Cu${}_x$Bi${}_2$Se${}_3$ has been proposed as a potential topological superconductor characterized by an odd-parity full bulk superconducting gap and zero-energy surface Andreev bound states (Majorana fermions). A predicted consequence of such Majorana fermions is a peak in the zero-energy density of states, which should lead to a persistent zero bias conductance peak (ZBCP) in Andreev reflection (AR) or tunneling experiments. Here, we employ a newly developed nanoscale AR spectroscopy method to study normal metal/superconductor (N-S) devices featuring Cu${}_x$Bi${}_2$Se${}_3$. The results show that a ZBCP can be tuned in or out from Cu${}_x$Bi${}_2$Se${}_3$ samples depending on the N-S barrier strength. While the appearance of ZBCP may be traced to different origins, its absence under finite barrier strength represents the absence of zero-energy Majorana fermions. The present observations thus call for a reexamination of the intriguing superconductivity in Cu${}_x$Bi${}_2$Se${}_3$.

It is well known that one signature of the three-dimensional electron topological insulator is the Witten effect: if the system is coupled to a compact electromagnetic gauge field, a monopole in the bulk acquires a half-odd-integer polarization charge. In the present work, we propose a corresponding phenomenon for the topological insulator of bosons in three dimensions protected by particle number conservation and time-reversal symmetry. We claim that although a monopole inside a topological insulator of bosons can remain electrically neutral, its statistics are transmuted from bosonic to fermionic. We demonstrate that this “statistical Witten effect” directly implies that if the surface of the topological insulator is neither gapless, nor spontaneously breaks the symmetry, it necessarily supports an intrinsic two-dimensional topological order. Moreover, the surface properties can not be fully realized in a purely two-dimensional system. We also confirm that the surface phases of the bosonic topological insulator proposed by Vishwanath and Senthil [Phys. Rev. X 3, 011016 (2013)] provide a consistent termination of a bulk exhibiting the statistical Witten effect. In a forthcoming paper, we will provide an explicit field-theoretic, lattice-regularized construction of the three-dimensional topological insulator of bosons, employing a parton decomposition and subsequent condensation of parton-monopole composites.

We present a microscopic theory of neutral excitons and charged excitons (trions) in monolayers of transition metal dichalcogenides, including molybdenum disulfide. Our theory is based on an effective mass model of excitons and trions, parameterized by ab initio calculations and incorporating a proper treatment of screening in two dimensions. The calculated exciton binding energies are in good agreement with high-level many-body computations based on the Bethe-Salpeter equation. Furthermore, our calculations for the more complex trion species compare very favorably with recent experimental measurements and provide atomistic insight into the microscopic features which determine the trion binding energy.

Precipitate hardening is commonly used in materials science to control strength by acting on the number density, size distribution, and shape of solute precipitates in the hardened matrix. The Fe-Cu system has attracted much attention over the last several decades due to its technological importance as a model alloy for Cu steels. In spite of these efforts several aspects of its phase diagram remain unexplained. Here we use atomistic simulations to characterize the polymorphic phase diagram of Cu precipitates in body-centered cubic (BCC) Fe and establish a consistent link between their thermodynamic and mechanical properties in terms of thermal stability, shape, and strength. The size at which Cu precipitates transform from BCC to a close-packed 9R structure is found to be strongly temperature dependent, ranging from approximately 4 nm in diameter ($\sim 2700\text{atoms}$) at 200 K to about 8 nm ($\sim 22800\text{atoms}$) at 700 K. These numbers are in very good agreement with the interpretation of experimental data given Monzen et al. [Philos. Mag. A 80, 711 (2000)]. The strong temperature dependence originates from the entropic stabilization of BCC Cu, which is mechanically unstable as a bulk phase. While at high temperatures the transition exhibits first-order characteristics, the hysteresis, and thus the nucleation barrier, vanish at temperatures below approximately 300 K. This behavior is explained in terms of the mutual cancellation of the energy differences between core and shell (wetting layer) regions of BCC and 9R nanoprecipitates, respectively. The proposed mechanism is not specific for the Fe-Cu system but could generally be observed in immiscible systems, whenever the minority component is unstable in the lattice structure of the host matrix. Finally, we also study the interaction of precipitates with screw dislocations as a function of both structure and orientation. The results provide a coherent picture of precipitate strength that unifies previous calculations and experimental observations.

Cooling of a gas of trapped paraexcitons in Cu${}_2$O to 100 mK, close to the lattice temperature, is reported. We show that the activation of a transverse acoustic scattering mechanism by the applied stress is responsible for the production of ultracold excitons. This low temperature is indispensable to achieving a stable and pure Bose-Einstein condensate of three-dimensional excitons in a strongly inelastic environment.

Closed quantum systems with quenched randomness exhibit many-body localized regimes wherein they do not equilibrate, even though prepared with macroscopic amounts of energy above their ground states. We show that such localized systems can order, in that individual many-body eigenstates can break symmetries or display topological order in the infinite-volume limit. Indeed, isolated localized quantum systems can order even at energy densities where the corresponding thermally equilibrated system is disordered, i.e., localization protects order. In addition, localized systems can move between ordered and disordered localized phases via nonthermodynamic transitions in the properties of the many-body eigenstates. We give evidence that such transitions may proceed via localized critical points. We note that localization provides protection against decoherence that may allow experimental manipulation of macroscopic quantum states. We also identify a “spectral transition” involving a sharp change in the spectral statistics of the many-body Hamiltonian.

In Bi${}_2$Te${}_2$Se, the period of quantum oscillations arising from surface Dirac fermions can be increased sixfold using ionic liquid gating. At high gate voltages, the Fermi energy reaches the $N=1$ Landau level in a 14-T field. This enables the $\frac{1}{2}$ shift predicted for the Dirac spectrum to be measured accurately. A surprising result is that liquid gating strongly enhances the surface mobility. By analyzing the Hall conductivity, we show that the enhancement occurs on only one surface. We present evidence that the gating process is fully reversible (hence consistent with band bending by the $E$ field from the anion layer accumulated). In addition to the surface carriers, the experiment yields the mobility and density of the bulk carriers in the impurity band. By analyzing the charge accumulation vs gate voltage, we also obtain estimates of the depletion width and the areal depletion capacitance $C_d/A$. The value of $C_d/A$ implies an enhanced electronic polarizability in the depletion region.

We study the quantum corrections to the polarizability of isolated metallic mesoscopic systems using the loop expansion in diffusive propagators. We show that the difference between connected (grand-canonical ensemble) and isolated (canonical ensemble) systems appears only in subleading terms of the expansion, and can be neglected if the frequency of the external field, $\omega$, is of the order of (or even slightly smaller than) the mean level spacing, $\Delta$. If $\omega \ll \Delta$, the two-loop correction becomes important. We calculate it by systematically evaluating the ballistic parts (the Hikami boxes) of the corresponding diagrams and exploiting electroneutrality. Our theory allows one to take into account a finite dephasing rate, $\gamma$, generated by electron interactions, and it is complementary to the nonperturbative results obtained from a combination of random matrix theory (RMT) and the $\sigma$-model, valid at $\gamma \to 0$. Remarkably, we find that the two-loop result for isolated systems with moderately weak dephasing, $\gamma \sim \Delta$, is similar to the result of the RMT+$\sigma$-model even in the limit $\omega \to 0$. For smaller $\gamma$, we discuss the possibility to interpolate between the perturbative and the nonperturbative results. We compare our results for the temperature dependence of the polarizability of isolated rings to the experimental data of Deblock et al. [Phys. Rev. Lett. 84, 5379 (2000); Phys. Rev. B 65, 075301 (2002)], and we argue that the elusive 0D regime of dephasing might have manifested itself in the observed magneto-oscillations. Besides, we thoroughly discuss possible future measurements of the polarizability, which could aim to reveal the existence of 0D dephasing and the role of the Pauli blocking at small temperatures.

An ideal emitter of entangled photon pairs combines the perfect symmetry of an atom with the convenient electrical trigger of light sources based on semiconductor quantum dots. Our source consists of strain-free GaAs dots self-assembled on a triangular symmetric (111)$A$ surface. The emitted photons reveal a fidelity to the Bell state as high as 86($\pm 2$)% without postselection. We show a violation of Bell's inequality by more than five times the standard deviation, a prerequisite to test a quantum cryptography channel for eavesdropping. Due to the strict nonlocal nature the source can be used for real quantum processing without any postprocessing. The remaining decoherence channel of the photon source is ascribed to random charge and nuclear spin fluctuations in and near the dot.

We present a study of exchange bias generated at the interface between a polycrystalline Co film sputtered on a cleavage plane of single-crystal Ca${}_2$Ru${}_{0.98}$Fe${}_{0.02}$FeO${}_4$. The exchange bias is accompanied by an extremely large vertical magnetization shift that is characterized by 60$\%$ of the saturation magnetization in a 70-kOe cooling field. This phenomenon is seldom observed in other heterostructures. The effects of cooling-field amplitude and temperature on the exchange bias indicate that the magnetization shift results from a ferromagnetic contribution of canted moments in Ca${}_2$Ru${}_{0.98}$Fe${}_{0.02}$O${}_4$. A Type-I training effect is also observed, in which the hysteresis loop shrinks from both sides with cycling of the applied field.

We report magnetotransport measurements for the fractional quantum Hall state at filling factor $\nu =$ 5/2 as a function of applied parallel magnetic field ($B_{\left|\right|}$). As $B_{\left|\right|}$ is increased, the 5/2 state becomes increasingly anisotropic, with the in-plane resistance along the direction of $B_{\left|\right|}$ becoming more than 30 times larger than in the perpendicular direction. Despite the very large resistance anisotropy, the anisotropy ratio remains constant over a relatively large temperature range, yielding an energy gap which is the same for both directions. Our data are qualitatively consistent with a fractional quantum Hall nematic phase.

While the bulk, stoichiometric Bi${}_2$Te${}_3$ single crystals often exhibit $p$-type metallic electrical conduction due to the Bi${}_{\mathrm{Te}}$-type antisite defects, doping by thallium (Bi${}_{2-x}$Tl${}_x$Te${}_3$, $x=0-0.30$) progressively changes the electrical conduction of single crystals from $p$ type (0 ≤ $x$ ≤ 0.08) to $n$ type (0.12 ≤ $x$ ≤ 0.30). This is observed via measurements of both the Seebeck coefficient and the Hall effect performed in the crystallographic (0001) plane in the temperature range of 2–300 K. Since any kind of substitution of Tl on the Bi or Te sublattices would result in an enhancement of the density of holes rather than its decrease, and because simple incorporation of Tl at interstitial sites or in the van der Waals gap is unlikely as it would increase the lattice parameters which is not observed in experiments, incorporation of Tl likely proceeds via the formation of TlBiTe${}_2$ fragments coexisting with the quintuple layer structure of Bi${}_2$Te${}_3$. At low levels of Tl, 0 ≤ $x$ ≤ 0.05, the temperature-dependent in-plane ($I\perp c$) electrical resistivity maintains its metallic character as the density of holes decreases. Heavier Tl content with 0.08 ≤ $x$ ≤ 0.12 drives the electrical resistivity into a prominent nonmetallic regime displaying characteristic metal-insulator transitions upon cooling to below ∼100 K. At the highest concentrations of Tl, 0.20 ≤ $x$ ≤ 0.30, the samples revert back into the metallic state with low resistivity. Thermal conductivity measurements of Bi${}_2$Te${}_3$ single crystals containing Tl, as examined by the Debye-Callaway phonon conductivity model, reveal a generally stronger point-defect scattering of phonons with the increasing Tl content. The systematic evolution of transport properties suggests that the Fermi level of Bi${}_2$Te${}_{3,}$ which initially lies in the valence band (for $x$ = 0), gradually shifts toward the top of the valence band (for 0.01 ≤ $x$ ≤ 0.05), then moves into the band gap (for 0.08 ≤ $x$ ≤ 0.12), and eventually intersects the conduction band (for 0.20 ≤ $x$ ≤ 0.30).

Our experiments show that in ${}^4$He crystals, the binding of ${}^3$He impurities to dislocations does not necessarily imply their pinning. Indeed, in these crystals, there are two different regimes of the motion of dislocations when impurities bind to them. At low driving strain $\epsilon$ and frequency $\omega$, where the dislocation speed is less than a critical value (45 $\mu$m/s), dislocations and impurities apparently move together. Impurities really pin the dislocations only at higher values of $\epsilon \omega$. The critical speed separating the two regimes is two orders of magnitude smaller than the average speed of free ${}^3$He impurities in the bulk crystal lattice. We obtained this result by studying the dissipation of dislocation motion as a function of the frequency and amplitude of a driving strain applied to a crystal at low temperature. Our results solve an apparent contradiction between some experiments, which showed a frequency-dependent transition temperature from a soft to a stiff state, and other experiments or models where this temperature was assumed to be independent of frequency. The impurity pinning mechanism for dislocations appears to be more complicated than previously assumed.

We present neutron-scattering measurements on single crystals of lightly doped La${}_{2-x}$Ba${}_x$CuO${}_4$, with $0\le x\le 0.035$. These reveal the evolution of the magnetism in this prototypical doped Mott insulator from a three-dimensional (3D) commensurate (C) antiferromagnetic ground state, which orders at a relatively high $T_N$, to a two-dimensional (2D) incommensurate (IC) ground state with finite-ranged static correlations, which appear below a relatively low effective $T_N$. At low temperatures, the 2D IC magnetism coexists with the 3D C magnetism for doping concentrations as low as $\sim$0.0125. We find no signal of a 3D C magnetic ground state by $x\sim 0.025$, consistent with the upper limit of $x\sim 0.02$ observed in the sister family of doped Mott insulators, La${}_{2-x}$Sr${}_x$CuO${}_4$. The 2D IC ground states observed for $0.0125\le x\le 0.035$ are diagonal, and are rotated by 45 degrees within the orthorhombic basal plane compared with those previously reported for samples with superconducting ground states: La${}_{2-x}$Ba${}_x$CuO${}_4$, with $0.05\le x\le 0.095$. We construct a phase diagram based solely on magnetic order-parameter measurements, which displays much of the complexity of standard high-temperature superconductivity phase diagrams discussed in the literature. Analysis of high-energy resolution inelastic neutron scattering at moderately low temperatures shows a progressive depletion of the very low-energy dynamic magnetic susceptibility as $x$ increases from 0.0125 to 0.035. This low-energy, dynamic susceptibility falls off with increasing temperature on a scale much higher than the effective 2D IC $T_N$ appropriate to these materials. Appreciable dynamic 2D IC magnetic fluctuations inhabit much of the “pseudogap” regime of the phase diagram.

Low-temperature transport experiments on a $p$-type GaAs quantum dot capacitively coupled to a quantum point contact are presented. The time-averaged as well as time-resolved detection of charging events of the dot are demonstrated and they are used to extract the tunneling rates into and out of the quantum dot. The extracted rates exhibit a super-linear enhancement with the bias applied across the dot, which is interpreted in terms of a dense spectrum of excited states contributing to the transport, characteristic for heavy hole systems. The full counting statistics of charge transfer events and the effect of back action is studied. The normal cumulants as well as the recently proposed factorial cumulants are calculated and discussed in view of their importance for interacting systems.

Imaging of flux vortices in high quality MgB${}_2$ single crystals has been successfully performed in a commercial field-emission gun-based transmission electron microscope. In cryo-Lorentz microscopy, the sample quality and the vortex lattice can be monitored simultaneously, allowing one to relate microscopically the surface quality and the vortex dynamics. Such a vortex motion ultimately determines the flow resistivity ${\rho }_f$, the knowledge of which is indispensable for practical applications such as superconducting magnets or wires for magnetic resonance imaging. The observed patterns have been analyzed and compared with other studies by cryo-Lorentz microscopy or Bitter decoration. We find that the vortex lattice arrangement depends strongly on the surface quality obtained during the specimen preparation, and tends to form a hexagonal Abrikosov lattice at a relatively low magnetic field. Stripes or gossamerlike patterns, recently suggested as potential signatures of an unconventional behavior of MgB${}_2$, were not observed.

We consider the transport properties in an applied magnetic field of the spin $S=1/2$ Kondo model with ferromagnetic exchange coupling to electronic reservoirs, a description relevant for the strong-coupling limit of underscreened spin $S=1$ Kondo impurities. Because the ferromagnetic Kondo interaction is marginally irrelevant, perturbative methods should prove accurate down to low energies. For the purpose of this study, we use a combination of Majorana diagrammatic theory with density matrix numerical renormalization group simulations. In the standard case of antiferromagnetic Kondo exchange, we first show that our simple analytical technique recovers results for the $\mathcal{T}$-matrix and spin relaxation at weak coupling (above the Kondo temperature), which were previously obtained using functional renormalization tools. Considering then the ferromagnetic case, we demonstrate how the low-energy Kondo anomaly splits for arbitrary small values of the Zeeman energy, in contrast to fully screened Kondo impurities near the strong-coupling Fermi liquid fixed point, and in agreement with recent experimental findings for spin $S=1$ molecular quantum dots.

We performed tunneling spectroscopy of a carbon nanotube quantum dot (QD) coupled to a metallic reservoir either in the normal or in the superconducting state. We explore how the Kondo resonance, observed when the QD's occupancy is odd and the reservoir is normal, evolves towards Andreev bound states (ABS) in the superconducting state. Within this regime, the ABS spectrum observed is consistent with a quantum phase transition from a singlet to a degenerate magnetic doublet ground state, in quantitative agreement with a single-level Anderson model with superconducting leads.

It is argued on the basis of the BCS theory that the zero-$T$ penetration depth satisfies ${\lambda }^{-2}\left(0\right)\propto \sigma T_c$ ($\sigma$ is the normal state dc conductivity) not only in the extreme dirty limit ${\xi }_0/\ell \gg 1$, but in a broad range of scattering parameters down to ${\xi }_0/\ell \sim 1$ (${\xi }_0$ is the zero-$T$ BCS coherence length and $\ell$ is the mean free path). Hence, the scaling ${\lambda }^{-2}\left(0\right)\propto \sigma T_c$, suggested as a new universal property of superconductors [Dordevic, Basov, and Homes, Sci. Rep. 3, 1713 (2013)], finds a natural explanation within the BCS theory.

We have completely determined the Fermi surface in KFe${}_2$As${}_2$ via de Haas–van Alphen (dHvA) measurements. Fundamental frequencies $\epsilon$, $\alpha$, $\zeta$, and $\beta$ are observed in KFe${}_2$As${}_2$. The first one is attributed to a hole cylinder near the $X$ point of the Brillouin zone while the others to hole cylinders at the $\Gamma$ point. We also observe magnetic breakdown frequencies between $\alpha$ and $\zeta$ and suggest a plausible explanation for them. The experimental frequencies show deviations from frequencies predicted by band-structure calculations. Large effective masses up to 19 $m_e$ for $B\parallel c$ have been found, $m_e$ being the free-electron mass. The carrier number and Sommerfeld coefficient of the specific heat are estimated to be 1.01–1.03 holes per formula unit and 82–94 mJmol${}^{-1}$ K${}^{-2}$, respectively, which are consistent with the chemical stoichiometry and a direct measure of 93 mJmol${}^{-1}$ K${}^{-2}$ [Fukazawa et al., J. Phys. Soc. Jpn. 80, SA118 (2011)]. The Sommerfeld coefficient is about nine times enhanced over a band value, suggesting the importance of low-energy spin and/or orbital fluctuations, and places KFe${}_2$As${}_2$ among strongly correlated metals. We have also performed dHvA measurements on Ba${}_{0.07}$K${}_{0.93}$Fe${}_2$As${}_2$ and have observed the $\alpha$ and $\beta$ frequencies.