New noise exponents in random conductor-superconductor and conductor-insulator mixtures

Abstract

Time dependent fluctuations of the fraction of normal-conducting part in random resistorsuperconductor (RS) and resistor-insulator (RI) networks lead to a novel effect close to the percolation threshold. The normalized noise scales as a function of the resistance with a characteristic exponent X. The value of X is different from the value found in classical percolation models but can be related to the resistivity exponent s (t) of the RS (RI) transition by a simple scaling relation: X=2/s (2/t). Results of recent experiments on high-r c superconducting thin films are interpreted in terms of this new effect and a crossover from three to two dimensional percolation behavior is found.PACS numbers: 74.40.+k, 64.60.Ak, 72.70.+m, 74.76.Bz The electrical conductance and conductance noise in random resistor-superconductor (RS) and resistor-insulator (RI) composites have been extensively studied during the last decade [1][2][3][4][5][6][7][8][9][10]. Such studies are interesting not only for fundamental reasons but also for technological applications. An important example of such materials is high-T c superconductors, which show a random RS composite nature in the superconducting transition region (e.g., [11][12][13][14]). Another example is thick film resistors [15][16][17][18][19], which are widely used in electronics. Such resistors consist of metal particles embedded in a glass medium and behave as random RI composites [19].Random resistor networks are applied in modeling the physical behavior of granular superconductors and metal-insulator composites [1-10]. One can start from a spatially homogeneous lattice of resistors representing a homogeneous material. Introducing short circuits parallel to some resistor elements, selected at random, yields a network representing a random RS mixture. Cutting out some resistors, selected at random, yields a network representing a random RI mixture.The physics of random resistor networks is governed by the characteristic cluster size § of the superconducting phase in RS composites and of the conducting phase in RI composites. In the percolation region, these length scales can be expressed as a function of the volume frac-tion p r of resistors (0 :< p r < 1), ^rs cc (pr-Pcr)~V (pr > Per) and €ri « (Pr -Per) ~V (pr > Per) ,(lb)where pc r = 1 -p cs , p C s is the percolation threshold of the superconductor component, p cr is the percolation threshold of the conducting component, and v is a critical exponent (v-j in 2D; v=0.89±0.01 in 3D). This critical behavior leads to the following scaling behavior of the macroscopic resistance R: pr>Per) andRri « (Pr -Per) ' (pr > Per)where R rs is the resistance of the RS composite and R ri is the resistance of the RI composite. Values of the universal exponents s and t [1-10] are shown in Table I. Studies of noise in classical percolation models are based on the assumptions that the resistor elements in the network fluctuate independently of each other and that the fluctuation is small in comparison to the mean value of the resistance, ...

Percolative switching in transition metal dichalcogenide field-effect transistors at room temperature

“…3b and supplementary material for more detail), which makes identifying the transport mechanism at switching from T -dependence of σ alone a very difficult task. The exponents ν in N σ − σ scaling, however, provide a direct evidence of a percolative transport, with the noise peak signifying the percolation threshold at V g ≈ V c g [40,42,58]. Below the percolation threshold (V g < V c g : Region I), called the "dielectric regime", transport occurs by hopping or tunneling through disconnected metallic puddles [59], and approaches a finite device-dependent magnitude at low V g away from the threshold.…”

“…Hence despite compelling evidence of long range inhomogeneity in the charge distribution in MoS 2 FETs [21,22], its manifestation in transport remains indirect and confined only to low temperatures. A way to circumvent this difficulty involves measuring the lowfrequency noise, or 1 f -noise, in the channel conductivity σ, which also scales with p with independent characteristic scaling exponents [40,42], and diverges at the percolation threshold (p c ) [41]. A direct relation between the normalized noise magnitude N σ and σ thus eliminates the necessity to know either p or p c accurately.…”

“…Theoretically, clas-sical percolation-limited conductivity in metal-insulator composites is characterized by established critical exponents [21,24,25,[40][41][42][43][44], but the experimental difficulty lies in accurately determining the fraction p of the conducting region, or "puddles", embedded inside the insulating matrix. Hence despite compelling evidence of long range inhomogeneity in the charge distribution in MoS 2 FETs [21,22], its manifestation in transport remains indirect and confined only to low temperatures.…”

“…At low carrier density, for example, hopping via single particle states trapped at short-range background potential fluctuations (∼few lattice constants [23]) is incompatible to the observation of classical percolative conduction that requires long-range inhomogeneity in charge distribution, created when linear screening of the underlying charge disorder breaks down [24][25][26][27]. Observations of metal-insulator transition [7,22] [21,24,25,[40][41][42][43][44], but the experimental difficulty lies in accurately determining the fraction p of the conducting region, or "puddles", embedded inside the insulating matrix. Hence despite compelling evidence of long range inhomogeneity in the charge distribution in MoS 2 FETs [21,22], its manifestation in transport remains indirect and confined only to low temperatures.…”

“…In the 2D lattice models of random resistor network, for example, ν ≈ 0.86 or 1.5, [REF: [40,45]] whereas in the continuum percolation framework, such as the "swisscheese model" [44], ν ≈ 3.2 for random void (RV, insulating voids in a conducting background) and ≈ 0.87 for inverted random void (IRV, weakly connected conducting regions in an insulating matrix), respectively [41,42]. In this work we have investigated the switching process in TMDC FETs by simultaneously measuring N σ and σ as the electrical transport is tuned from the strongly insulating to the quasi-metallic regime using a gate voltage.…”