We propose a torsional response raised by lattice dislocation in Weyl semimetals akin to chiral magnetic effect; i.e. a fictitious magnetic field arising from screw or edge dislocation induces charge current. We demonstrate that, in sharp contrast to the usual chiral magnetic effect which vanishes in real solid state materials, the torsional chiral magnetic effect exists even for realistic lattice models, which implies the experimental detection of the effect via SQUID or nonlocal resistivity measurements in Weyl semimetal materials. 11.30.Rd, 11.15.Yc Recently, many candidate materials for Dirac semimetals and Weyl semimetals (WSMs) [1][2][3][4], have been discovered [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. These topological semimetals are intriguing because of exotic transport phenomena associated with the chiral anomaly in quantum field theory [24], such as the anomalous Hall effect [25,26], chiral magnetic effect (CME) [27], negative longitudinal magnetoresistance [5, 12, 19-21, 28, 29], and chiral gauge field [30].Among them, the CME has been discussed in broad areas of quantum many-body physics, including nuclear and nonequilibrium physics as well as condensed matter physics. It is the generation of charge current parallel to an applied magnetic field even in the absence of electric fields. In nuclear physics, together with the chiral vortical effect [31], it is expected to play an important role in heavy ion collisions experiments [32,33]. The CME also caused a stir in nonequilibrium statistical physics, since it leads to the existence of the ground state which, recently, attracts a renewed interest in connection with the realization of quantum time crystal [34], and then the CME has been studied from this point of view [35,36]. However, unfortunately, their results are negative for its realization: the macroscopic ground state current in realistic WSMs is always absent.In this letter, we propose a chiral response in WSMs, named "torsional chiral magnetic effect (TCME)", in which the ground state charge current is caused by the effective magnetic field induced by lattice dislocation as shown in FIG.1. By using the Cartan formalism of the differential geometry, we can describe the lattice strain and dislocation in terms of vielbein and torsion [37]. From the viewpoint of the quantum field theory in curved space-time, the TCME is raised by the mixed action of electromagnetic and torsional fields that is prohibited in four-dimensional spacetime with the Lorentz symmetry, but made possible in non-relativistic band electrons in solid state systems. Furthermore, we demonstrate that the TCME is possible in realistic lattice models by carrying out numerical calculations. Our results imply the existence of experimentally observable current induced by the TCME in real WSM materials. We also resolve the relation between our results and the no-go theorem that the CME is absent in equilibrium states [35,36]. First of all, we clarify the notations. The indices i, j, · · · = x, y, z a...

We discuss thermal transport of two-dimensional topological superconductors (TSCs) with broken time reversal symmetry, which are described by Bogoliubov-de Gennes (BdG) Hamiltonians. From the calculations of bulk quantities only, without refereeing to Majorana edge states, we show that the thermal Hall conductivity of two-dimensional TSCs in the lowtemperature limit is quantized in multiples of 1 2 πT 6 , which is exactly one half of the value of quantization in the case of the integer quantum Hall effect, and that this exact halfquantization is caused by the structure of the Nambu spinor and the particle-hole symmetry, which BdG Hamiltonians generally have. In the case of spinless chiral p-wave superconductors, this result is in perfect agreement with the argument based on the Ising conformal field theory with the central charge c = 1/2, which is an effective low-energy theory of the Majorana edge states. KEYWORDS: thermal Hall effect, topological superconductorIntroduction -Topological insulators (TIs) and superconductors (TSCs) are new quantum phases which are characterized by bulk topological invariants. It has been found that some of these invariants directly characterize the transport properties of the system. For example, the integer quantum Hall effect (IQHE) state is characterized by the topological number, the TKNN (or first Chern) number C 1 , and this invariant appears in the Hall conductivity σ xy in the low-temperature limit: σ xy = C 1 e 2 /h, which has been derived from the linear response theory. 1, 2 A similar idea is also applicable to topological superconductors without time reversal symmetry in two dimensions (i.e. class C and D in the topological periodic table 3 ), for which topological nontriviality is characterized by the nonzero TKNN number. However, in this case, it is not charge transport but thermal transport that characterizes the topological feature, since charge is not conserved, while energy is still a conserved quantity in supercon- * LETTERS ducting states. For instance, in the case of spinless chiral p-wave superconductors, which have the TKNN number C 1 = ±1, 4 Read and Green showed that by using the effective low-energy theory for Majorana edge states, the thermal Hall coefficient in the low-temperature limit is precisely given by c πT 6 (in the unit of k B = 1, = 1), where c = 1/2 is the central charge of the Ising conformal field theory (CFT) which describes the Majorana edge state. 5,6 Note that this value is one half of the value of IQHE states, which have edge modes described by the chiral Luttinger liquid theory, i.e. CFT with the central charge c = 1. 5 The Read-Green's

The superconducting fluctuation e ect, due to preformed Cooper pairs above the critical temperature T c , has been generally understood by the standard Gaussian fluctuation theories in most superconductors 1 . The transverse thermoelectric (Nernst) e ect is particularly sensitive to the fluctuations, and the large Nernst signal found in the pseudogap regime of the underdoped cuprates 2,3 has raised much debate. Here we report on the observation of a colossal Nernst signal due to the superconducting fluctuations in the heavy-fermion superconductor URu 2 Si 2 . The Nernst coe cient is anomalously enhanced (by a factor of ∼10 6 ) as compared with the theoretically expected value of the Gaussian fluctuations. Moreover, contrary to the conventional wisdom, the enhancement is more significant with a reduction of the impurity scattering rate. This unconventional Nernst e ect intimately reflects the highly unusual superconducting state of URu 2 Si 2 . The results invoke possible chiral or Berry-phase fluctuations associated with the broken time-reversal symmetry 4-7 of the superconducting order parameter.

We consider the Nernst and Hall effects in fluctuation regime of chiral superconductors above transition temperatures, that are raised not by conventional Lorentz force, but by asymmetric scattering due to fluctuations of the Berry phase of the Bogoliubov-de Gennes Hamiltonian. It is found that these effects can be more significant than conventional ones for cleaner samples, exhibiting qualitatively distinct behaviors. The results provide systematic and comprehensive understanding for recent experimental observations of the Nernst effect in a clean URu2Si2 sample, which is suggested to be a chiral superconductor. In a certain class of superconductors, fluctuations toward ordered states above transition temperatures give rise to dramatic effects on many-body electron states. It is known that a powerful probe for such phenomena is the Nernst effect. For instance, giant Nernst signals have been observed in near and above transition temperatures T c of cuprate high-T c superconductors [1] and dirty superconducting thin films [2]. In normal metals, the Nernst signal is generally weak owing to the Sondheimer cancelation [3] and then, these unexpected experimental observations inspired succeeding extensive studies, leading to various theoretical proposals such as scenarios based on short-lived Cooper pairs [4], Josephson electromotive force due to the vortex motion [5], and strong coupling with antiferromagnetic fluctuations [6].In this letter, we propose an unconventional mechanism for the giant Nernst effect above T c in chiral superconductors, which has not been discussed so far. In chiral superconductors, time-reversal symmetry (TRS) is spontaneously broken, and total angular momentum carried by Cooper pairs is nonzero. The "chirality" of this superconducting state is characterized by the Berry phase of the Bogoliubov-de Gennes mean-field Hamiltonian, which is an Aharonov-Bohm (AB) phase whose adiabatic parameters are the wave number [7]. In the superconducting phase below T c , the intrinsic magnetic field induced by it causes exotic transverse transport phenomena under zero external magnetic field, such as the Kerr effect [8,9], which was observed in Sr 2 RuO 4 [10], and the anomalous thermal Hall effect, which was theoretically predicted [11][12][13]. It is natural to expect that also in the superconducting fluctuation regime above T c , characteristic transverse transport phenomena can be induced by fluctuations of the chirality or the Berry phase. We investigate this possibility, and clarify a novel mechanism of the giant Nernst and Hall effects above and near T c , caused by Berry phase fluctuations. In this scenario, quasiparticles are scattered asymmetrically by fluctuating Cooper pairs with angular momentum, even without Lorentz force, and then, such effects can be regarded as an analog of the skew scattering process of the anoma-lous Hall effect, which is caused by a spin-orbit coupling involving impurity scattering [14], but a major difference is that the scattering kernels are dynamical in this case.The...

The chiral magnetic effect is a phenomenon where an electromagnetic current is generated along a magnetic field. Recently, in nonequilibrium systems, negative longitudinal magnetoresistance has been observed experimentally in Dirac/Weyl semimetals, which provides evidence for the chiral magnetic effect as a nonequilibrium current. On the other hand, the emergence of the chiral magnetic effect as an equilibrium current is still controversial. We propose a possible realization of the chiral magnetic effect as an equilibrium current using inhomogeneous magnetic fields. By employing tight-binding calculations and linear response theory, we demonstrate that a finite current density is generated by inhomogeneous magnetic fields, while the spatial integration of the current is equal to zero, which is consistent with the so-called "no-go theorem" of the chiral magnetic effect in real lattice systems. Moreover, we propose an experimental setup to detect the effect in Weyl semimetal materials. 1 arXiv:1605.04567v3 [cond-mat.mes-hall]