Jiang-Ping Hu, Shou-Cheng Zhang
A key prediction of the SO(5) theory is the antiferromagnetic vortex state. Recent neutron scattering experiment on LSCO superconductors revealed enhanced antiferromagnetic order in the vortex state. Here we review theoretical progress since the original proposal and present a theory of static and dynamic antiferromanetic vortices in LSCO superconductors. It is shown that the antiferromagnetic region induced by the vortices can be greater than the coherence length, due to the light effective mass of the dynamic antiferromagnetic fluctuations at optimal doping, and close promixity to the antiferromagentic state in the underdoped regime. Systematic experiments are proposed to unambiguously determine that the field induced magnetic scattering originates from the vortices and not from the bulk.
Shou-Cheng Zhang, Jiang-Ping Hu, Enrico Arrigoni, Werner Hanke, Assa Auerbach
Apr 10, 1999·cond-mat·PDF We construct a class of projected SO(5) models where the Gutzwiller constraint of no-double-occupancy is implemented exactly. We introduce the concept of projected SO(5) symmetry where all static correlation functions are exactly SO(5) symmetric and discuss the signature of the projected SO(5) symmetry in dynamical correlation functions. We show that this class of projected SO(5) models can give a realistic description of the global phase diagram of the high T_c superconductors and account for many of their physical properties.
Jiangping Hu, Shou-Cheng Zhang
In this work we investigate collective excitations at the boundary of a recently constructed 4D quantum Hall state. Local bosonic operators for creating these collective excitations can be constructed explicitly. Massless relativistic wave equations with helicity $S$ can be derived exactly for these operators from their Heisenberg equation of motion. For the S=1 and S=2 cases these equations reduce to the free Maxwell and linearized Einstein equation respectively. These collective excitations can be interpreted as hydrodynamical modes at the boundary of the 4D QHE droplet. Outstanding issues are critically discussed.
Shou-Cheng Zhang, Jiangping Hu
Oct 27, 2001·cond-mat·PDF We construct a generalization of the quantum Hall effect, where particles move in four dimensional space under a SU(2) gauge field. This system has a macroscopic number of degenerate single particle states. At appropriate integer or fractional filling fractions the system forms an incompressible quantum liquid. Gapped elementary excitations in the bulk interior and gapless elementary excitations at the boundary are investigated.
Shou-Cheng Zhang
This paper gives a simple introduction to the SO(5) theory of high T_c superconductivity. Current status and relation to experiments are summarized.
Shou-Cheng Zhang
In this talk I give a brief update on the recent progress in the SO(5) theory of high T_c superconductivity (Science, 275: 1089,1997). Reviewed topics include SO(5) ladders, the unification of BCS and SDW quasi-particles in the SO(5) theory and the microscopic origin of the condensation energy.
Shou-Cheng Zhang
In this talk I outline the general strategy behind the SO(5) theory of high $T_c$ superconductivity. Progress in the direction of exact SO(5) models, numerical exact diagonalization and possible experimental tests are reviewed. I also address the criticisms raised recently against the SO(5) theory and point out directions for future exploration.
Jiang-Ping Hu, Shou-Cheng Zhang
According to Wilson's theory of critical phenomena, critical exponents are universal functions of $d$, the dimension of space, and $n$, the dimension of the symmetry group. SO(5) theory of antiferromagnetism and superconductivity predicts a bicritical point where $T_N$ and $T_c$ intersect. By measuring critical exponents close to the bicritical point, and knowing that $d=3$, one can experimentally measure the number 5 of the SO(5) theory.
Shou-Cheng Zhang
The higher dimensional quantum Hall liquid constructed recently supports stable topological membrane excitations. Here we introduce a microscopic interacting Hamiltonian and present its exact ground state wave function. We show that this microscopic ground state wave function describes a topological quantum membrane. We also construct variational wave functions for excited states using the non-commutative algebra on the four sphere. Our approach introduces a non-perturbative method to quantize topological membranes.
D. Scalapino, Shou-Cheng Zhang, W. Hanke
We construct an SO(5) symmetric electron model on a two-chain ladder with purely local interactions on a rung. The ground state phase diagram of this model is determined in the strong-coupling limit. The relationship between the spin-gap magnon mode of the spin-gap insulator and the $π$ resonance mode of the d-wave pairing phase is discussed. We also present the exact ground state for an SO(5) superspin model.
Jiang-Ping Hu, Shou-Cheng Zhang
The generic symmetry of a system under a uniform Zeeman magnetic field is U(1) x U(1). However, we show that SO(5) models in the presence of a finite chemical potential and a finite Zeeman magnetic field can have a exact SU(2) x U(1) symmetry. This principle can be used to test SO(5) symmetry at any doping level.
Shou-Cheng Zhang
Throughout John Wheeler's career, he wrestled with big issues like the fundamental length, the black hole and the unification of quantum mechanics and relativity. In this essay, I argue that solid state physics -- historically the study of silicon, semiconductors and sand grains -- can give surprisingly deep insights into the big questions of the world.
Shou-Cheng Zhang
We show that the complex phase diagram of high $T_c$ superconductors can be deduced from a simple symmetry principle, a $SO(5)$ symmetry which unifies antiferromagnetism with $d$ wave superconductivity. We derive the approximate $SO(5)$ symmetry from the microscopic Hamiltonian and show furthermore that this symmetry becomes exact under the renormalization group flow towards a bicritical point. With the help of this symmetry, we construct a $SO(5)$ quantum nonlinear $σ$ model to describe the effective low energy degrees of freedom of the high $T_c$ superconductors, and use it to deduce the phase diagram and the nature of the low lying collective excitations of the system. We argue that this model naturally explains the basic phenomenology of the high $T_c$ superconductors from the insulating to the underdoped and the optimally doped region.
B. Andrei Bernevig, Shou-Cheng Zhang
We show that two types of spin-orbit coupling in the 2 dimensional hole gas (2DHG), with and without inversion symmetry breaking, contribute to the intrinsic spin Hall effect\cite{murakami2003,sinova2003}. Furthermore, the vertex correction due to impurity scattering vanishes in both cases, in sharp contrast to the case of usual Rashba coupling in the electron band. Recently, the spin Hall effect in a hole doped $GaAs$ semiconductor has been observed experimentally by Wunderlich \emph{et al}\cite{wunderlich2004}. From the fact that the life time broadening is smaller than the spin splitting, and the fact impurity vertex corrections vanish in this system, we argue that the observed spin Hall effect should be in the intrinsic regime.
S. Chadov, X. -L. Qi, J Kübler, G. H. Fecher, C. Felser, S. -C. Zhang
Recently the Quantum Spin Hall effect (QSH) was theoretically predicted and experimentally realized in a quantum wells based on binary semiconductor HgTe[1-3]. QSH state and topological insulators are the new states of quantum matter interesting both for fundamental condensed matter physics and material science[1-11]. Many of Heusler compounds with C1b structure are ternary semiconductors which are structurally and electronically related to the binary semiconductors. The diversity of Heusler materials opens wide possibilities for tuning the band gap and setting the desired band inversion by choosing compounds with appropriate hybridization strength (by lattice parameter) and the magnitude of spin-orbit coupling (by the atomic charge). Based on the first-principle calculations we demonstrate that around fifty Heusler compounds show the band inversion similar to HgTe. The topological state in these zero-gap semiconductors can be created by applying strain or by designing an appropriate quantum well structure, similar to the case of HgTe. Many of these ternary zero-gap semiconductors (LnAuPb, LnPdBi, LnPtSb and LnPtBi) contain the rare earth element Ln which can realize additional properties ranging from superconductivity (e. g. LaPtBi[12]) to magnetism (e. g. GdPtBi[13]) and heavy-fermion behavior (e. g. YbPtBi[14]). These properties can open new research directions in realizing the quantized anomalous Hall effect and topological superconductors.
Chao-Xing Liu, Xiao-Liang Qi, HaiJun Zhang, Xi Dai, Zhong Fang, Shou-Cheng Zhang
In this paper we give the full microscopic derivation of the model Hamiltonian for the three dimensional topological insulators in the $Bi_2Se_3$ family of materials ($Bi_2Se_3$, $Bi_2Te_3$ and $Sb_2Te_3$). We first give a physical picture to understand the electronic structure by analyzing atomic orbitals and applying symmetry principles. Subsequently, we give the full microscopic derivation of the model Hamiltonian introduced by Zhang {\it et al} [\onlinecite{zhang2009}] based both on symmetry principles and the ${\bf k}\cdot{\bf p}$ perturbation theory. Two different types of $k^3$ terms, which break the in-plane full rotation symmetry down to three fold rotation symmetry, are taken into account. Effective Hamiltonian is derived for the topological surface states. Both the bulk and the surface models are investigated in the presence of an external magnetic field, and the associated Landau level structure is presented. For more quantitative fitting to the first principle calculations, we also present a new model Hamiltonian including eight energy bands.
Can-Li Song, Yi-Lin Wang, Ye-Ping Jiang, Yi Zhang, Cui-Zu Chang, Lili Wang, Ke He, Xi Chen, Jin-Feng Jia, Yayu Wang, Zhong Fang, Xi Dai, Xin-Cheng Xie, Xiao-Liang Qi, Shou-Cheng Zhang, Qi-Kun Xue, Xucun Ma
Atomically flat thin films of topological insulator Bi2Se3 have been grown on double-layer graphene formed on 6H-SiC(0001) substrate by molecular beam epitaxy. By a combined study of reflection high energy electron diffraction and scanning tunneling microscopy, we identified the Se-rich condition and temperature criterion for layer-by-layer growth of epitaxial Bi2Se3 films. The as-grown films without doping exhibit a low defect density of 1.0\pm 0.2x1011/cm2, and become a bulk insulator at a thickness of 10 quintuple layers, as revealed by in situ angle resolved photoemission spectroscopy measurement.
Binghai Yan, Hai-Jun Zhang, Chao-Xing Liu, Xiao-Liang Qi, Thomas Frauenheim, Shou-Cheng Zhang
A new class of three-dimensional topological insulator, ternary rare earth chalcogenides, is theoretically investigated with ab initio calculations. Based on both bulk band structure analysis and the direct calculation of topological surface states, we demonstrate that LaBiTe3 is a topological insulator. La can be substituted by other rare earth elements, which provide candidates for novel topological states such as quantum anomalous Hall insulator, axionic insulator and topological Kondo insulator. Moreover, YBiTe3 and YSbTe3 are found to be normal insulators. They can be used as protecting barrier materials for both LaBiTe3 and Bi2Te3 families of topological insulators for their well matched lattice constants and chemical composition.
Hong-Chen Jiang, Stephan Rachel, Zheng-Yu Weng, Shou-Cheng Zhang, Zhenghan Wang
We systematically study the phase diagram of S=2 spin chain, by means of density-matrix renormalization group and exact diagonalization methods and confirm the presence of a dimer phase in the AKLT--SZH model. We find that the whole phase boundary between the dimer and SZH phases, including the multicritical point, is a critical line with the same central charge $c=5/2$. Finally, we propose and confirm that this line can be described by the $\rm SO(5)_1$ Wess-Zumino-Witten (WZW) conformal field theory.
Suk Bum Chung, Xiao-Liang Qi, Joseph Maciejko, Shou-Cheng Zhang
We propose a conductance measurement to detect the backscattering of chiral Majorana edge states. Because normal and Andreev processes have equal probability for backscattering of a single chiral Majorana edge state, there is qualitative difference from backscattering of a chiral Dirac edge state, giving rise to half-integer Hall conductivity and decoupling of fluctuation in incoming and outgoing modes. The latter can be detected through thermal noise measurement. These experimental signatures of Majorana fermions are robust at finite temperature and do not require the size of the backscattering region to be mesoscopic.