Several small-bandgap semiconductors are now known to have protected metallic surface states as a consequence of the topology of the bulk electron wavefunctions. The known "topological insulators" with this behavior include the important thermoelectric materials Bi_2Te_3 and Bi_2Se_3, whose surfaces are observed in photoemission experiments to have an unusual electronic structure with a single Dirac cone. We study in-plane (i.e., horizontal) transport in thin films made of these materials. The surface states from top and bottom surfaces hybridize, and conventional diffusive transport predicts that the tunable hybridization-induced band gap leads to increased thermoelectric performance at low temperatures. Beyond simple diffusive transport, the conductivity shows a crossover from the spin-orbit induced anti-localization at a single surface to ordinary localization.
We measure gate-tuned thermoelectric power of mechanically exfoliated Bi2Se3 thin films in the topological insulator regime. The sign of the thermoelectric power changes across the charge neutrality point as the majority carrier type switches from electron to hole, consistent with the ambipolar electric field effect observed in conductivity and Hall effect measurements. Near charge neutrality point and at low temperatures, the gate dependent thermoelectric power follows the semiclassical Mott relation using the expected surface state density of states, but is larger than expected at high elect…
Thermoelectric coefficients of an ultra-thin topological insulator are presented here. The hybridization between top and bottom surface states of a topological insulator plays a significant role. In absence of magnetic field, thermopower increases and thermal conductivity decreases with increase of the hybridization energy. In presence of magnetic field perpendicular to the ultra-thin topological insulator, thermoelectric coefficients exhibit quantum oscillations with inverse magnetic field, whose frequency is strongly modified by the Zeeman energy and phase factor is governed by the product o…
The thermoelectric response of 80-nm-thick strained HgTe films of a three-dimensional topological insulator (3D TI) has been studied experimentally. An ambipolar thermopower is observed where the Fermi energy moves from conducting to the valence bulk band. The comparison between theory and experiment shows that the thermopower is mostly due to the phonon drag contribution. In the region where the 2D Dirac electrons coexist with bulk hole states, the Seebeck coefficient is modified due to 2D electron - 3D hole scattering.
In this paper we consider charge current generated by maintaining a temperature difference over a nanowire at zero voltage bias. For topological insulator nanowires in a perpendicular magnetic field the current can change sign as the temperature of one end is increased. Here we study how this thermoelectric current sign reversal depends on magnetic field and how impurities affect the size of the thermoelectric current. We consider both scalar and magnetic impurities and show that their influence on the current are quite similar, although the magnetic impurities seem to be more effective in red…
We have studied thermoelectric effect of a Kane-Mele normal-insulator-superconductor (KMNIS) junction at ultra-low temperatures using a modified version of the well-known Blonder-Tinkham-Klapwijk (BTK) theory. Since both the (electronic) charge and thermal current due to the carriers are sensitive to the strengths of the spin-orbit coupling (SOC) present in the Kane-Mele model, a tunability of this junction device with regard to its thermoelectric properties can be experimentally achieved by certain techniques that are used to manipulate the values of the spin-orbit couplings. We have computed…
Topological edge states are predicted to be responsible for the high efficient thermoelectric response of topological insulators, currently the best thermoelectric materials. However, to explain their figure of merit the coexistence of topological electrons, entropy and phonons can not be considered independently. In a background that puts together electrodynamics and topology, through an expression for the topological intrinsic field, we treat relativistic phonons within the topological surface showing their ability to modulate the Berry curvature of the bands and then playing a fundamental r…
We consider thermoelectric transport properties of the edge states of a two dimensional topological insulator in a double quantum point contact geometry coupled to two thermally biased reservoirs. Both spin-preserving and spin-flipping tunneling processes between opposite edges are analyzed in the presence of electron-electron interactions. We demonstrate that the simultaneous presence of spin-flipping processes and interactions gives rise to a finite longitudinal spin current. Moreover, its sign and amplitude can be tuned by means of gate voltages with the possibility to generate a pure spin …
We study thermoelectric transport in ultrathin topological insulators under the application of circularly polarized off-resonant light of frequency Ω and amplitude A. We derive analytical expressions for the band structure, orbital magnetization Morb, and the thermal (\k{appa}xy) and Nernst (αxy) conductivities. Reversing the light polarization from right to left leads to an exchange of the conduction and valence bands of the symmetric and antisymmetric surface states and to a sign change in Morb,αxy, and \k{appa}xy. Varying the sample thickness or A/Ω leads to a strong enhancement of Morb and…
Using first-principles calculations and Boltzmann theory, we explore the feasibility to maximize the thermoelectric figure of merit (ZT) of topological insulator Bi2Te3 films in the few-quintuple layer regime. We discover that the delicate competitions between the surface and bulk contributions, coupled with the overall quantum size effects, lead to a novel and generic non-monotonous dependence of ZT on the film thickness. In particular, when the system crosses into the topologically non-trivial regime upon increasing the film thickness, the much longer surface relaxation time associated with …
The spin momentum non-orthogonality in 3D topological insulators leads to modification of the spin texture and brings in an out-of-plane spin polarization component. Apart from spin texture, the anomalous thermoelectric properties of these materials are worth studying. In this paper, we have pointed out that the off resonant light used to irradiate the surface states, induces a gap, which becomes momentum dependent due to the presence of non-orthogonal terms in the Hamiltonian. Importantly, to maintain the off resonant condition of light, the momentum value should satisfy a bound. Furthermore,…
At present, topological insulators are the most efficient thermoelectric materials at room temperature. However, at non-zero temperatures, it seems to arise a conflict between having time-reversal symmetry, which implies minimal entropy, and the Seebeck coefficient, which is the entropy carried by each electric charge unit. This has obliged us to analyze the mathematical and physical background taking into account relativistic phonons besides the electrons within quantum field theory. In this search, we found an approximate expression for the intrinsic topological field b in terms of the Chern…
Bismuth telluride (Bi2Te3) and its alloys are the best bulk thermoelectric materials known today. The stacked quasi-two-dimensional (2D) layers of Bi2Te3 were also identified as topological insulators. In this paper we describe a method for graphene-inspired exfoliation of crystalline bismuth telluride films with a thickness of a few atoms. The atomically thin films were suspended across trenches in Si/SiO2 substrates, and subjected to detail characterization. The presence of the van der Waals gaps allowed us to disassemble Bi2Te3 crystal into its quintuple building blocks - five mono-atomic s…
The thermoelectric response of HgTe quantum wells in the state of two-dimensional topological insulator (2D TI) has been studied experimentally. Ambipolar thermopower, typical for an electron-hole system, has been observed across the charge neutrality point, where the carrier type changes from electrons to holes according to the resistance measurements. The hole-type thermopower is much stronger than the electron-type one. The thermopower linearly increases with temperature. We present a theoretical model which accounts for both the edge and bulk contributions to the electrical conductivity an…
Designing thermoelectric materials with high figure of merit $ZT=S^2 G T/κ$ requires fulfilling three often irreconcilable conditions, i.e., the high electrical conductance $G$, small thermal conductance $κ$ and high Seebeck coefficient $S$. Nanostructuring is one of the promising ways to achieve this goal as it can substantially suppress lattice contribution to $κ$. However, it may also unfavorably influence the electronic transport in an uncontrollable way. Here we theoretically demonstrate that this issue can be ideally solved by fabricating graphene nanoribbons with heavy adatoms and nanop…
Topological insulators have gapless edge/surface states with novel transport properties. Among these, there are two classes of perfectly conducting channels which are free from backscattering: the edge states of two-dimensional topological insulators and the one-dimensional states localized on dislocations of certain three-dimensional topological insulators. We show how these novel states affect thermoelectric properties of the systems and discuss possibilities to improve the thermoelectric figure of merit using these materials with perfectly conducting channels.
We investigate thermoelectric transport through interfaces with inelastic scatterings by developing a quantum theory, which has been extensively validated by existing theories. We find that under temperature bias, while a two-terminal conductor-insulator interface behaves only as a thermal resistor, a three-terminal conductor-insulator-conductor interface can function as an electricity generator caused by phonon-mediated electron scatterings with heat-charge current separation. Unlike conventional thermoelectrics which is a property of a bulk caused by the Seebeck effect, this thermoelectric b…
This paper reviews recent developments in quantum transport and it presents recent efforts to explore the contribution of topological insulator boundary states to thermoelectricity in Bi$_2$Te$_3$ thin films. Although Bi$_2$Te$_3$ has been used as a thermoelectric material for many years, it is only recently that thin films of this material have been synthesized as 3D topological insulators with interesting physics and potential applications related to topologically protected surface states. A major bottleneck in Bi$_2$Te$_3$ thin films has been eliminating its bulk conductivity while increasi…
Thermoelectric materials intrigue much interest due to their wide range of application such as power generators and refrigerators. The efficiency of thermoelectric materials is quantified by the figure of merit, and a figure greater than unity is desired. To achieve this, a large Seebeck coefficient and low phonon thermal conductivity are required. We show that this can be achieved with a thin film of topological nodal line semimetals. We also discusses the correlation effect and spin current induced by a temperature gradient. The obtained results provide insight for the improvement of thermoe…
We report on "graphene-like" mechanical exfoliation of single-crystal Bi2Te3 films and thermoelectric characterization of the stacks of such films. Thermal conductivity of the resulting "pseudo-superlattices" was measured by the "hot disk" and "laser flash" techniques. The room-temperature in-plane (cross-plane) thermal conductivity of the stacks decreases by a factor of ~2.4 (3.5) as compared to bulk. The thermal conductivity reduction with preserved electrical properties leads to strong increase in the thermoelectric figure of merit. It is suggested that the film thinning to few-quintuples a…
We study the thermoelectric properties of three-dimensional topological Anderson insulators with line dislocations. We show that at high densities of dislocations the thermoelectric figure of merit ZT can be dominated by one-dimensional topologically-protected conducting states channeled through the lattice screw dislocations in the topological insulator materials with a non-zero time-reversal-invariant momentum such as Bi_{1-x}Sb_x. When the chemical potential does not exceed much the mobility edge the ZT at room temperatures can reach large values, much higher than unity for reasonable param…
Improving the thermoelectric figure of merit zT is one of the greatest challenges in material science. Recent discovery of topological insulators (TIs) offers new promise in this prospect. In this work, we demonstrate theoretically that zT is strongly size dependent in TI, and the size parameter can be tuned to enhance zT to be significantly greater than 1. Furthermore, we show that the life time of the edge states in TI is strongly energy dependent, leading to large and anomalous Seebeck effects with an opposite sign to the Hall effect. These striking properties make TIs the promising materia…
Effects of electron-electron and spin-orbit interactions on the ground-state magnetic configuration and on the corresponding thermoelectric and spin thermoelectric properties in zigzag nanoribbons of two-dimensional hexagonal crystals are analyzed theoretically. Thermoelectric properties of quasi-stable magnetic states are also considered. Of particular interest is the influence of Coulomb and spin-orbit interactions on the topological edge states and on the transition between the topological insulator and conventional gap insulator states. It is shown that the interplay of both interactions h…
We report transport studies on (Bi,Sb)2Te3 topological insulator thin films with tunable electronic band structure. We find a doping and temperature regime in which the Hall coefficient is negative indicative of electron-type carriers, whereas the Seebeck coefficient is positive indicative of hole-type carriers. This sign anomaly is due to the distinct transport behaviors of the bulk and surface states: the surface Dirac fermions dominate magnetoelectric transport while the thermoelectric effect is mainly determined by the bulk states. These findings may inspire new ideas for designing topolog…
We investigate the electrical conductivity and thermoelectric effects in topological crystalline insulators in the presence of short- and long-range impurity interactions. We employ the generalized Boltzmann formalism for anisotropic Fermi surface systems. The conductivity exhibits a local minimum as doping varies owing to the Van Hove singularity in the density of states originated from the saddle point in the surface states band structure. Suppression of the interband scattering of the charge carriers at high-energy Dirac points results in a maximum in the electrical conductivity. Whenever t…
We study the thermoelectric properties of three-dimensional topological insulators in magnetic fields with many holes (or pores) in the bulk. We find that at high density of these holes in the transport direction the thermoelectric figure of merit, ZT, can be large due to the contribution of the topologically protected conducting surfaces and the suppressed phonon thermal conductivity. By applying an external magnetic field a subgap can be induced in the surface states spectrum. We show that the thermoelectric efficiency can be controlled by this tunable subgap leading to the values of ZT much…
We consider spin-polarized transport in a quantum spin Hall antidot system coupled to normal leads. Due to the helical nature of the conducting edge states, the screening potential at the dot region becomes spin dependent without external magnetic fields nor ferromagnetic contacts. Therefore, the electric current due to voltage or temperature differences becomes spin polarized, its degree of polarization being tuned with the dot level position or the base temperature. This spin-filter effect arises in the nonlinear transport regime only and has a purely interaction origin. Likewise, we find a …
Considering metallic films at room temperature, we present the first theoretical study of the spin Nernst and thermal Edelstein effects which takes into account dynamical spin-orbit coupling, i.e., direct spin-orbit coupling with the vibrating lattice (phonons) and impurities. This gives rise to two novel processes, namely a dynamical Elliott-Yafet spin relaxation and a dynamical side-jump mechanism. Both are the high-temperature counterparts of the well-known $T = 0$ Elliott-Yafet and side-jump, central to the current understanding of the spin Hall, spin Nernst and Edelstein effects at low $T…
The thermoelectric properties of the surface states in three-dimensional topological insulator nanowires are studied. The Seebeck coefficients $S_c$ and the dimensionless thermoelectrical figure of merit $ZT$ are obtained by using the tight-binding Hamiltonian combining with the nonequilibrium Green's function method. They are strongly dependent on the gate voltage and the longitudinal and perpendicular magnetic fields. By changing the gate voltage or magnetic fields, the values of $S_c$ and $ZT$ can be easily controlled. At the zero magnetic fields and zero gate voltage, or at the large perpe…
The electronic properties of disordered systems at the Anderson metal-insulator transition (MIT) have been the subject of intense study for several decades. Thermoelectric properties at the MIT, such as thermopower and thermal conductivity, however, have been relatively neglected. Using the recursive Green's function method and the Chester-Thellung-Kubo-Greenwood formalism, we calculate numerically the low temperature behaviour of all kinetic coefficients. From these we can deduce for example the electrical conductivity and the thermopower at finite temperatures. Here we present results for th…
Topological Insulators are the best thermoelectric materials involving a sophisticated physics beyond their solid state and electronic structure. We show that exists a topological contribution to the thermoelectric effect that arise between topological and thermal quantum field theories applied at very low energies. This formalism provides us with a quantized topological mass proportional to the temperature T, being both quantities directly related with an electric potential V and getting a Seebeck coefficient where we identify an anomalous contribution that we associate to the creation of rea…
Thermoelectric (TE) refrigeration such as Peltier cooler enables a unique opportunity in electric energy to directly convert thermal energy. Here, we propose a TE module with both refrigeration and power generation modes by utilizing asymmetric surfaces of a magnetic topological insulator (quantum anomalous Hall insulator) with a periodic array of hollows filled with two different dielectrics. Based on the Boltzmann transport theory, we show that its efficiency, i.e., the dimensionless figure of merit ZT exceeds 1 in the low-temperature regime below 300 K. The proposed device could be utilized…
We study transport phenomena cross-correlated among the heat and electric currents of magnons and Dirac electrons on the surface of ferromagnetic topological insulators. For a perpendicular magnetization, we calculate magnon- (electron-) drag anomalous Nernst/Seebeck (anomalous Ettingshausen/Peltier) effects and magnon-/electron-drag thermal Hall effects. The magnon-drag thermoelectric effects are interpreted to be caused by magnon-induced electromotive force. When the magnetization has in-plane components, there arise thermal/thermoelectric analogs of anisotropic magnetoresistance (AMR). In t…
Topological insulators (TI) realize a novel state of quantum matter that are distinguished by topological invariants of bulk band structure rather than spontaneously broken symmetries. A number of exotic quantum phenomena have been predicted to exist in multiply-connected geometries which require an enormous amount of materials flexibility. We have extended our previous search for TI materials from binary (Bi2X3 series) to the thermoelectric ternary compounds. We discover that the distorted LuPtSb is the first ternary compound harboring a 3D topological insulator state. We also show that the h…
We study spin conductivity of the surface states in a thin film of a topological insulator with Kubo formulas. Hybridization between the different sides of the film opens a gap at the Dirac point. We found that in the gapped region spin conductivity remains finite. In the gapless region near the band gap spin conductivity is enhanced. These findings make a thin film of a topological insulator as a promising material for spintronic applications.
Thermoelectric response of a ferroelectric insulator
National Institute for Materials Science（物质材料研究机构）；Okayama University（冈山大学）；Institute of Science Tokyo（东京科学大学）；Murata Manufacturing Co., Ltd.（村田制作所）；Tohoku University（东北大学）；The University of Tokyo（东京大学）
Insulating substrates are crucial for electrical transport study and room temperature application of topological insulator films at thickness of only several nanometers. High quality quantum well films of Bi2Se3, a typical three-dimensional topological insulator, have been grown on α-Al2O3 (sapphire) (0001) by molecular beam epitaxy. The films exhibit well-defined quantum well states and surface states, suggesting the uniform thickness over macroscopic area. The Bi2Se3 thin films on sapphire (0001) provide a good system to study low-dimensional physics of topological insulators since conductio…
The spin-Seebeck effect mediated thermoelectric energy conversion can provide efficient alternative to traditional thermoelectrics for waste heat recovery. To achieve this goal, efficient spin to charge conversion using earth-abundant materials is essential. Proximity induced Rashba effect arises from the charge potential mediated by structural inversion asymmetry, which has been reported in Si thin films and can be manipulated by controlling the thickness of Rashba layer. We demonstrate a giant Rashba spin-Seebeck effect in NiFe/p-Si (polycrystalline) bilayer thin films. The bilayer thin film…
The possibility of electrically exciting and detecting magnon currents in magnetic insulators has opened exciting perspectives for transporting spin information in electronic devices. However, the role of the magnetic field and the nonlocal thermal gradients on the magnon transport remain unclear. Here, by performing nonlocal harmonic voltage measurements, we investigate magnon transport in perpendicularly magnetized ultrathin Tm3Fe5O12 (TmIG) films coupled to Pt electrodes. We show that the first harmonic nonlocal voltage captures spin-driven magnon transport in TmIG, as expected, and the sec…
Transient reflectivity measurements of thin films, ranging from 6 to 40 nm in thickness, of the topological insulator Bi2Se3 revealed a strong dependence of the carrier relaxation time on the film thickness. For thicker films the relaxation dynamics are similar to those of bulk Bi2Se3, where the contribution of the bulk insulating phase dominates over that of the surface metallic phase. The carrier relaxation time shortens with decreasing film thickness, reaching values comparable to those of noble metals. This effect may result from the hybridization of Dirac cone states at the opposite surfa…
Axion insulator is an exotic magnetic topological insulator with zero Chern number but a nonzero quantized Chern-Simons magnetoelectric coupling. A conclusive experimental evidence for axion insulators is still lacking due to the small signal of topological magnetoelectric effect (TME). Here we show that the dynamical magnetoelectric coupling can be induced by the \emph{out-of-plane} surface magnetization dynamics in axion insulator thin films, which further generates a polarization current in the presence of an external magnetic field in the same direction. Such a current is finite in the bul…
In this review, we present a summary of some recent experiments on topological insulators (TIs) and superconducting nanowires and films. Electron-electron interaction (EEI), weak anti-localization (WAL) and anisotropic magneto-resistance (AMR) effect found in TI films by transport measurements are reported. Then, transport properties of superconducting films, bridges and nanowires and proximity effect in non-superconducting nanowires are described. Finally, the interplay between TIs and superconductors (SCs) is also discussed.
The last several years have witnessed the rapid developments in the study and understanding of topological insulators. In this review, after a brief summary of the history of topological insulators, we focus on the recent progress made in transport experiments on topological insulator films and nanowires. Some quantum phenomena, including the weak antilocalization, the Aharonov Bohm effect and the Shubnikov de Haas oscillations, observed in these nanostructures are described. In addition, the electronic transport evidence of the superconducting proximity effect as well as an anomalous resistan…
The recently discovered topological Dirac semimetal represents a new exotic quantum state of matter. Topological Dirac semimetals can be viewed as three dimensional analogues of graphene, in which the Dirac nodes are protected by crystalline symmetry. It has been found that quantum confinement effect can gap out Dirac nodes and convert Dirac semimetal to a band insulator. The band insulator is either normal insulator or quantum spin Hall insulator depending on the thin film thickness. We present the study of disorder effects in thin film of Dirac semimetals. It is found that moderate Anderson …
In this work, we have designed and simulated new thermoelectric generator based on monolayer and few-layer MoS2 nanoribbons. The proposed thermoelectric generator is composed of thermocouples made of both n-type and p-type MoS2 nanoribbon legs. Density Functional Tight-Binding Non-Equilibrium Green's Function (DFTB-NEGF) method has been used to calculate the transmission spectrum of MoS2 armchair and zigzag nanoribbons. Phonon transmission spectrum are calculated based on parameterization of Stillinger-Weber potential. Thermoelectric figure of merit, ZT, is calculated using these electronic an…
We measured the response of the surface state spectrum of epitaxial Sb2Te3 thin films to applied gate electric fields by low temperature scanning tunneling microscopy. The gate dependent shift of the Fermi level and the screening effect from bulk carriers vary as a function of film thickness. We observed a gap opening at the Dirac point for films thinner than four quintuple layers, due to the coupling of the top and bottom surfaces. Moreover, the top surface state band gap of the three quintuple layer films was found to be tunable by back gate, indicating the possibility of observing a topolog…
We present a study of the proximity effect between a ferromagnet and a paramagnetic metal of varying disorder. Thin beryllium films are deposited onto a 5 nm-thick layer of the ferromagnetic insulator EuS. This bilayer arrangement induces an exchange field, $H_{ex}$, of a few tesla in low resistance Be films with sheet resistance $R\ll R_Q$, where $R_Q=h/e^2$ is the quantum resistance. We show that $H_{ex}$ survives in very high resistance films and, in fact, appears to be relatively insensitive to the Be disorder. We exploit this fact to produce a giant low-field magnetoresistance in the corr…
Topological insulators can exhibit strong magnetoelectric effects when their time-reversal symmetry is broken. In this Letter we consider the magneto-optical Kerr and Faraday effects of a topological insulator thin film weakly exchange-coupled to a ferromagnet. We find that its Faraday rotation has a universal value at low-frequencies, $θ_{\mathrm{F}} = \mathrm{tan}^{-1}\,α$ where $α$ is the vacuum fine structure constant, and that it has a giant Kerr rotation $θ_{\mathrm{K}} = π/2$. These properties follow from a delicate interplay between thin-film cavity confinement and the surface Hall con…
We found a giant Seebeck effect in semiconducting single-wall carbon nanotube (SWCNT) films, which exhibited a performance comparable to that of commercial Bi2Te3 alloys. Carrier doping of semiconducting SWCNT films further improved the thermoelectric performance. These results were reproduced well by first-principles transport simulations based on a simple SWCNT junction model. These findings suggest strategies that pave the way for emerging printed, all-carbon, flexible thermoelectric devices.
Thermoelectric (TE) devices have been attracting increasing attention because of their ability to convert heat directly to electricity. To date, improving the TE figure of merit remains the key challenge. The advent of the topological insulator and the emerging nanotechnology open a new way to design high-performance TE devices. In this paper, we investigate the TE transport properties of the Bi2Se3 thin film by the first-principle calculations and the Boltzmann transport theory. By comparing our calculations with the earlier experimental data, we demonstrate that, for the Bi2Se3 film of thick…
The spin Seebeck effect (SSE) refers to the generation of a spin current as a result of a temperature gradient in magnetic materials including insulators. The SSE is applicable to thermoelectric generation because the thermally generated spin current can be converted into a charge current via spin-orbit interaction in conductive materials adjacent to the magnets. The insulator-based SSE device exhibits unconventional characteristics potentially useful for thermoelectric applications, such as simple structure, device-design flexibility, and convenient scaling capability. In this article, we rev…
We investigate the thermoelectric current and heat conductance in a chiral Josephson contact on a surface of a 3D topological insulator, covered with superconducting and magnetic insulator films. The contact consists of two junctions of Majorana and Dirac channels next to two superconductors. Geometric asymmetry results in a supercurrent without a phase bias. The interference of Dirac fermions causes oscillations of the electric and heat currents with an unconventional period $2Φ_0=h/e$ as functions of the Aharonov-Bohm flux. Due to the gapless character of Majorana modes, there is no threshol…
Study on Thickness and Temperature Dependence of Thermoelectric Properties in SnS Nanofilms
School of Energy and Power Engineering, Dalian University of Technology（大连理工大学能源与动力学院）；Dalian University of Technology（大连理工大学）；School of Physics and Technology, Nanjing Normal University（南京师范大学物理科学与技术学院）；Nanjing Normal University（南京师范大学）
