We have accurately measured the effective mass in a dilute two-dimensional electron system in silicon by analyzing temperature dependence of the Shubnikov-de Haas oscillations in the lowtemperature limit. A sharp increase of the effective mass with decreasing electron density has been observed. Using tilted magnetic fields, we have found that the enhanced effective mass is independent of the degree of spin polarization, which points to a spin-independent origin of the mass enhancement and is in contradiction with existing theories.PACS numbers: 71.30.+h,73.40.Qv,71.18.+y The ground state of an ideal, strongly interacting two-dimensional (2D) electron system is predicted to be Wigner crystal [1]. The strength of the interactions is usually characterized by the ratio between the Coulomb energy and the Fermi energy, r s = E c /E F . Assuming that the effective electron mass is equal to the band mass, the interaction parameter r s in the single-valley case reduces to the Wigner-Seitz radius, 1/(πn s ) 1/2 a B and therefore increases as the electron density, n s , decreases (here a B is the Bohr radius in semiconductor). In the strongly-interacting limit, no analytical theory has been developed to date. According to numeric simulations [2], Wigner crystallization is expected in a very dilute regime, when r s reaches approximately 35. The refined numeric simulations [3] have predicted that prior to the crystallization, in the range of the interaction parameter 25 r s 35, the ground state of the system is a strongly correlated ferromagnetic Fermi liquid. At yet higher electron densities, at r s ∼ 1, the (weaklyinteracting) electron liquid is expected to be paramagnetic, with the effective mass, m, and Landé g factor renormalized by interactions. Enhancement of g and m within the Fermi liquid theory is due to spin exchange effects, with renormalization of the g factor being dominant compared to that of the effective mass [4]. In contrast, the dominant increase of m near the onset of Wigner crystallization follows from an alternative description of the strongly-interacting electron system beyond the Fermi liquid approach, which also predicts the renormalization of m to be strongly sensitive to the polarization of spins [5,6].In dilute silicon metal-oxide-semiconductor-fieldeffect-transistors (MOSFETs), a strong metallic temperature dependence of the resistance was observed a decade ago [7]. Although this anomaly was almost immediately attributed to strong electron-electron interactions, only after a strongly enhanced ratio of the spin and the cyclotron splittings was found at low n s [8] has it become clear that the system behaves well beyond the weakly interacting Fermi liquid. Later, it was reported that the magnetic field required to produce complete spin polarization, B c ∝ n s /gm, tends to vanish at a finite electron density ≈ 8 × 10 10 cm −2 [9, 10]. These findings point to a sharp increase of the spin susceptibility and possible ferromagnetic instability in dilute silicon MOSFETs. In very dilute GaAs/AlGaAs he...

Sequencing the genomes of individual cancer cells provides the highest resolution picture of intratumoral heterogeneity. To enable high throughput single cell DNA-Seq across thousands of individual cells per sample, we developed a droplet-based, automated partitioning technology for whole genome sequencing. We applied this approach on a set of gastric cancer cell lines and a primary gastric tumor. In parallel, we conducted a separate single cell RNA-Seq analysis on these same cancers and used copy number to compare results. This joint study, covering thousands of single cell genomes and transcriptomes, revealed extensive cellular diversity based on distinct copy number changes, numerous subclonal populations and in the case of the primary tumor, subclonal gene expression signatures. We found genomic evidence of positive selection - where the percentage of replicating cells per clone is higher than expected - indicating ongoing tumor evolution. Our study demonstrates that joining single cell genomic DNA and transcriptomic features provides novel insights into cancer heterogeneity and biology.

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We have studied corrections to conductivity due to the coherent backscattering in low-disordered two-dimensional electron systems in silicon for a range of electron densities including the vicinity of the metal-insulator transition, where the dramatic increase of the spin susceptibility has been observed earlier. We show that the corrections, which exist deeper in the metallic phase, weaken upon approaching the transition and practically vanish at the critical density, thus suggesting that the localization is suppressed near and at the transition even in zero field.

We show that in dilute metallic p-SiGe heterostructures, magnetic field can cause multiple quantum Hall-insulator-quantum Hall transitions. The insulating states are observed between quantum Hall states with filling factors ν = 1 and 2 and, for the first time, between ν = 2 and 3 and between ν = 4 and 6. The latter are in contradiction with the original global phase diagram for the quantum Hall effect. We suggest that the application of a (perpendicular) magnetic field induces insulating behaviour in metallic p-SiGe heterostructures in the same way as in Si MOSFETs. This insulator is then in competition with, and interrupted by, integer quantum Hall states leading to the multiple re-entrant transitions. The phase diagram which accounts for these transition is similar to that previously obtained in Si MOSFETs thus confirming its universal character.