This article is an introductory review of the physics of quantum spin liquid (QSL) states. Quantum magnetism is a rapidly evolving field, and recent developments reveal that the ground states and low-energy physics of frustrated spin systems may develop many exotic behaviors once we leave the regime of semi-classical approaches. The purpose of this article is to introduce these developments. The article begins by explaining how semi-classical approaches fail once quantum mechanics become important and then describes the alternative approaches for addressing the problem. We discuss mainly spin 1/2 systems, and we spend most of our time in this article on one particular set of plausible spin liquid states in which spins are represented by fermions. These states are spin-singlet states and may be viewed as an extension of Fermi liquid states to Mott insulators, and they are usually classified in the category of so-called SU (2), U (1) or Z 2 spin liquid states. We review the basic theory regarding these states and the extensions of these states to include the effect of spin-orbit coupling and to higher spin (S > 1/2) systems. Two other important approaches with strong influences on the understanding of spin liquid states are also introduced: (i) matrix product states and projected entangled pair states and (ii) the Kitaev honeycomb model. Experimental progress concerning spin liquid states in realistic materials, including anisotropic triangular lattice systems (κ-(ET) 2 Cu 2 (CN) 3 and EtMe 3 Sb[(Pd(dmit) 2 ] 2 ), kagome lattice systems (ZnCu 3 (OH) 6 Cl 2 ) and hyperkagome lattice systems (Na 4 Ir 3 O 8 ), is reviewed and compared against the corresponding theories.

Topological insulators display unique properties, such as the quantum spin Hall effect, because time-reversal symmetry allows charges and spins to propagate along the edge or surface of the topological insulator without scattering. However, the direct manipulation of these edge/surface states is difficult because they are significantly outnumbered by bulk carriers. Here, we report experimental evidence for the modulation of these surface states by using a gate voltage to control quantum oscillations in Bi(2)Te(3) nanoribbons. Surface conduction can be significantly enhanced by the gate voltage, with the mobility and Fermi velocity reaching values as high as ~5,800 cm(2) V(-1) s(-1) and ~3.7 × 10(5) m s(-1), respectively, with up to ~51% of the total conductance being due to the surface states. We also report the first observation of h/2e periodic oscillations, suggesting the presence of time-reversed paths with the same relative zero phase at the interference point. The high surface conduction and ability to manipulate the surface states demonstrated here could lead to new applications in nanoelectronics and spintronics.

Majorana fermion (MF) whose antiparticle is itself has been predicted in condensed matter systems. Signatures of the MFs have been reported as zero energy modes in various systems. More definitive evidences associated with MF's novel properties are highly desired to verify the existence of the MF. Very recently, theory has predicted MFs to induce spin selective Andreev reflection (SSAR), a novel magnetic property which can be used to detect the MFs. Here we report the first observation of the SSAR from MFs inside vortices in Bi 2 Te 3 /NbSe 2 hetero-structure, in which topological superconductivity was previously established. By using spin-polarized scanning tunneling

We report the first experimental demonstration of electrical spin injection, transport and detection in bulk germanium (Ge). The non-local magnetoresistance in n-type Ge is observable up to 225K. Our results indicate that the spin relaxation rate in the n-type Ge is closely related to the momentum scattering rate, which is consistent with the predicted Elliot-Yafet spin relaxation mechanism for Ge. The bias dependence of the nonlocal magnetoresistance and the spin lifetime in n-type Ge is also investigated. a these authors contributed equally to this work

Scattering mechanisms in graphene are critical to understanding the limits of signal-to-noise ratios of unsuspended graphene devices. Here we present the four-probe low-frequency noise (1/f) characteristics in back-gated single layer graphene (SLG) and bilayer graphene (BLG) samples. Contrary to the expected noise increase with the resistance, the noise for SLG decreases near the Dirac point, possibly due to the effects of the spatial charge inhomogeneity. For BLG, a similar noise reduction near the Dirac point is observed, but with a different gate dependence of its noise behavior. Some possible reasons for the different noise behavior between SLG and BLG are discussed.

Non-centrosymmetric transition metal monopnictides, including TaAs, TaP, NbAs, and NbP, are emergent topological Weyl semimetals (WSMs) hosting exotic relativistic Weyl fermions. In this letter, we elucidate the physical origin of the unprecedented charge carrier mobility of NbP, which can reach 1 × 10 7 cm 2 V −1 s −1 at 1.5 K. Angle-and temperature-dependent quantum oscillations, supported by density function theory calculations, reveal that NbP has the coexistence of p-and n-type WSM pockets in the kz=1.16π/c plane (W1-WSM) and in the kz=0 plane near the high symmetry points Σ (W2-WSM), respectively. Uniquely, each W2-WSM pocket forms a large dumbbell-shaped Fermi surface (FS) enclosing two neighboring Weyl nodes with the opposite chirality. The magneto-transport in NbP is dominated by these highly anisotropic W2-WSM pockets, in which Weyl fermions are well protected from defect backscattering by real spin conservation associated to the chiral nodes. However, with a minimal doping of ∼1% Cr, the mobility of NbP is degraded by more than two order of magnitude, due to the invalid of helicity protection to magnetic impurities. Helicity protected Weyl fermion transport is also manifested in chiral anomaly induced negative magnetoresistance, controlled by the W1-WSM states. In the quantum regime below 10 K, the intervalley scattering time by impurities becomes a large constant, producing the sharp and nearly identical conductivity enhancement at low magnetic field.Topological Weyl semimetals (WSMs) are regarded as the next wonderland in condensed matter physics [1][2][3][4] for exploring fascinating quantum phenomena [5][6][7][8][9][10]. Unlike Dirac semimetals (DSMs) [11,12], band crossing points in WSMs, i.e. Weyl nodes, always appear in pair with opposite chirality, due to the lifting of spin degeneracy by breaking either time reversal symmetry [1] or inversion symmetry [3,4]. Fermi surfaces (FSs) enclosing the chiral Weyl nodes are characterized by helicity, i.e. the spin orientation is either parallel or antiparallel to the momentum. Such helical Weyl fermions are expected to be remarkably robust against non-magnetic disorders, and may lead to novel device concepts for spintronics and quantum computing.The recent proposed non-centrosymmetric TaAs, TaP, NbAs and NbP, have stimulated immense interests, due to the binary, non-magnetic crystal structure. The existence of Weyl nodes has soon been discovered in TaAs by angle-resolved photoemission spectroscopy (ARPES) [13,14], and by quantum transport measurements of NMR and a non-trivial Berry's phase (Φ B ) of π [15,16]. Transport studies of NbAs [17] and NbP [18] also show ultrahigh mobility and non-saturating MR, but no convincing evidence on the existence of Weyl fermions in these two compounds. However, ARPES resolves tadpoleshaped Fermi arcs on the (001) surface of both NbAs [19] and NbP [20]. It also shows pronounced changes in the * phyzhengyi@zju.edu.cn † zhuan@zju.edu.cn electronic structures of NbAs and NbP compared to TaAs [19], mainly due to weaker sp...

Spin liquid states for spin-1/2 antiferromagnetic Heisenberg model on a hyperkagome lattice are studied. We classify and study flux states according to symmetries. Applying this model to Na4Ir3O8, we propose that the high temperature state may be described by a spinon Fermi surface, which forms a paired state with line nodes below 20 K. The possible mixed spin singlet and spin triplet pairing states are discussed according to the lattice symmetry which breaks inversion.PACS numbers: 71.27.+a, 75.10.Jm A spin liquid is a spin system where quantum fluctuations dominate its low energy behavior, thereby a long range spin order can not be established even at zero temperature. A spin liquid is expected to have exotic properties such as spinons carrying S = 1/2 excitations. After a long search, promising examples in two dimensions (2D) have been identified.[1] Recently a spinel related oxide, Na 4 Ir 3 O 8 , was proposed as the first candidate for a 3D spin liquid [2]. Temperature dependent spin susceptibility around room temperature yields an antiferromagnetic (AFM) Curie-Weiss constant θ W ∼ 650 K, and there is no anomaly indicative of long range spin ordering down to 2K. Some kind of phase transition or cross-over seems to occur at a temperature T c ∼ 20K in that the specific heat C V divided by T shows a rather sharp peak. On the other hand, the spin susceptibility χ (T ) is almost temperature independent. Using the experimental value of spin susceptibility χ and specific heat ratio γ at the specific heat peak at ∼ 20K, we find that the Wilson ratio R W = π 2 k 2 B χ 3µ 2

We examine the spin-triplet superconducting state of even parity mediated by ferromagnetic Hund's coupling between electrons in two almost degenerate orbital bands. This state may be realized in the recently discovered LaFeAsO(1-x)F(x). It is robust against orbital-independent disorder. The splitting of the orbital degeneracy suppresses superconductivity and leads to an anisotropic spectrum in the Bogoliubov quasiparticle. The former predicts a strong pressure dependence of T(c) and the latter predicts Fermi pockets, which may be tested in angle resolved photoemission spectra.