We present field effect measurements on discontinuous 2D thin films which are composed of a sub monolayer of nano-grains of Au, Ni, Ag or Al. Like other electron glasses these systems exhibit slow conductance relaxation and memory effects. However, unlike other systems, the discontinuous films exhibit a dramatic slowing down of the dynamics below a characteristic temperature T * . T * is typically between 10-50K and is sample dependent. For T < T * the sample exhibits a few other peculiar features such as repeatable conductance fluctuations in millimeter size samples. We suggest that the enhanced system sluggishness is related to the current carrying network becoming very dilute in discontinuous films so that the system contains many parts which are electrically very weakly connected and the transport is dominated by very few weak links. This enables studying the glassy properties of the sample as it transitions from a macroscopic sample to a mesocopic sample, hence, the results provide new insight on the underlying physics of electron glasses.PACS numbers: 75.75.Lf; 72.80.Ng; 72.20.Ee; 73.40.Rw Glassy behavior of the conductivity, σ, in strongly disordered systems that are characterized by strong electronic interactions were predicted by several groups [1][2][3][4][5]. Exciting such a system out of equilibrium leads to an increase in conductivity, σ, after which the relaxation towards equilibrium is characterized by extremely long times, memory phenomena and aging. Since the slow dynamics are related to their electronic properties these systems were termed electron glasses [4]. Experimentally, glassy features were observed in a verity of systems including granular Au [6], amorphous and poly-crystalline indium oxide films [7][8][9][10][11], ultrathin Pb films [12], granular aluminum [13,14] and thin beryllium films [15]. A standard way of excitation in these experiments is by applying a gate voltage, V g , in a MOSFET setup. Conductivity increases for both orientations of V g followed by very slow relaxation of σ which is found to follow an approximate logarithmic dependence on time and may be measured over time-scales of days. A typical feature which has been suggested as the hallmark of intrinsic electron glasses [16] is a "memory dip" (MD) which shows up as a minimum in the σ(V g ) curve when V g is scanned fast compared to the characteristic relaxation time. The dip is centered around the gate voltage at which the sample was allowed to equilibrate.The origin of the extremely slow relaxation and the memory dip as well as their dependence on parameters such as temperature, bias voltage, carrier concentration etc. are still under debate and more experimental information may help shedding light on the physics of electron glasses. In this letter we present results on the glassy properties of two dimensional discontinuous films. We find that these systems exhibit a dramatic slowing down of the dynamics below a characteristic temperature T * . For T < T * the conductance of the sample exhibits reproducible fluct...

Using exact diagonalization for non-interacting systems and density matrix renormalization group for interacting systems we show that Li and Haldane's conjecture on the correspondence between the low-lying many-particle excitation spectrum and the entanglement spectrum holds for disordered ballistic one-dimensional many-particle systems. In order to demonstrate the correspondence we develope a computational efficient way to calculate the ES of low-excitation of non-interacting systems. We observe and explain the presence of an unexpected shell structure in the excitation structure. The low-lying shell are robust and survive even for strong electronelectron interactions.

Memory is one of the unique qualities of a glassy system. The relaxation of a glass to equilibrium contains information on the sample's excitation history, an effect often refer to as "aging." We demonstrate that under the right conditions a glass can also possess a different type of memory. We study the conductance relaxation of electron glasses that are fabricated at low temperatures. Remarkably, the dynamics are found to depend not only on the ambient measurement temperature but also on the maximum temperature to which the system was exposed. Hence the system "remembers" its highest temperature. This effect may be qualitatively understood in terms of energy barriers and local minima in configuration space and therefore may be a general property of the glass state.

This corrects the article DOI: 10.1103/PhysRevLett.117.116601.

Connections between the electronic eigenstates and conductivity of one-dimensional disordered systems is studied in the framework of the tight-binding model. We show that for weak disorder only part of the states exhibit resonant transmission and contribute to the conductivity. The rest of the eigenvalues are not associated with peaks in transmission and the amplitudes of their wave functions do not exhibit a significant maxima within the sample. Moreover, unlike ordinary states, the lifetimes of these 'hidden' modes either remain constant or even decrease (depending on the coupling with the leads) as the disorder becomes stronger. In a wide range of the disorder strengths, the averaged ratio of the number of transmission peaks to the total number of the eigenstates is independent of the degree of disorder and is close to the value 2/5 , which was derived analytically in the weak-scattering approximation. These results are in perfect analogy to the spectral and transport properties of light in one-dimensional randomly inhomogeneous media [1], which provides strong grounds to believe that the existence of hidden, non-conducting modes is a general phenomenon inherent to 1D open random systems, and their fraction of the total density of states is the same for quantum particles and classical waves.