Fermionic symmetry-protected topological state in strained graphene

The low-energy physics of graphene is described by relativistic Dirac fermions with spin and valley degrees of freedom. Mechanical strain can be used to create a pseudo magnetic field pointing to opposite directions in the two valleys. We study interacting electrons in graphene exposed to both an external real magnetic field and a strain-induced pseudo magnetic field. For a certain ratio between these two fields, it is proposed that a fermionic symmetry-protected topological state can be realized. The state is characterized in detail using model wave functions, Chern-Simons field theory, and numerical calculations. Our paper suggests that graphene with artificial gauge fields may host a rich set of topological states.Comment: 8 pages, 4 figure

Deterministic Constructions of Binary Measurement Matrices from Finite Geometry

Deterministic constructions of measurement matrices in compressed sensing (CS) are considered in this paper. The constructions are inspired by the recent discovery of Dimakis, Smarandache and Vontobel which says that parity-check matrices of good low-density parity-check (LDPC) codes can be used as {provably} good measurement matrices for compressed sensing under $\ell_1$-minimization. The performance of the proposed binary measurement matrices is mainly theoretically analyzed with the help of the analyzing methods and results from (finite geometry) LDPC codes. Particularly, several lower bounds of the spark (i.e., the smallest number of columns that are linearly dependent, which totally characterizes the recovery performance of $\ell_0$-minimization) of general binary matrices and finite geometry matrices are obtained and they improve the previously known results in most cases. Simulation results show that the proposed matrices perform comparably to, sometimes even better than, the corresponding Gaussian random matrices. Moreover, the proposed matrices are sparse, binary, and most of them have cyclic or quasi-cyclic structure, which will make the hardware realization convenient and easy.Comment: 12 pages, 11 figure

Dynamic investment, debt structure and debt overhang

We study the impact of the optimal debt and priority structure on the intertwined corporate financing and investment decisions in a dynamic trade-off model, where the firm simultaneously uses bank and market debt for project financing. Private bank debt is renegotiable during financial distress, thus it avoids inefficient and costly bankruptcy losses should the renegotiation be successful. Our model shows: (i) Shareholders' bargaining power, renegotiation friction, growth potential, and bankruptcy costs limits bank debt capacity; (ii) The substitution effect between bank and market debt dominates in most cases; (iii) Bank debt issuance reduces the bankruptcy risk and speeds firm investment, which mitigates the debt overhand effect; (iv) Debt priority structure has a monotonic positive effect on firms' optimal capital structure, the net benefit of mixed debt financing, and firm valuation, the effect of which is much stronger for weaker shareholders, therefore, it would be optimal to place bank debt as senior for firm value maximization; (v) The benefit of mixed debt financing is significant (a firm valuation boost between 5%- 10% ) compared to either the bank debt exclusive or market debt exclusive debt structure