Axionic tunneling from a topological Kondo insulator

Abstract

Discoveries over the past two decades have revealed the remarkable ability of quantum materials to emulate relativistic properties of the vacuum, from Dirac cones in graphene to the Weyl surface states of topological insulators. Yet the most elusive consequence of topology in quantum matter is the axionic $E\cdot B$ term in the electromagnetic response. Here we report a direct signature of axionic physics obtained through scanning tunneling microscopy (STM). Although recent STM experiments using SmB$_6$ nanowires have been interpreted as evidence for spin-polarized currents arising from topological surface states, we show that the observed spin polarization instead originates from axionic electrodynamics. Our analysis reveals a striking voltage-induced magnetization: extremely small voltages ($\sim$ 30 meV) generate tip moments of order 0.1 $μ_B$ that reverse sign with the applied bias. The magnitude, tunability, and reversibility of this signal are consistent with an axionic $E \cdot B$ coupling, and fully account for the magnetic component of the tip density of states, ruling out static magnetism. Millivolt-scale control of spin polarization in a tunnel junction provides a new route for probing axionic electrodynamics and opens avenues for future STM and spintronics applications.

Figures (4)

• Figure 1: Scanning tunneling spectroscopy obtained using an SmB$_6$ nanowire tip on the lattice antiferromagnet Fe$_{1+x}$Te. a. Schematic of the STM tunnel junction where SmB$_6$ nanowire forms the tip and the antiferromagnet Fe$_{1+x}$Te is the sample. b. Graphic showing the bicollinear antiferromagnetic structure on the surface of Fe$_{1+x}$Te. The spins on the iron atoms point into/out of the plane. c. Average $dI/dV$ spectra obtained with the nanowire tip on Fe$_{1+x}$Te. The blue shaded region highlights the Fano lineshape, and the pink shaded area within it denotes the feature associated with the topological surface state Jiao2016. d. Electric field penetrating the SmB$_6$ nanowire induces an axionic Hall current around the wire, and a spin magnetization at its tip. e: The induced tip magnetization is linear in the tip magnetization. f. The last Sm atom in the STM tip is spin polarized by the axionic magnetization leading to a voltage-tuned spin contrast. g. Topography obtained with the SmB$_6$ tip on the surface of Fe$_{1+x}$Te at $T = 1.7$ K showing the spin contrast associated with the antiferromagnetic lattice. The white dashed line marks the line along which point spectra shown in h. have been obtained. h. Differential conductance data ($\tfrac{dI(\mathbf{x})}{dV}$) collected over a 100Å region of the crossing several periods of the antiferromagnetic lattice constant ($T = 1.7$ K, $I_{\rm{set}}$ = 120 pA, $V_{\rm{Bias}}$ = 50 mV, $V_{\rm{mod}}$ = 600 $\mu$V). White vertical dashed lines serve as a guide to the eye and clearly show the oscillation of the feature close to 0 meV with the same period as the antiferromagnetic lattice constant.
• Figure 2: Odd-voltage signal in the one-dimensional (1D) Fast Fourier Transform (FFT) of the $\tfrac{dI(\mathbf{x})}{dV}$ spectra at ${\mathbf{Q}}$.a. Absolute 1D FFT as a function of bias of the $\tfrac{dI(\mathbf{x})}{dV}$ spectra shown in Fig. \ref{['fig:Fig1']}e. b. Plot showing the relative contrast between the odd-voltage and even voltage signal at the ${\mathbf{Q}}$ as a function of applied bias voltage. c. Plot of the ratio of the intensity of the signal from ${\bf q}_{\rm AFM}$ to the Bragg peak (${\bf q}_{\rm Te}$) as a function of temperature. Black dashed line is a guide to the eye. The spin contrast signal from the AFM stripes is highly suppressed at $\sim 10$ K, at the onset of the proposed axionic coupling. Reproduced from Ref. Aishwarya2022. d. Interpolated (magnetic part) current-voltage plot obtained from the phase-referenced differential conductance data measured in our experiment. e. Representative line cut of the odd-voltage signal at two meV as a function of wave-vector showing a clear signal at ${\mathbf{Q}}$.
• Figure 3: Axionic spectrum The real a. and imaginary b. part of the magnetic spectrum $m_{\rm t}(\omega,V) = V{\rm X}(\omega)$ obtained from the phase-referenced differential conductance data.
• Figure S1: Spin contrast. Spin contrast comparison of the tunneling between the SmB$_6$ ( a, b, c) and Cr ( d, e, f) tips into the anti-ferromagnetic (AFM) sample Fe$_{1+x}$Te. a, b, d, e Phase-referenced FFT amplitudes of the height-profile obtained between $\pm 30$ meV. Relative phase amplitudes as a function of the AFM wave vector explicitly showing the contrast between SmB$_6$ ( c) and Cr ( f) tips. Reproduced from Ref. Aishwarya2022.