Fermi-edge singularity in resonant tunneling

Geim, A. K.; Main, P. C.; Scala, Newton La; Eaves, L.; Foster, T.J.; Beton, Peter H.; Sakai, J.W.; Sheard, F. W.; Henini, M.; Hill, G.; Pate, M.A.

doi:10.1103/physrevlett.72.2061

Cited by 171 publications

(117 citation statements)

References 24 publications

(17 reference statements)

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“…Being one of the very few known examples of a solvable nonequilibrium many-body problems, the OC also provides a conceptual framework for understanding several fundamental phenomena in solid-state physics, including the Kondo effect [17], resonant tunneling in mesoscopic structures [18][19][20][21][22][23], 1D quantum physics beyond the Luttinger-liquid paradigm [24][25][26], and the motion of a heavy particle in a Fermi gas [27]. For a recent review of the OC, see Ref.…”

Section: Introductionmentioning

confidence: 99%

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Time-Dependent Impurity in Ultracold Fermions: Orthogonality Catastrophe and Beyond

et al. 2012

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The recent experimental realization of strongly imbalanced mixtures of ultracold atoms opens new possibilities for studying impurity dynamics in a controlled setting. In this paper, we discuss how the techniques of atomic physics can be used to explore new regimes and manifestations of Anderson's orthogonality catastrophe (OC), which could not be accessed in solid-state systems. Specifically, we consider a system of impurity atoms, localized by a strong optical-lattice potential, immersed in a sea of itinerant Fermi atoms. We point out that the Ramsey-interference-type experiments with the impurity atoms allow one to study the OC in the time domain, while radio-frequency (RF) spectroscopy probes the OC in the frequency domain. The OC in such systems is universal, not only in the long-time limit, but also for all times and is determined fully by the impurity-scattering length and the Fermi wave vector of the itinerant fermions. We calculate the universal Ramsey response and RF-absorption spectra. In addition to the standard power-law contributions, which correspond to the excitation of multiple particle-hole pairs near the Fermi surface, we identify a novel, important contribution to the OC that comes from exciting one extra particle from the bottom of the itinerant band. This contribution gives rise to a nonanalytic feature in the RF-absorption spectra, which shows a nontrivial dependence on the scattering length, and evolves into a true power-law singularity with the universal exponent 1=4 at the unitarity. We extend our discussion to spin-echo-type experiments, and show that they probe more complicated nonequilibirum dynamics of the Fermi gas in processes in which an impurity switches between states with different interaction strength several times; such processes play an important role in the Kondo problem, but remained out of reach in the solid-state systems. We show that, alternatively, the OC can be seen in the energy-counting statistics of the Fermi gas following a sudden quench of the impurity state. The energy distribution function, which can be measured in time-of-flight experiments, exhibits characteristic power-law singularities at low energies. Finally, systems in which the itinerant fermions have two or more hyperfine states provide an even richer playground for studying nonequilibrium impurity physics, allowing one to explore the nonequilibrium OC and even to simulate quantum transport through nanostructures. This provides a previously missing connection between cold atomic systems and mesoscopic quantum transport.

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Section: Introductionmentioning

confidence: 99%

“…[18][19][20][21][22][23][51][52][53][54][55][56][57]), it is useful to start by summarizing the new aspects of the OC in cold atomic systems.…”

Section: Introductionmentioning

confidence: 99%

Time-Dependent Impurity in Ultracold Fermions: Orthogonality Catastrophe and Beyond

et al. 2012

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“…Recently, we developed a technique to image the LDOS in heavily doped GaAs [7], which is based on resonant tunneling through impurity states [5,[8][9][10] in asymmetric double-barrier heterostructures. In agreement with theory [4,5], we found at low magnetic fields strong irregular LDOS fluctuations [7].…”

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confidence: 99%

Observation of the Local Structure of Landau Bands in a Disordered Conductor

et al. 1997

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“…In the tunneling-spectroscopy experiments [21,22,10,11,23,24,[12][13][14] the measured quantity is a resonant-tunneling current, I sd , through a localized impurity state as a function of the source-drain bias, V sd . Such an impurity plays the role of a "spectrometer" since its energy position, ǫ 0 , changes with V sd .…”

Section: Manifestation In the Tunneling Spectroscopymentioning

confidence: 99%

“…Within a narrow range, δV , of V sd this change is linear, i.e., ∆ = ǫ 0 (V +δV )−ǫ 0 (V ) ≈ βδV , where β is the structure-specific parameter. Experimentally [21,22,10,11,23,24,[12][13][14], measurements are performed in the plateau regime when the temperature is much lower than V sd , so that the value of resonant-tunneling current…”

Section: Manifestation In the Tunneling Spectroscopymentioning

confidence: 99%

Spin-orbit-induced correlations of the local density of states in a two-dimensional electron gas

2006

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We study the local density of states (LDOS) of two-dimensional electrons in the presence of spin-orbit (SO) coupling. Although SO coupling has no effect on the average density of states, it manifests itself in the correlations of the LDOS. Namely, the correlation function acquires two satellites centered at energy difference equal to the SO splitting, 2ωSO, of the electron Fermi surface. For a smooth disorder the satellites are well separated from the main peak. Weak Zeeman splitting ωZ ≪ ωSO in a parallel magnetic field causes an anomaly in the shape of the satellites. We consider the effect of SO-induced satellites in the LDOS correlations on the shape of the correlation function of resonant-tunneling conductances at different source-drain biases, which can be measured experimentally. This shape is strongly sensitive to the relation between ωSO and ωZ.

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Fermi-edge singularity in resonant tunneling

Cited by 171 publications

References 24 publications

Time-Dependent Impurity in Ultracold Fermions: Orthogonality Catastrophe and Beyond

Time-Dependent Impurity in Ultracold Fermions: Orthogonality Catastrophe and Beyond

Observation of the Local Structure of Landau Bands in a Disordered Conductor

Spin-orbit-induced correlations of the local density of states in a two-dimensional electron gas

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