Theory of the soft-x-ray edge problem in simple metals: historical survey and recent developments

Ohtaka, K.; Tanabe, Yukito

doi:10.1103/revmodphys.62.929

Cited by 211 publications

(197 citation statements)

References 133 publications

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“…The valley and spin (VS) degrees are coupled because of the lack of inversion symmetry in monolayer MoS 2 . As has been recently shown experimentally, this allows optical pumping of a single valley (and spin) with circularly polarized light [7][8][9] .…”

mentioning

confidence: 96%

“…The optical response of a doped direct-gap semiconductor in 2D has been extensively investigated theoretically 5, 8,11,12 . At low-temperature, the many-body interactions are predicted to give rise to a single-sided power-law dependence for the absorption spectrum !…”

Section: S3 Many-body Optical Response Of a Doped 2d Semiconductormentioning

confidence: 99%

“…In general there could be other types of excitations, such as continua. The power-law spectral dependence arises from a real-time dependence of for the optical conductivity of the n-doped 2D semiconductor following the creation of a hole by optical excitation 5,8 . It reflects the evolution of the 2DEG to a new equilibrium configuration of excitation X 5, 8 .…”

Section: S3 Many-body Optical Response Of a Doped 2d Semiconductormentioning

confidence: 99%

“…In contrast to graphene, monolayer MoS 2 is a non-centrosymmetric material with a direct energy gap 2-5 . Strong photoluminescence 2,3 , a current on-off ratio exceeding 10 8 in field-effect transistors 6 , and efficient valley and spin control by optical helicity [7][8][9] have recently been demonstrated in this material. Here we report the spectroscopic identification in doped monolayer MoS 2 of tightly bound negative trions, a quasi-particle composed of two electrons and a hole.…”

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Tightly bound trions in monolayer MoS2

Mak¹,

He²,

Lee³

et al. 2012

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Two-dimensional (2D) atomic crystals, such as graphene and transition-metal dichalcogenides, have emerged as a new class of materials with remarkable physical properties 1 . In contrast to graphene, monolayer MoS 2 is a non-centrosymmetric material with a direct energy gap 2-5 . Strong photoluminescence 2,3 , a current on-off ratio exceeding 10 8 in field-effect transistors 6 , and efficient valley and spin control by optical helicity 7-9 have recently been demonstrated in this material. Here we report the spectroscopic identification in doped monolayer MoS 2 of tightly bound negative trions, a quasi-particle composed of two electrons and a hole. These quasiparticles, which can be created with valley and spin polarized holes, have no analogue in other materials. They also possess a large binding energy (~ 20 meV), rendering them significant even at room temperature. Our results open up new avenues both for fundamental studies of many-body interactions and for optoelectronic and valleytronic applications in 2D atomic crystals.The trion binding energy that we observe in monolayer MoS 2 is nearly an order of magnitude larger than that found in conventional quasi-2D systems, such as semiconductor quantum wells (QWs) [10][11][12][13] . This is a consequence of the greatly enhanced Coulomb interactions in monolayer MoS 2 , arising from reduced dielectric screening in gapped 2D crystals and the relatively heavy carrier band masses associated with the Mo d-manifolds 4,5,14 . For an electron density as high as n = 10 11 cm -2 , for instance, the dimensionless interaction parameter r s is ~60 in monolayer MoS 2 (Supplementary Information S1). This value is significantly larger than that for carriers in QWs even at very low doping levels 15 . Monolayer MoS 2 is a strongly interacting system even in the presence of relatively high carrier densities; it thus presents an ideal laboratory for exploring many-body phenomena, such as carrier multiplication and Wigner crystallization 16 .The atomic structure of MoS 2 consists of hexagonal planes of S and Mo atoms in a trigonal prismatic structure (Fig. 1a) 17 . The two sublattices of the hexagonal MoS 2 structure are occupied, respectively, by one Mo and two S atoms (Fig. 1b). Monolayer MoS 2 is a direct gap semiconductor with energy gaps located at the K and K' points of the Brillouin zone (Fig. 1c). Both the highest valence bands and the lowest conduction bands are formed primarily from the Mo d-orbitals 4,17 . The large spin-orbit interaction 2 splits the highest valence bands at the K (K') point by ~ 160 meV 2,3,7,14,18 . The valley and spin (VS) degrees are coupled because of the lack of inversion symmetry in monolayer MoS 2 . As has been recently shown experimentally, this allows optical pumping of a single valley (and spin) with circularly polarized light 7-9 .Here we investigate the optical response of monolayer MoS 2 as a function of carrier density by means of absorption and photoluminescence (PL) spectroscopy. In our investigations we have made use of MoS 2 monolayers p...

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mentioning

confidence: 96%

Section: S3 Many-body Optical Response Of a Doped 2d Semiconductormentioning

confidence: 99%

Section: S3 Many-body Optical Response Of a Doped 2d Semiconductormentioning

confidence: 99%

mentioning

confidence: 99%

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Tightly bound trions in monolayer MoS2

Mak¹,

He²,

Lee³

et al. 2012

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“…[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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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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Optical Properties of Metals and Inelastic Scattering

Marder¹

2010

Condensed Matter Physics

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Theory of the soft-x-ray edge problem in simple metals: historical survey and recent developments

Cited by 211 publications

References 133 publications

Tightly bound trions in monolayer MoS2

Tightly bound trions in monolayer MoS2

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

Optical Properties of Metals and Inelastic Scattering

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