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Monolayer transition-metal dichalcogenides in the T′ phase could enable the realization of the quantum spin Hall effect1 at room temperature, because they exhibit a prominent spin–orbit gap between inverted bands in the bulk2,3. Here we show that the binding energy of electron–hole pairs excited through this gap is larger than the gap itself in the paradigmatic case of monolayer T′ MoS2, which we investigate from first principles using many-body perturbation theory4. This paradoxical result hints at the instability of the T′ phase in the presence of spontaneous generation of excitons, and we predict that it will give rise to a reconstructed ‘excitonic insulator’ ground state5–7. Importantly, we show that in this monolayer system, topological and excitonic order cooperatively enhance the bulk gap by breaking the crystal inversion symmetry, in contrast to the case of bilayers8–16 where the frustration between the two orders is relieved by breaking time reversal symmetry13,15,16. The excitonic topological insulator is distinct from the bare topological phase because it lifts the band spin degeneracy, which results in circular dichroism. A moderate biaxial strain applied to the system leads to two additional excitonic phases, different in their topological character but both ferroelectric17,18 as an effect of electron–electron interaction.Topological insulators have been studied primarily with regard to the behaviour of electrons. A theoretical study now shows that a single layer of a metal dichalcogenide can become a topological insulator for excitons.

We present evidence that the two-dimensional bulk of monolayer WTe 2 contains electrons and holes bound by Coulomb attraction—excitons—that spontaneously form in thermal equilibrium. On cooling from room temperature to 100 K, the conductivity develops a V-shaped dependence on electrostatic doping, while the chemical potential develops a step at the neutral point. These features are much sharper than is possible in an independent-electron picture, but they can be accounted for if electrons and holes interact strongly and are paired in equilibrium. Our calculations from first principles show that the exciton binding energy is larger than 100 meV and the radius as small as 4 nm, explaining their formation at high temperature and doping levels. Below 100 K, more strongly insulating behaviour is seen, suggesting that a charge-ordered state forms. The observed absence of charge density waves in this state is surprising within an excitonic insulator picture, but we show that it can be explained by the symmetries of the exciton wavefunction. Therefore, in addition to being a topological insulator, monolayer WTe 2 exhibits strong correlations over a wide temperature range. Exciton condensation has been observed in various three-dimensional (3D) materials. Now, monolayer WTe 2 —a 2D topological insulator—also shows the phenomenon. Strong electronic interactions allow the excitons to form and condense at high temperature.

Fifty years ago Walter Kohn speculated that a zero-gap semiconductor might be unstable against the spontaneous generation of excitons–electron–hole pairs bound together by Coulomb attraction. The reconstructed ground state would then open a gap breaking the symmetry of the underlying lattice, a genuine consequence of electronic correlations. Here we show that this excitonic insulator is realized in zero-gap carbon nanotubes by performing first-principles calculations through many-body perturbation theory as well as quantum Monte Carlo. The excitonic order modulates the charge between the two carbon sublattices opening an experimentally observable gap, which scales as the inverse of the tube radius and weakly depends on the axial magnetic field. Our findings call into question the Luttinger liquid paradigm for nanotubes and provide tests to experimentally discriminate between excitonic and Mott insulators. It has long been anticipated theoretically that semiconductors with small band gaps may form a correlated exciton insulator phase, but it has been difficult to find material realisations. Here, the authors predict numerically that zero-gap armchair carbon nanotubes could be exciton insulators.

The competition between the electron-hole Coulomb attraction and the 3D dielectric screening dictates the optical properties of layered semiconductors. In low-dimensional materials, the equilibrium dielectric environment can be significantly altered by the ultrafast excitation of photo-carriers, leading to renormalized band gap and exciton binding energies. Recently, black phosphorus emerged as a 2D material with strongly layer-dependent electronic properties. Here, we resolve the response of bulk black phosphorus to mid-infrared pulses tuned across the band gap. We find that, while above-gap excitation leads to a broadband light-induced transparency, sub-gap pulses drive an anomalous response, peaked at the single-layer exciton resonance. With the support of DFT calculations, we tentatively ascribe this experimental evidence to a non-adiabatic modification of the screening environment. Our work heralds the non-adiabatic optical manipulation of the electronic properties of 2D materials, which is of great relevance for the engineering of versatile van der Waals materials. Here, the authors investigate the optical response of bulk black phosphorus to mid-infrared pulses, and find that while above-gap excitation leads to a broadband light-induced transparency, sub-gap pulses drive an anomalous response, peaked at the single-layer exciton resonance.

Carbon nanotubes (CNTs) are a promising material for high-performance electronics beyond silicon. But unlike silicon, the nature of the transport band gap in CNTs is not fully understood. The transport gap in CNTs is predicted to be strongly driven by electron-electron (e-e) interactions and correlations, even at room temperature. Here, we use dielectric liquids to screen e-e interactions in individual suspended ultra-clean CNTs. Using multiple techniques, the transport gap is measured as dielectric screening is increased. Changing the dielectric environment from air to isopropanol, we observe a 25% reduction in the transport gap of semiconducting CNTs, and a 32% reduction in the band gap of narrow-gap CNTs. Additional measurements are reported in dielectric oils. Our results elucidate the nature of the transport gap in CNTs, and show that dielectric environment offers a mechanism for significant control over the transport band gap.

Four electrons in a semiconductor quantum dot exhibit similar correlation effects to those found in a molecule. Excitations of these electrons can be probed by inelastic light scattering, which reveals a decoupling of their rigid rotational motion from their spin excitations. Correlation among particles in finite quantum systems leads to complex behaviour and novel states of matter. One remarkable example is predicted to occur in a semiconductor quantum dot 1 , 2 , 3 , where at vanishing electron density the Coulomb interaction between electrons rigidly fixes their relative positions as those of the nuclei in a molecule 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 . In this limit, the neutral few-body excitations are roto-vibrations, which have either rigid-rotor or relative-motion character 15 . In the weak correlation regime, on the contrary, the Coriolis force mixes rotational and vibrational motions. Here, we report evidence for roto-vibrational modes of an electron molecular state at densities for which electron localization is not yet fully achieved. We probe these collective modes by using inelastic light scattering 16 , 17 , 18 in quantum dots containing four electrons 19 . Spectra of low-lying excitations associated with changes of the relative-motion wavefunction—the analogues of the vibration modes of a conventional molecule—do not depend on the rotational state represented by the total angular momentum. Theoretical simulations by the configuration-interaction method 20 are in agreement with the observed roto-vibrational modes and indicate that such molecular excitations develop at the onset of short-range correlation.

Spontaneous condensation of excitons is a long-sought phenomenon analogous to the condensation of Cooper pairs in a superconductor. It is expected to occur in a semiconductor at thermodynamic equilibrium if the binding energy of the excitons—electron (e) and hole (h) pairs interacting by Coulomb force—overcomes the band gap, giving rise to a new phase: the “excitonic insulator” (EI). Transition metal dichalcogenides are excellent candidates for the EI realization because of reduced Coulomb screening, and indeed a structural phase transition was observed in few-layer systems. However, previous work could not disentangle to which extent the origin of the transition was in the formation of bound excitons or in the softening of a phonon. Here we focus on bulk MoS₂ and demonstrate theoretically that at high pressure it is prone to the condensation of genuine excitons of finite momentum, whereas the phonon dispersion remains regular. Starting from first-principles many-body perturbation theory, we also predict that the self-consistent electronic charge density of the EI sustains an out-of-plane permanent electric dipole moment with an antiferroelectric texture in the layer plane: At the onset of the EI phase, those optical phonons that share the exciton momentum provide a unique Raman fingerprint for the EI formation. Finally, we identify such fingerprint in a Raman feature that was previously observed experimentally, thus providing direct spectroscopic confirmation of an ideal excitonic insulator phase in bulk MoS₂ above 30 GPa.

Tunnelling and capacitance spectroscopies are able to image the wavefunctions of electrons in atom-like solid-state systems as they are shaped by an external magnetic field.

The Stark effect can be used to address two qubits independently that are represented by semiconductor quantum dots, placed only a few nanometres apart. The control of orbitals and spin states of single electrons is a key ingredient for quantum information processing 1 , 2 , 3 , 4 , 5 and novel detection schemes 6 , 7 , 8 and is, more generally, of great relevance for spintronics 9 . Coulomb 10 and spin blockade 11 in double quantum dots 12 enable advanced single-spin operations that would be available even for room-temperature applications with sufficiently small devices 13 . To date, however, spin operations in double quantum dots have typically been observed at sub-kelvin temperatures, a key reason being that it is very challenging to scale a double quantum dot system while retaining independent field-effect control of individual dots. Here, we show that the quantum-confined Stark effect allows two dots only 5 nm apart to be independently addressed without the requirement for aligned nanometre-sized local gating. We thus demonstrate a scalable method to fully control a double quantum dot device, regardless of its physical size. In the present implementation we present InAs/InP nanowire double quantum dots that display an experimentally detectable spin blockade up to 10 K. We also report and discuss an unexpected re-entrant spin blockade lifting as a function of the magnetic field intensity.

Tunnelling and capacitance spectroscopies are able to image the wavefunctions of electrons in atom-like solid-state systems as they are shaped by an external magnetic field.