The quantum Hall effect in two-dimensional electron gases involves the flow of topologically protected dissipationless charge currents along the edges of a sample. Integer or fractional electrical conductance is associated with edge currents of electrons or quasiparticles with fractional charges, respectively. It has been predicted that quantum Hall phenomena can also be created by edge currents with a fundamentally different origin: the fractionalization of quantum spins. However, such quantization has not yet been observed. Here we report the observation of this type of quantization of the Hall effect in an insulating two-dimensional quantum magnet, α-RuCl, with a dominant Kitaev interaction (a bond-dependent Ising-type interaction) on a two-dimensional honeycomb lattice. We find that the application of a magnetic field parallel to the sample destroys long-range magnetic order, leading to a field-induced quantum-spin-liquid ground state with substantial entanglement of local spins. In the low-temperature regime of this state, the two-dimensional thermal Hall conductance reaches a quantum plateau as a function of the applied magnetic field and has a quantization value that is exactly half of the two-dimensional thermal Hall conductance of the integer quantum Hall effect. This half-integer quantization of the thermal Hall conductance in a bulk material is a signature of topologically protected chiral edge currents of charge-neutral Majorana fermions (particles that are their own antiparticles), which have half the degrees of freedom of conventional fermions. These results demonstrate the fractionalization of spins into itinerant Majorana fermions and Z fluxes, which is predicted to occur in Kitaev quantum spin liquids. Above a critical magnetic field, the quantization disappears and the thermal Hall conductance goes to zero rapidly, indicating a topological quantum phase transition between the states with and without chiral Majorana edge modes. Emergent Majorana fermions in a quantum magnet are expected to have a great impact on strongly correlated quantum matter, opening up the possibility of topological quantum computing at relatively high temperatures.

Spin-orbit coupling has proven indispensable in realizing topological materials and more recently Ising pairing in two-dimensional superconductors. This pairing mechanism relies on inversion symmetry breaking and sustains anomalously large in-plane polarizing magnetic fields whose upper limit is expected to diverge at low temperatures, although experimental demonstration of this has remained elusive due to the required fields. In this work, the recently discovered superconductor few-layer stanene, i.e. epitaxially strained -Sn, is shown to exhibit a new type of Ising pairing between carriers residing in bands with different orbital indices near the Γ-point. The bands are split as a result of spin-orbit locking without the participation of inversion symmetry breaking. The in-plane upper critical field is strongly enhanced at ultra-low temperature and reveals the sought for upturn.

Liquid/solid interfaces are attracting growing interest not only for applications in catalytic activities and energy storage, but also for their new electronic functions in electric double-layer transistors (EDLTs) exemplified by high-performance organic electronics, field-induced electronic phase transitions, as well as superconductivity in SrTiO(3) (ref. 12). Broadening EDLTs to induce superconductivity within other materials is highly demanded for enriching the materials science of superconductors. However, it is severely hampered by inadequate choice of materials and processing techniques. Here we introduce an easy method using ionic liquids as gate dielectrics, mechanical micro-cleavage techniques for surface preparation, and report the observation of field-induced superconductivity showing a transition temperature T(c)=15.2 K on an atomically flat film of layered nitride compound, ZrNCl. The present result reveals that the EDLT is an extremely versatile tool to induce electronic phase transitions by electrostatic charge accumulation and provides new routes in the search for superconductors beyond those synthesized by traditional chemical methods.

The notion of quantum spin-liquids (QSLs), antiferromagnets with quantum fluctuation-driven disordered ground states, is now firmly established in one-dimensional (1D) spin systems as well as in their ladder cousins. The spin-1/2 organic insulator κ-(bis(ethylenedithio)-tetrathiafulvalene) 2 Cu 2 (CN) 3 (κ-(BEDT-TTF) 2 Cu 2 (CN) 3 ; ref. 1) with a 2D triangular lattice structure is very likely to be the first experimental realization of this exotic state in D ≥ 2. Of crucial importance is to unveil the nature of the low-lying elementary spin excitations 2,3 , particularly the presence/absence of a 'spin gap', which will provide vital information on the universality class of this putative QSL. Here, we report on our thermal-transport measurements carried out down to 80 mK. We find, rather unexpectedly, unambiguous evidence for the absence of a gapless excitation, which sharply contradicts recent reports of heat capacity measurements 4 . The low-energy physics of this intriguing system needs be reinterpreted in light of the present results indicating a spin-gapped QSL phase.In antiferromagnetically coupled spin systems, geometrical frustrations enhance quantum fluctuations. Largely triggered by the proposal of the resonating-valence-bond theory for S = 1/2 degrees of freedom residing on a frustrated twodimensional (2D) triangular lattice 5-7 and its possible application to high-T c cuprates with a doped 2D square lattice 8,9 , realizing/detecting QSLs in 2D systems has been a longsought goal. Recently, discoveries of QSL states on S = 1/2 triangular lattices have been reported in organic compounds, κ-(BEDT-TTF) 2 Cu 2 (CN) 3 (Fig. 1, inset) 1,10,11 , C 2 H 5 (CH 3 ) 3 Sb

Recently emerging two-dimensional (2D) superconductors in atomically thin layers and at heterogeneous interfaces are attracting growing interest in condensed matter physics. Here, we report that an ion-gated zirconium nitride chloride surface, exhibiting a dome-shaped phase diagram with a maximum critical temperature of 14.8 kelvin, behaves as a superconductor persisting to the 2D limit. The superconducting thickness estimated from the upper critical fields is ≅ 1.8 nanometers, which is thinner than one unit-cell. The majority of the vortex phase diagram down to 2 kelvin is occupied by a metallic state with a finite resistance, owing to the quantum creep of vortices caused by extremely weak pinning and disorder. Our findings highlight the potential of electric-field-induced superconductivity, establishing a new platform for accessing quantum phases in clean 2D superconductors.

We show that the charge and thermal transport measurements on ultraclean crystals of URu2Si2 reveal a number of unprecedented superconducting properties. The uniqueness is best highlighted by the peculiar field dependence of thermal conductivity including the first order transition at Hc2 with a reduction of entropy flow. This is a consequence of multi-band superconductivity with compensated electronic structure in the hidden order state of this system. We provide strong evidence for a new type of unconventional superconductivity with two distinct gaps having different nodal topology.The heavy-Fermion compound URu 2 Si 2 has mystified researchers since the superconducting state (T c = 1.5 K) is embedded within the "hidden order" phase (T h = 17.5 K) [1,2,3]. Although several exotic order parameters have been proposed for the hidden order phase [4], it is not identified yet. According to several experimental observations, most of the carriers disappear below T h resulting in a density one order of magnitude smaller than in other heavy-Fermion superconductors [5,6,7]. Superconductivity with such a low density is remarkablesince the superfluid density is very low in some way reminiscent of underdoped cuprates. Moreover, pressure studies reveal that the superconductivity coexists with the hidden order but is suppressed by antiferromagnetic ordering [8].In this Letter, using ultraclean single crystals, we report various anomalous superconducting properties in URu 2 Si 2 . We show that a peculiar electronic structure appearing below the hidden order transition provides an intriguing stage on which a new type of unconventional superconducting state appears.Single crystals of URu 2 Si 2 were grown by the Czochralski pulling method in a tetra-arc furnace. The welldefined superconducting transition was confirmed by the specific heat measurements. The thermal conductivity κ was measured using a standard four-wire steady state method along the a-axis (heat current q a). The contact resistance at low temperatures is less than 10 mΩ.We first discuss the electronic structure below T h . Figure 1 shows the temperature dependence of the resistivity ρ along the a-axis and Hall coefficient R H (solid circles) defined as R H ≡ dρxy dH at H → 0 T for H c in the tetragonal crystal structure. In zero field, ρ depends on T as ρ = ρ 0 + AT 2 below 6 K down to T c . The exceptionally low residual resistivity ρ 0 = 0.48 µΩ cm and large residual resistivity ratio RRR = 670 attest the highest crystal quality currently achievable. R H exhibits an eight-fold increase below T h and attains a T -independent value at low temperatures, associated with a strong reduction of the carrier density. Most remarkably, the magnetoresistance (MR) increases with decreasing temperature and becomes extremely large at the lowest temperatures. The inset of Fig.

The Kitaev quantum spin liquid displays the fractionalization of quantum spins into Majorana fermions. The emergent Majorana edge current is predicted to manifest itself in the form of a finite thermal Hall effect, a feature commonly discussed in topological superconductors. Here we report on thermal Hall conductivity κ_{xy} measurements in α-RuCl_{3}, a candidate Kitaev magnet with the two-dimensional honeycomb lattice. In a spin-liquid (Kitaev paramagnetic) state below the temperature characterized by the Kitaev interaction J_{K}/k_{B}∼80  K, positive κ_{xy} develops gradually upon cooling, demonstrating the presence of highly unusual itinerant excitations. Although the zero-temperature property is masked by the magnetic ordering at T_{N}=7  K, the sign, magnitude, and T dependence of κ_{xy}/T at intermediate temperatures follows the predicted trend of the itinerant Majorana excitations.

A superconductivity dome is created by the electronic structure of the molecular building block of an unconventional superconductor.