe such hysteretic behavior to different do…
The goal of this paper is to highlight several issues which are most crucial for the understanding of the ``metal-insulator transition'' in two dimensions. We discuss some common problems in interpreting experimental results on high mobility Si MOSFETs. We analyze concepts and methods used to determine the critical density of electrons at the metal-insulator transition. In particular, we discuss the origin of the temperature dependence of the resistivity and reasons for this dependence to flatten out at some electron density in the vicinity of the metal-insulator transition. This flattening ha…
Metallic oxides encased within Metal-Insulator-Metal (MIM) structures can demonstrate both unipolar and bipolar switching mechanisms, rendering them the capability to exhibit a multitude of resistive states and ultimately function as memory elements. Identifying the vital physical mechanisms behind resistive switching can enable these devices to be utilized more efficiently, reliably and in the long-term. In this paper, we present a new approach for analysing resistive switching by modelling the active core of two terminal devices as 2D and 3D grid circuit breaker networks. This model is emplo…
Theory of quantum corrections to conductivity of granular metal films is developed for the realistic case of large randomly distributed tunnel conductances. Quantum fluctuations of intergrain voltages (at energies E much below bare charging energy scale E_C) suppress the mean conductance \bar{g}(E) much stronger than its standard deviation σ(E). At sufficiently low energies E_* any distribution becomes broad, with σ(E_*) ~ \bar{g}(E_*), leading to strong local fluctuations of the tunneling density of states. Percolative nature of metal-insulator transition is established by combination of anal…
The 2D HgTe quantum well is analyzed based on the assumption that the width fluctuations convert the system to a random mixture of domains with positive and negative energy gaps. The borders between ordinary and topological insulator phases form a network of the edge states covering the overall sample. The optical transitions within the edge states yield the 2D absorption. The qualitative consideration is based on the model of optical intraedge transitions in curved edge states together with the percolation arguments.
Graphane is obtained by perfectly hydrogenating graphene. There exists an intermediate material, partially hydrogenated graphene (which we call \textit{hydrographene}), interpolating from pure graphene to pure graphane. It has various intriguing electronic and magnetic properties. We investigate a metal-insulator transition, employing a quantum-site percolation model together with a graph theoretical approach. Hydrographene is an exceptional case in which electronic properties cannot be determined solely by the density of states at the Fermi energy. Though there are plenty of zero energy state…
Electronically phase separated manganite wires are found to exhibit controllable metal-insulator transitions under local electric fields. The switching characteristics are shown to be fully reversible, polarity independent, and highly resistant to thermal breakdown caused by repeated cycling. It is further demonstrated that multiple discrete resistive states can be accessed in a single wire. The results conform to a phenomenological model in which the inherent nanoscale insulating and metallic domains are rearranged through electrophoretic-like processes to open and close percolation channels.
Quantum site percolation as a limiting case of binary alloy is studied numerically in 2D within the tight-binding model. We address the transport properties in all regimes - ballistic, diffusive (metallic), localized and crossover between the latter two. Special attention is given to the region close to the conduction band center, but even there the Anderson localization persists, without signs of metal - insulator transition. We found standard localization for sufficiently large samples. For smaller systems, novel partial quantization of Landauer conductances, i. e. most values close to small…
In this work, we experimentally and theoretically explore voltage controlled oscillations occurring in micro-beams of vanadium dioxide. These oscillations are a result of the reversible insulator to metal phase transition in vanadium dioxide. Examining the structure of the observed oscillations in detail, we propose a modified percolative-avalanche model which allows for voltage-triggering. This model captures the periodicity and waveshape of the oscillations as well as several other key features. Importantly, our modeling shows that while temperature plays a critical role in the vanadium diox…
We report a continuous phase transition between quantum-anomalous-Hall and trivial-insulator phases in a magnetic topological insulator upon magnetization rotation. The Hall conductivity transits from one plateau of quantized Hall conductivity $e^2/h$ to the other plateau of zero Hall conductivity. The transition curves taken at various temperatures cross almost at a single point, exemplifying the critical behavior of the transition. The slope of the transition curves follows a power-law temperature dependence with a critical exponent of $-0.61$. This suggests a common underlying origin in the…
Electrons in graphene aligned with hexagonal boron nitride are modelled by Dirac fermions in a correlated random-mass landscape subject to a scalar- and vector-potential disorder. We find that the system is insulating in the commensurate phase since the average mass deviates from zero. At the transition the mean mass is vanishing and electronic conduction in a finite sample can be described by a critical percolation along zero-mass lines. In this case graphene at the Dirac point is in a critical state with the conductivity $\sqrt{3}e^2/h$. In the incommensurate phase the system behaves as a sy…
The axion insulator is a higher-order topological insulator protected by inversion symmetry. We show that under quenched disorder respecting inversion symmetry {\it on average}, the topology of the axion insulator stays robust, and an intermediate metallic phase in which states are delocalized is unavoidable at the transition from an axion insulator to a trivial insulator. We derive this conclusion from general arguments, from classical percolation theory, and from the numerical study of a 3D quantum network model simulating a disordered axion insulator through a layer construction. We find th…
