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.
The exactly solvable Kitaev model of two-dimensional honeycomb magnets has a quantum spin liquid phase characterized by the emergence of fractionalized Majorana fermion excitations. In the ...paramagnetic state of α-RuCl3 at high magnetic fields, a half-integer quantization of thermal Hall conductivity has been reported as a signature of edge currents carried by Majorana fermions, but the bulk nature of this state remains unconfirmed. Here, by measuring the heat capacity for different in-plane rotations of an applied magnetic field, we find strongly angle-dependent low-energy excitations in bulk α-RuCl3. The excitation gap has a sextuple node structure, and the gap amplitude increases with the field, as expected for itinerant Majorana fermions in the Kitaev model. Our thermodynamic observations of the opening and closing of the bulk gap according to the magnetic-field direction fully correspond with changes in the edge transport. Moreover, the behaviour at higher magnetic fields where the quantum thermal Hall effect vanishes is consistent with a nematic quantum spin liquid state with two-fold rotational symmetry.α-RuCl has a quantum magnetic phase that may be a spin liquid hosting Majorana fermion excitations. Heat capacity measurements show an anisotropic dependence on magnetic-field direction, consistent with predictions for the putative spin liquid.
The coexistence and competition between superconductivity and electronic orders, such as spin or charge density waves, have been a central issue in high transition-temperature (Tc) superconductors. ...Unlike other iron-based superconductors, FeSe exhibits nematic ordering without magnetism whose relationship with its superconductivity remains unclear. Moreover, a pressure-induced fourfold increase of Tc has been reported, which poses a profound mystery. Here we report high-pressure magnetotransport measurements in FeSe up to ∼15 GPa, which uncover the dome shape of magnetic phase superseding the nematic order. Above ∼6 GPa the sudden enhancement of superconductivity (Tc≤38.3 K) accompanies a suppression of magnetic order, demonstrating their competing nature with very similar energy scales. Above the magnetic dome, we find anomalous transport properties suggesting a possible pseudogap formation, whereas linear-in-temperature resistivity is observed in the normal states of the high-Tc phase above 6 GPa. The obtained phase diagram highlights unique features of FeSe among iron-based superconductors, but bears some resemblance to that of high-Tc cuprates.
Abstract
A fundamental issue concerning iron-based superconductivity is the roles of electronic nematicity and magnetism in realising high transition temperature (
T
c
). To address this issue, FeSe ...is a key material, as it exhibits a unique pressure phase diagram involving non-magnetic nematic and pressure-induced antiferromagnetic ordered phases. However, as these two phases in FeSe have considerable overlap, how each order affects superconductivity remains perplexing. Here we construct the three-dimensional electronic phase diagram, temperature (
T
) against pressure (
P
) and isovalent S-substitution (
x
), for FeSe
1−
x
S
x
. By simultaneously tuning chemical and physical pressures, against which the chalcogen height shows a contrasting variation, we achieve a complete separation of nematic and antiferromagnetic phases. In between, an extended non-magnetic tetragonal phase emerges, where
T
c
shows a striking enhancement. The completed phase diagram uncovers that high-
T
c
superconductivity lies near both ends of the dome-shaped antiferromagnetic phase, whereas
T
c
remains low near the nematic critical point.
The transition temperature Tc of iron-based superconductors has a dome-shaped dependence on chemical doping, and the superconductivity that develops underneath may obscure a potential quantum ...critical point (QCP) residing at absolute zero. With the aim of detecting signatures of this quantum criticality, Hashimoto et al. (p 1554; see the Perspective by Sachdev ) measured the penetration depth of the pnictide series BaFe2(As1-x Px )2 as a function of x. A sharp peak right around the point where Tc has a maximum (x = 0.30) was observed, implying that the superfluid density diminishes sharply where one would expect it to be the most robust. This unusual finding is interpreted as a sign of a QCP at x = 0.30. In a superconductor, the ratio of the carrier density, n, to its effective mass, m*, is a fundamental property directly reflecting the length scale of the superfluid flow, the London penetration depth, λL. In two-dimensional systems, this ratio n/m* (~1/λL2) determines the effective Fermi temperature, TF. We report a sharp peak in the x-dependence of λL at zero temperature in clean samples of BaFe2(As1-xPx)2 at the optimum composition x = 0.30, where the superconducting transition temperature Tc reaches a maximum of 30 kelvin. This structure may arise from quantum fluctuations associated with a quantum critical point. The ratio of Tc/TF at x = 0.30 is enhanced, implying a possible crossover toward the Bose-Einstein condensate limit driven by quantum criticality. PUBLICATION ABSTRACT
Abstract
The pseudogap phenomenon in the cuprates is arguably the most mysterious puzzle in the field of high-temperature superconductivity. The tetragonal cuprate HgBa
2
CuO
4+
δ
, with only one CuO
...2
layer per primitive cell, is an ideal system to tackle this puzzle. Here, we measure the magnetic susceptibility anisotropy within the CuO
2
plane with exceptionally high-precision magnetic torque experiments. Our key finding is that a distinct two-fold in-plane anisotropy sets in below the pseudogap temperature
T
*
, which provides thermodynamic evidence for a nematic phase transition with broken four-fold symmetry. Surprisingly, the nematic director orients along the diagonal direction of the CuO
2
square lattice, in sharp contrast to the bond nematicity along the Cu-O-Cu direction. Another remarkable feature is that the enhancement of the diagonal nematicity with decreasing temperature is suppressed around the temperature at which short-range charge-density-wave formation occurs. Our result suggests a competing relationship between diagonal nematic and charge-density-wave order in HgBa
2
CuO
4+
δ
.
Abstract
The interplay among magnetism, electronic nematicity, and superconductivity is the key issue in strongly correlated materials including iron-based, cuprate, and heavy-fermion ...superconductors. Magnetic fluctuations have been widely discussed as a pairing mechanism of unconventional superconductivity, but recent theory predicts that quantum fluctuations of nematic order may also promote high-temperature superconductivity. This has been studied in FeSe
1−
x
S
x
superconductors exhibiting nonmagnetic nematic and pressure-induced antiferromagnetic orders, but its abrupt suppression of superconductivity at the nematic end point leaves the nematic-fluctuation driven superconductivity unconfirmed. Here we report on systematic studies of high-pressure phase diagrams up to 8 GPa in high-quality single crystals of FeSe
1−
x
Te
x
. When Te composition
x
(Te) becomes larger than 0.1, the high-pressure magnetic order disappears, whereas the pressure-induced superconducting dome near the nematic end point is continuously found up to
x
(Te) ≈ 0.5. In contrast to FeSe
1−
x
S
x
, enhanced superconductivity in FeSe
1−
x
Te
x
does not correlate with magnetism but with the suppression of nematicity, highlighting the paramount role of nonmagnetic nematic fluctuations for high-temperature superconductivity in this system.
In superconductors with unconventional pairing mechanisms, the energy gap in the excitation spectrum often has nodes, which allow quasiparticle excitations at low energies. In many cases, such as in ...d-wave cuprate superconductors, the position and topology of nodes are imposed by the symmetry, and thus the presence of gapless excitations is protected against disorder. Here we report on the observation of distinct changes in the gap structure of iron-pnictide superconductors with increasing impurity scattering. By the successive introduction of nonmagnetic point defects into BaFe2(As(1-x)P(x))(2) crystals via electron irradiation, we find from the low-temperature penetration depth measurements that the nodal state changes to a nodeless state with fully gapped excitations. Moreover, under further irradiation the gapped state evolves into another gapless state, providing bulk evidence of unconventional sign-changing s-wave superconductivity. This demonstrates that the topology of the superconducting gap can be controlled by disorder, which is a strikingly unique feature of iron pnictides.
Abstract
The recently discovered kagome superconductors
A
V
3
Sb
5
(
A
= K, Rb, Cs) exhibit unusual charge-density-wave (CDW) orders with time-reversal and rotational symmetry breaking. One of the ...most crucial unresolved issues is identifying the symmetry of the superconductivity that develops inside the CDW phase. Theory predicts a variety of unconventional superconducting symmetries with sign-changing and chiral order parameters. Experimentally, however, superconducting phase information in
A
V
3
Sb
5
is still lacking. Here we report the impurity effects in CsV
3
Sb
5
using electron irradiation as a phase-sensitive probe of superconductivity. Our magnetic penetration depth measurements reveal that with increasing impurities, an anisotropic fully-gapped state changes to an isotropic full-gap state without passing through a nodal state. Furthermore, transport measurements under pressure show that the double superconducting dome in the pressure-temperature phase diagram survives against sufficient impurities. These results support that CsV
3
Sb
5
is a non-chiral, anisotropic
s
-wave superconductor with no sign change both at ambient and under pressure.
Quantum oscillations in transport and thermodynamic parameters at high magnetic fields are an unambiguous signature of the Fermi surface, the defining characteristic of a metal. Recent observations ...of quantum oscillations in insulating SmB6 and YbB12, therefore, have been a big surprise—despite the large charge gap inferred from the insulating behaviour of the resistivity, these compounds seemingly host a Fermi surface at high magnetic fields. However, the nature of the ground state in zero field has been little explored. Here, we report the use of low-temperature heat-transport measurements to discover gapless, itinerant, charge-neutral excitations in the ground state of YbB12. At zero field, sizeable linear temperature-dependent terms in the heat capacity and thermal conductivity are clearly resolved in the zero-temperature limit, indicating the presence of gapless fermionic excitations with an itinerant character. Remarkably, linear temperature-dependent thermal conductivity leads to a spectacular violation of the Wiedemann–Franz law: the Lorenz ratio is 104–105 times larger than that expected in conventional metals, indicating that YbB12 is a charge insulator and a thermal metal. Moreover, we find that these fermions couple to magnetic fields, despite their charge neutrality. Our findings expose novel quasiparticles in this unconventional quantum state.
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