Realizing Majorana Zero Modes by Proximity Effect between Topological Insulators and d-wave High-Temperature Superconductors

We theoretically study superconducting proximity effect between a topological insulator (TI) and a high-temperature d-wave superconductor (dSC). When the TI-dSC heterostructure violates 90 degree-rotation and certain reflection symmetries, we show that a sizable s-wave pairing, coexisting with a d-wave one, emerges in the proximity-induced superconductivity in the TI's top surface states. Weak disorder further suppresses d-wave pairing but not s-wave one in the TI's surface states. More importantly, the pairing gap in surface states is found to be nodeless and nearly-isotropic when the Fermi pocket of surface states is relatively small. Our theoretical results qualitatively explain recent experimental evidences of a nearly-isotropic pairing gap on surface states of Bi_2Se_3 induced by proximity with high-T_c cuprate Bi_2Ca_2Cu_2O_{8+\delta}. We also demonstrate convincing evidences of Majorana zero modes in a magnetic hc/2e vortex core, which may be detectable in future experiments.Comment: 4.5 pages, 4 figure

Majorana-time-reversal symmetries: a fundamental principle for sign-problem-free quantum Monte Carlo simulations

A fundamental open issue in physics is whether and how the fermion sign problem in quantum Monte Carlo (QMC) simulations can be solved generically. Here, we show that Majorana-time-reversal (MTR) symmetries can provide a unifying principle to solve the fermion sign problem in interacting fermionic models. By systematically classifying Majorana-bilinear operators according to the anti-commuting MTR symmetries they respect, we rigorously proved that there are two and only two fundamental symmetry classes which are sign-problem-free and which we call the "Majorana class" and "Kramers class", respectively. Novel sign-problem-free models in the Majorana class include interacting topological superconductors and interacting models of charge-4e superconductors. We believe that our MTR unifying principle could shed new light on sign-problem-free QMC simulation on strongly correlated systems and interacting topological matters.Comment: Accepted by Phys. Rev. Lett. Added more references and moved part of the paper into the Supplemental Materia

Fermion-sign-free Majarana-quantum-Monte-Carlo studies of quantum critical phenomena of Dirac fermions in two dimensions

Quantum critical phenomena may be qualitatively different when massless Dirac fermions are present at criticality. Using our recently-discovered fermion-sign-free Majorana quantum Monte Carlo (MQMC) method introduced by us in Ref. [1], we investigate the quantum critical phenomena of {\it spinless} Dirac fermions at their charge-density-wave (CDW) phase transitions on the honeycomb lattice having $N_s=2L^2$ sites with largest $L=24$. By finite-size scaling, we accurately obtain critical exponents of this so-called Gross-Neveu chiral-Ising universality class of {\it two} (two-component) Dirac fermions in 2+1D: $\eta=0.45(2)$, $\nu=0.77(3)$, and $\beta=0.60(3)$, which are qualitatively different from the mean-field results but are reasonably close to the ones obtained from renormalization group calculations.Comment: 5.3 pages, Published as part of "Focus on Topological Physics: From Condensed Matter to Cold Atoms and Optics" in New Journal of Physic

Solving fermion sign problem in quantum Monte Carlo by Majorana representation

In this paper, we discover a new quantum Monte Carlo (QMC) method to solve the fermion sign problem in interacting fermion models by employing Majorana representation of complex fermions. We call it "Majorana QMC" (MQMC). Especially, MQMC is fermion sign free in simulating a class of spinless fermion models on bipartite lattices at half filling and with arbitrary range of (unfrustrated) interactions. To the best of our knowledge, MQMC is the first auxiliary field QMC method to solve fermion sign problem in spinless (more generally, odd number of species) fermion models. MQMC simulations can be performed efficiently both at finite and zero temperatures. We believe that MQMC could pave a new avenue to solve fermion sign problem in more generic fermionic models.Comment: Selected as an Editors' Suggestion in PRB Rapid Communication, published version with updated referenc

Statistical properties and decoherence of two-mode photon-subtracted squeezed vacuum

We investigate the statistical properties of the photon-subtractions from the two-mode squeezed vacuum state and its decoherence in a thermal environment. It is found that the state can be considered as a squeezed two-variable Hermite polynomial excitation vacuum and the normalization of this state is the Jacobi polynomial of the squeezing parameter. The compact expression for Wigner function (WF) is also derived analytically by using the Weyl ordered operators' invariance under similar transformations. Especially, the nonclassicality is discussed in terms of the negativity of WF. The effect of decoherence on this state is then discussed by deriving the analytical time evolution results of WF. It is shown that the WF is always positive for any squeezing parameter and photon-subtraction number if the decay time exceeds an upper bound (}$\kappa t>{1/2}\ln \frac{2\bar{n}+2}{2\bar{n}+1}).Comment: 17 pages, 11 figure

Study on the radiative decays of Υ(nS)→ηb+γ\Upsilon(nS)\to \eta_b+\gamma

In this work, we investigate the characteristics of the spin-singlet state $\eta_b$ of the bottomonia family via the radiative decays of $\Upsilon(nS)\to \eta_b+\gamma$. The theoretical estimation of the decay widths is carried out in terms of the light-front quark model (LFQM). Recently CLEO and BaBar collaborations have measured $\mathcal{B}(\Upsilon(3S)\to\gamma\eta_b)$ and the mass of ${\eta_b}$. In terms of the data we fix the concerned input parameters in our calculations of $\Upsilon(nS)\to \eta_b+\gamma$. A special attention is paid on the transition of $\Upsilon(5S)\to \eta_b+\gamma$. The BELLE data showed that the width of $\Upsilon(5S)\to \Upsilon(2S,1S)+\pi\pi$ is two orders larger than that of $\Upsilon(4S)\to \Upsilon(2S,1S)+\pi\pi$, thus some theoretical explanations have been proposed. Among them, it is suggested the inelastic final state interaction (IFSI) $\Upsilon(5S)\to B\bar B\to \Upsilon(1S)+\pi\pi$ may be a natural one. If so, a similar mechanism also applies to $\Upsilon(5S)\to B^{(*)}\bar B^{(*)}\to \eta_b+\gamma$, the precise measurement would serve as a good test whether $\Upsilon(5S)$ possess exotic components. Our calculation in the LFQM indicates that the rate of the direct process $\Upsilon(5S)\to\eta_b+\gamma$ is not anomalous compared to $\Upsilon(mS)\to\eta_b+\gamma (m=1,2,3,4)$, thus if the IFSI does apply, the rate of $\Upsilon(5S)\to\eta_b+\gamma$ should be larger than the others by orders.Comment: 7 pages, 4 figures; Rectification made and a footnote adde

The heavy-to-light transitions in the light-cone QCD sum rules

We have analyzed the $B\to \pi$ and $B_{s}\to K$ semileptonic form factors and $B\to V\gamma (V=K^*,\rho,\omega)$ processes in the light-cone QCD sum rules. In order to enhance the predictivity and reliability of numerical results the chiral-current correlator is employed and the twist-3 light-cone wavefunction can be effectively eliminated from the sum rules.Comment: Talk given at Internatinal Comference on Flavor Physics (ICFP 2001), Zhang-Jia-Jie city, Hunan, China, 31 May - 6 Jun, 200

Deconfined quantum criticality and emergent SO(5) symmetry in fermionic systems

Deconfined quantum criticality with emergent SO(5) symmetry in correlated systems remains elusive. Here, by performing numerically-exact state-of-the-art quantum Monte Carlo (QMC) simulations, we show convincing evidences of deconfined quantum critical points (DQCP) between antiferromagnetic and valence-bond-solid phases in the extended Hubbard model of fermions on the honeycomb lattice with large system sizes. We further demonstrate evidences of the SO(5) symmetry at the DQCP. It is important to note that the critical exponents obtained by finite-size scaling at the DQCP here are consistent with the rigourous conformal bounds. Consequently, we established a promising arena of DQCP with emergent SO(5) symmetry in interacting systems of fermions. Its possible experimental relevances in correlated systems of Dirac fermions will be discussed briefly.Comment: 5.6 pages + Supplemental Materials, 4 figure

New 3-mode squeezing operator and squeezed vacuum state in 3-wave mixing

In a 3-wave mixing process occurring in some nonlinear optical medium when }$a_{1}^{\dagger}${\small mode interacts with both }$a_{2}^{\dagger}${\small mode and }$a_{3}^{\dagger}${\small mode, we theoretically study the squeezing effect generated by the operator }$S_{3}\equiv \exp[\mu(a_{1}a_{2}-a_{1}^{\dagger}a_{2}^{\dagger})+\nu(a_{1}a_{3}-a_{1}^{\dagger}a_{3}^{\dagger})]${\small . The new 3-mode squeezed vacuum state in Fock space is derived, and the uncertainty relation for it is demonstrated, It turns out that }$S_{3}${\small may exhibit enhanced squeezing. By virtue of the technique of integration within an ordered product (IWOP) of operators, we also derive }$S_{3}${\small 's normally ordered expansion. The Wigner function of new 3-mode squeezed vacuum state is calculated by using the Weyl ordering invariance under similar transformations.Comment: 10 pages, 2 figures, submitted to EP

Atomic coherent state in Schwinger bosonic realization for optical Raman coherent effect

For optical Raman coherent effect we introduce the atomic coherent state (or the angular momentum coherent state with various angular momemtum values) in Schwinger bosonic realization, they are the eigenvectors of the Hamiltonian describing the Raman effect. Similar to the fact that the photon coherent state describes laser light, the atomic coherent state is related to Raman process.Comment: 6 page