Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden.
Phys Rev Lett. 2018 Sep 28;121(13):137601. doi: 10.1103/PhysRevLett.121.137601.
Quantum transport close to a critical point is a fundamental, but enigmatic problem due to fluctuations, persisting at all length scales. We report the scaling of optical conductivity (OC) in the collisionless regime (ℏω≫k_{B}T) in the vicinity of a relativistic quantum critical point, separating two-dimensional (d=2) massless Dirac fermions from a fully gapped insulator or superconductor. Close to such a critical point, gapless fermionic and bosonic excitations are strongly coupled, leading to a universal suppression of the interband OC as well as of the Drude peak (while maintaining its delta function profile) inside the critical regime, which we compute to the leading order in 1/N_{f}- and ε expansions, where N_{f} counts the fermion flavor number and ε=3-d. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalizations of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented, which can be tested numerically and possibly from nonperturbative gauge-gravity duality, for example.
在临界点附近的量子输运是一个基本但神秘的问题，因为波动会在所有长度尺度上持续存在。我们报告了在无碰撞区（ℏω≫k_{B}T）中，在相对论量子临界点附近的光学电导率（OC）的标度，该临界点将二维（d=2）无质量狄拉克费米子与完全带隙绝缘体或超导体分隔开来。在这样的临界点附近，无间隙的费米子和玻色子激发强烈耦合，导致带间 OC 以及临界区内 Drude 峰（同时保持其δ函数轮廓）的普遍抑制，我们在 1/N_{f}-和 ε 展开的主导阶上计算了这一点，其中 N_{f} 计数费米子的味道数，ε=3-d。由于长程库仑相互作用以及这些情况到强相互作用的三维狄拉克或外尔液体的推广，在这样的非高斯临界点处对 OC 的修正也被提出，这些修正可以通过数值和可能的非微扰规范 - 引力对偶性来进行检验，例如。
