Quantum In-Plane Magnetoresistance in 2D Electron Systems

Meyer, Jacques; Altshuler, B. L.

doi:10.1007/978-94-010-0530-2_7

Cited by 8 publications

(15 citation statements)

References 57 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This result, also given in 43 , is a finite-temperature generalization of the expression used by Benoit et al 59 A rigorous theoretical calculation of the Aharonov-Bohm oscillation amplitude ∆G h/e in presence of magnetic impurities under a large externally applied magnetic field was first presented by Fal'ko. 60 .…”

Section: Appendix C: Magnetic Field Dependence Of Spin-flip Scatsupporting

confidence: 52%

Dephasing of electrons in mesoscopic metal wires

et al. 2003

View full text Add to dashboard Cite

We have extracted the phase coherence time τ φ of electronic quasiparticles from the low field magnetoresistance of weakly disordered wires made of silver, copper and gold. In samples fabricated using our purest silver and gold sources, τ φ increases as T −2/3 when the temperature T is reduced, as predicted by the theory of electron-electron interactions in diffusive wires. In contrast, samples made of a silver source material of lesser purity or of copper exhibit an apparent saturation of τ φ starting between 0.1 and 1 K down to our base temperature of 40 mK. By implanting manganese impurities in silver wires, we show that even a minute concentration of magnetic impurities having a small Kondo temperature can lead to a quasi saturation of τ φ over a broad temperature range, while the resistance increase expected from the Kondo effect remains hidden by a large background. We also measured the conductance of Aharonov-Bohm rings fabricated using a very pure copper source and found that the amplitude of the h/e conductance oscillations increases strongly with magnetic field. This set of experiments suggests that the frequently observed "saturation" of τ φ in weakly disordered metallic thin films can be attributed to spin-flip scattering from extremely dilute magnetic impurities, at a level undetectable by other means. I. MOTIVATIONSThe time τ φ during which the quantum coherence of an electron is maintained is of fundamental importance in mesoscopic physics. The observability of many phenomena specific to this field relies on a long enough phase coherence time. 1 Amongst these are the weak localization correction to the conductance (WL), the universal conductance fluctuations (UCF), the Aharonov-Bohm (AB) effect, persistent currents in rings, the proximity effect near the interface between a superconductor and a normal metal, and others. Hence it is crucial to find out what mechanisms limit the quantum coherence of electrons.In metallic thin films, at low temperature, electrons experience mostly elastic collisions from sample boundaries, defects of the ion lattice and static impurities in the metal. These collisions do not destroy the quantum coherence of electrons. Instead they can be pictured as resulting from a static potential on which the diffusivelike electronic quantum states are built.What limits the quantum coherence of electrons are inelastic collisions. These are collisions with other electrons through the screened Coulomb interaction, with phonons, and also with extrinsic sources such as magnetic impurities or two level systems in the metal. Whereas above about 1 K electron-phonon interactions are known to be the dominant source of decoherence, 2 electron-electron interactions are expected to be the leading inelastic process at lower temperatures in samples without extrinsic sources of decoherence. 3 The theory of electron-electron interactions in the diffusive regime was worked out in the early 1980's (for a review see 4 ). It predicts a power law divergence of τ φ when the temperature T goes to zero....

show abstract

Section: Appendix C: Magnetic Field Dependence Of Spin-flip Scatsupporting

confidence: 52%

Dephasing of electrons in mesoscopic metal wires

et al. 2003

View full text Add to dashboard Cite

show abstract

“…The irrelevancy of the inelastic vertex for processes with typical energy transfer larger than 1= ' has been observed before by several authors (e.g., [11,14,17]): Semiclassically, vertex corrections describe the interference of two (time-reversed) electrons undergoing an interaction process [see Fig. 2(a)].…”

mentioning

confidence: 61%

Universal Dephasing Rate due to Diluted Kondo Impurities

et al. 2006

View full text Add to dashboard Cite

We calculate the dephasing rate due to magnetic impurities in a weakly disordered metal as measured in a weak-localization experiment. If the density n S of magnetic impurities is sufficiently low, the dephasing rate 1= ' is a universal function, 1= ' n S =fT=T K , where T K is the Kondo temperature and is the density of states. We show that inelastic vertex corrections with a typical energy transfer E are suppressed by powers of 1= ' E / n S . Therefore, the dephasing rate can be calculated from the inelastic cross section proportional to ImT ÿ jTj 2 , where T is the T matrix which is evaluated numerically exactly using the numerical renormalization group. DOI: 10.1103/PhysRevLett.96.226601 PACS numbers: 72.15.Lh, 72.15.Qm, 72.15.Rn, 75.20.Hr Dephasing, i.e., the loss of wave coherence, is a ubiquitous phenomenon in the quantum mechanics of complex systems. It is of relevance to any experiment where both interference and interactions play a role and is, therefore, of profound importance in all areas of nanoscopic and mesoscopic physics.While the basic phenomenon of dephasing as such is of a rather general nature, the concrete definition of a dephasing rate and its experimental determination vary from context to context. In this Letter, we consider the dephasing rate as determined by weak-localization (WL) measurements in metals [1]. In weakly disordered metals, the interference of electronic wave functions on time-reversed paths leads to a characteristic reduction (or enhancement in the presence of spin-orbit interactions) of the conductivity. The magnitude of this effect is controlled by the dephasing time ' -the typical time scale over which electrons get entangled with their environment (phonons, other electrons, or dynamical impurities), thereby losing the ability to interfere. Even small magnetic fields break time-reversal invariance, thus prohibiting the interference of time-reversed paths. Fitting the magnetoresistivity to WL theory is a means to determine the dephasing rate 1= ' with high precision. Surprisingly, most of these experiments [2] show a saturation of the dephasing rate at the lowest accessible temperatures T, while theoretically it is expected that in the limit T ! 0 all inelastic processes freeze out when the system approaches its (time-reversal invariant and unique) ground state. This has led to an intense discussion [2 -5] as to whether quantum fluctuations can induce dephasing at T 0. While we believe that this latter scenario is theoretically excluded for electrons in a disordered metal, the presence of only a few parts per million of dynamical impurities -realized by atomic two-level systems [6] or by magnetic impurities [7-10]-may be an alternative cause of the saturation phenomenon. Indeed, it has been shown experimentally that magnetic impurities lead to an apparent saturation of 1= ' at least in some T range [9]. In contrast, some extremely pure Au and Ag samples with a negligible concentration of impurities [10] show no saturation and seem to follow the predictions of Altshu...

show abstract

“…The logarithmic increase in the magnetoconductivity at large B , as shown in Fig. 4a, was observed in all devices irrespective of doping level, and known to represent suppression of weak localization due to the finite width of the δ-layers [36]. However, the negative magnetoconductivity around B = 0 often indicates the presence of local moments, because localization strengthens as phase coherence increases with the freezing of spin-flip scattering [36,37].…”

mentioning

confidence: 76%

“…However, the negative magnetoconductivity around B = 0 often indicates the presence of local moments, because localization strengthens as phase coherence increases with the freezing of spin-flip scattering [36,37]. In such a case, the activated spin-flip processes across the Zeeman gap, leads to magnetoconductivity decreasing linearly with B as ∆σ(B ) = −ηB /T , where η ∼ e 2 g imp µ B /hk B , and g imp is the g-factor of the magnetic impurity [36]. As shown in Fig.…”

mentioning

confidence: 99%

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

et al. 2014

View full text Add to dashboard Cite

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...

show abstract

Quantum In-Plane Magnetoresistance in 2D Electron Systems

Cited by 8 publications

References 57 publications

Dephasing of electrons in mesoscopic metal wires

Dephasing of electrons in mesoscopic metal wires

Universal Dephasing Rate due to Diluted Kondo Impurities

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

Contact Info

Product

Resources

About