Magnetic-field dependence of quasiparticle interference peaks in a $d$-wave superconductor with weak disorder

Quasiparticle interference in a $d$-wave superconductor with weak disorder produces distinctive peaks in the Fourier-transformed local density of states measured by scanning tunneling spectroscopy. We predict that amplitudes of these peaks can be enhanced or suppressed by applied magnetic field according to a very specific pattern governed by the symmetry of the superconducting order parameter. This calculated pattern agrees with the recent experimental measurement and suggests that the technique could be useful for probing the underlying normal state at high fields.

Figure 1

(Color online) (a) Contours of constant quasiparticle energy $\omega =0.1t$ in a $d$-wave superconductor in the first Brillouin zone. We use a standard tight-binding lattice model (Ref. 13) with $t^{\prime }=-0.3t$, ${\Delta }_0=0.2t$, and $\mu =-t$. (b) Positions of the quasiparticle interference peaks resulting from the octet model downfolded to the first Brillouin zone. The peaks enhanced (suppressed) by the magnetic field are marked by solid (open) circles.

Figure 2

(Color online) Enhancement of FT-LDOS peaks by magnetic field at octet vectors ${\mathit{q}}_i$ modeled by Eq. (10) with the band structure as in Fig. 1. In the calculation the field $H$ is represented by the vortex core scattering rate $V_1$ and $H_0$ is chosen such that $H/H_0=V_1/V_3$. The data are normalized to the $H=0$ value which we model by $V_1=0$ and $V_3>0$, i.e., charged impurities only.