Emergence of Supersymmetric Quantum Electrodynamics

Supersymmetric (SUSY) gauge theories such as the minimal supersymmetric standard model play a fundamental role in modern particle physics, but have not been verified so far in nature. Here, we show that a SUSY gauge theory with dynamical gauge bosons and fermionic gauginos emerges naturally at the pair-density-wave (PDW) quantum phase transition on the surface of a correlated topological insulator hosting three Dirac cones, such as the topological Kondo insulator ${\mathrm{SmB}}_6$. At the quantum tricritical point between the surface Dirac semimetal and nematic PDW phases, three massless bosonic Cooper pair fields emerge as the superpartners of three massless surface Dirac fermions. The resulting low-energy effective theory is the supersymmetric $XYZ$ model, which is dual by mirror symmetry to $\mathcal{N}=2$ supersymmetric quantum electrodynamics in $2+1$ dimensions, providing a first example of emergent supersymmetric gauge theory in condensed matter systems. Supersymmetry allows us to determine certain critical exponents and the optical conductivity of the surface states at the strongly coupled tricritical point exactly, which may be measured in future experiments.

Figure 1

(a) Hexagonal surface Brillouin zone of a TI with three Dirac cones ${\psi }_1$, ${\psi }_2$, and ${\psi }_3$, as in ${\mathrm{SmB}}_6$. The three intervalley PDW order parameters are labeled by ${\varphi }_1$, ${\varphi }_2$, and ${\varphi }_3$, which can be rotated into Dirac fermions by a SUSY transformation at the nematic PDW tricritical point. (b) Schematic quantum phase diagram. $U_1$, $U_2$ represent combinations of the couplings $r$, $u$, $u^{\prime }$, $u^{\prime \prime }$ in the Landau-Ginzburg theory (3). Solid (dashed) lines represent second- (first-) order transitions. The red circle represents the tricritical point between the Dirac SM and nematic PDW phases, where SUSY of the $XYZ/\mathrm{SQED}$ type emerges.