Critical conductivity exponent of Si:P in a magnetic field

Dai, Peihua; Zhang, Youzhu; Bogdanovich, S.; Sarachik, M. P.

doi:10.1103/physrevb.48.4941

Cited by 29 publications

(33 citation statements)

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“…Measurements were taken at temperatures between 0.037 K and 0.5 K in magnetic fields up to 90 kOe. Sample characterization and measurement techniques are described elsewhere [7,11].At temperatures sufficiently low that corrections due to localization are small, finite temperature corrections due to interactions are expected to yield a conductivity [12,13,14,15]:in the absence of a magnetic field. The slope A(n) = (σ ex −σ Har )/T 1/2 , where the exchange term, σ ex , and the Hartree term, σ Har , contribute with opposite sign.…”

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confidence: 99%

Metal-insulator transition in Si:X(X=P,B): Anomalous response to a magnetic field

et al. 1998

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The zero-temperature magnetoconductivity of just-metallic Si:P scales with magnetic field, H, and dopant concentration, n, lying on a single universal curve: σ(n, H)/σ(n, 0) = G[H −δ ∆n] with δ ≈ 2. We note that Si:P, Si:B, and Si:As all have unusually large magnetic field crossover exponents near 2, and suggest that this anomalously weak response to a magnetic field is a common feature of uncompensated doped semiconductors.PACS numbers: 71.30.+hThe metal-insulator transition (MIT) that occurs in doped semiconductors and in amorphous metalsemiconductor mixtures is a continuous phase transition [1,2,3]. Some difficulty has been encountered in demonstrating the scaling that is expected to hold near such a transition. Scaling with temperature and dopant concentration has been shown to hold for Si:P in the presence of a magnetic field of 75 kOe [2]. However, the conductivity does not appear to scale with temperature in the absence of a magnetic field: scaling [4] is obtained only if one chooses a critical conductivity exponent, µ ≈ 0.29, considerably smaller than the value found experimentally [5,6,7]. On the other hand, scaling of the zerotemperature conductivity has been demonstrated with magnetic field for p-type Si:B [8], albeit with an anomalously large magnetic field crossover exponent near 2. This raises the issue whether the anomalously weak response to a magnetic field is due to the spin-orbit scattering present in boron-doped silicon, or whether it is a general feature of uncompensated doped semiconductors near the metal-insulator transition. Si:P is considered the archetypical strongly correlated disordered system, and is used as a standard against which newer materials are compared [9]. It is therefore of great fundamental interest to determine the functional form of the magnetoresistance close to its MIT.To address these issues, we report measurements of the magnetoconductivity of Si:P. Detailed analysis of data taken at low temperatures in magnetic fields to 90 kOe allows us to identify separate, temperature-dependent components, yielding reliable determinations of the zerotemperature conductivity.Our results demonstrate that the zero-temperature conductivity scales with magnetic field and dopant concentrations, σ(n, H)/σ(n, 0) = G(H −δ ∆n) = F (H/H * ), with a crossover exponent, δ ≈ 2, comparable to the anomalously large crossover exponent of Si:B [8]. Moreover, earlier data of Shafarman et al. [10] indicate that the magnetoconductance of Si:As strongly resembles that of Si:P, scaling with a similar crossover function and exponent. We note that all the silicon-based doped semiconductors exhibit an anomalously weak response to a magnetic field, and suggest that this is a feature of the universality class of silicon-based doped semiconductors that is currently not understood.Four Czochralski-grown Si:P samples were used in our studies with dopant concentrations 3.60, 3.66, 3.95 and 4.21 × 10 18 cm −3 . Based on a critical concentration n c = 3.46 × 10 18 cm −3 [7], this corresponds to 1.04n c , 1.06n c...

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Metal-insulator transition in Si:X(X=P,B): Anomalous response to a magnetic field

et al. 1998

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“…Experimentally, µ ≈ 1 has been found for magnetic inductions B on the order of one tesla for nominally uncompensated semiconductors: Ge:Sb, 15,16 Si:B, 17 and Si:P (Ref. 18). Since these systems result in different values of µ ranging from 0.5 to 1.0 at B = 0, the applied magnetic field changes the value of µ for certain systems (Si:B and Si:P), while it does not 16 or does only change little 15 for the other (Ge:Sb).…”

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confidence: 99%

“…This result was obtained from precisely doped samples with a perfectly random distribution of impurities; our 70 Ge:Ga samples were prepared by neutrontransmutation doping (NTD), in which an ideally random distribution of dopants is inherently guaranteed down to the atomic level. [20][21][22][23] For the case of melt-(or metallurgically) doped samples that have been employed in most of the previous studies, [3][4][5][15][16][17][18][19] the spatial fluctuation of N due to dopant striations and segregation can easily be on the order of 1% or more across a typical sample for the four-point resistance measurement (length of ∼5 mm or larger), 24 and hence, it will not be meaningful to discuss physical properties in the critical regime (e.g., |N/N c − 1| < 0.01), unless one evaluates the macroscopic inhomogeneity in the samples and its influence on the results. A homogeneous distribution of impurities is important also for experiments in magnetic fields.…”

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Metal-insulator transition of isotopically enriched neutron-transmutation-doped70Ge:Gain magnetic fields

et al. 1999

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We have investigated the temperature dependence of the electrical conductivity σ(N, B, T ) of nominally uncompensated, neutron-transmutation-doped 70 Ge:Ga samples in magnetic fields up to B = 8 T at low temperatures (T = 0.05 − 0.5 K). In our earlier studies at B = 0, the critical exponent µ = 0.5 defined by σ(N, 0, 0) ∝ (N − Nc) µ has been determined for the same series of 70 Ge:Ga samples with the doping concentration N ranging from 1.861×10 17 cm −3 to 2.434×10 17 cm −3 . In magnetic fields, the motion of carriers loses time-reversal symmetry, the universality class may change and with it the value of µ. In this work, we show that magnetic fields indeed affect the value of µ (µ changes from 0.5 at B = 0 to 1.1 at B ≥ 4 T). The same exponent µ ′ = 1.1 is also found in the magnetic-field-induced MIT for three different 70 Ge:Ga samples, i.e., σ (Nwhere Bc(N ) is the concentration-dependent critical magnetic induction. We show that σ(N, B, 0) obeys a simple scaling rule on the (N, B) plane. Based on this finding, we derive from a simple mathematical argument that µ = µ ′ as has been observed in our experiment. 71.30.+h, 72.80.Cw

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“…Spin-orbit interaction is also known to be small for P-doped (bulk) Si and Ge [22,23], and independent of the density of the dopants. Any long range magnetic order is also unlikely because the Hall resistance was found to vary linearly with B ⊥ at all T (see SI, section S7) in all our devices [17].…”

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Spontaneous Breaking of Time-Reversal Symmetry in Strongly Interacting Two-Dimensional Electron Layers in Silicon and Germanium

et al. 2014

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We report experimental evidence of a remarkable spontaneous time reversal symmetry breaking in two dimensional electron systems formed by atomically confined doping of phosphorus (P) atoms inside bulk crystalline silicon (Si) and germanium (Ge). Weak localization corrections to the conductivity and the universal conductance fluctuations were both found to decrease rapidly with decreasing doping in the Si:P and Ge:P δ−layers, suggesting an effect driven by Coulomb interactions. In-plane magnetotransport measurements indicate the presence of intrinsic local spin fluctuations at low doping, providing a microscopic mechanism for spontaneous lifting of the time reversal symmetry. Our experiments suggest the emergence of a new many-body quantum state when two dimensional electrons are confined to narrow half-filled impurity bands.Invariance to time reversal is among the most fundamental and robust symmetries of nonmagnetic quantum systems. Its violation often leads to new and exotic phenomena, particularly in two dimensions (2D), such as the quantized Hall conductance in semiconductor heterostructures [1], the quantum anomalous Hall effect in topological insulators [2] or the predicted chiral superconductivity in graphene [3]. The breaking of time reversal invariance is experimentally achieved either by an external magnetic field or intentional magnetic doping. Here we show that strong Coulomb interactions can also lift the time reversal symmetry in nonmagnetic 2D systems at zero magnetic field.While bulk P-doped Si and Ge have been extensively studied in the context of electron localization in three dimensions [4][5][6][7][8][9], confining the dopants to one or few atomic planes (δ−layers) of the host semiconductor has recently led to a new class of 2D electron system [10][11][12][13]. Electron transport in these atomically confined 2D layers occurs within a 2D impurity band where the effective Coulomb interaction is parameterized in terms of U/γ, with U being the Coulomb energy required to add an additional electron to a dopant site, and γ, the hopping integral between adjacent dopants. Since each dopant P atom contributes one valence electron, the impurity band is intrinsically 'half filled' (schematic in Fig. 1a), which reinforces the interaction effects due to the inbuilt electron-hole symmetry, and forms an ideal platform to explore the rich phenomenology of the 2D MottHubbard model, ranging from Mott metal-insulator transition (MIT) to novel spin excitations and magnetic ordering [14][15][16][17].In this Letter we show evidence of spontaneously broken time reversal symmetry in 2D Si:P and Ge:P δ-layers as the on-site effective Coulomb interaction is increased by decreasing the doping density of P atoms. Quantum transport and noise experiments indicate a strong suppression of quantum interference effects at low doping densities. We could attribute this to a spontaneous breaking of time reversal symmetry which manifest in an unambiguous suppression of universal conductance fluctuations (UCF) at zero magnetic fiel...

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Critical conductivity exponent of Si:P in a magnetic field

Cited by 29 publications

References 24 publications

Metal-insulator transition in Si:X(X=P,B): Anomalous response to a magnetic field

Metal-insulator transition in Si:X(X=P,B): Anomalous response to a magnetic field

Metal-insulator transition of isotopically enriched neutron-transmutation-doped70Ge:Gain magnetic fields

Spontaneous Breaking of Time-Reversal Symmetry in Strongly Interacting Two-Dimensional Electron Layers in Silicon and Germanium

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