In planar tilted Dirac cone systems, the tilt parameter can be made space-dependent by either a perpendicular displacement field or by chemical substitution in certain systems. We show that the symmetric partial derivative of the tilt parameter generates non-Abelian synthetic gauge fields in these systems. The small velocity limit of these gauge forces corresponds to Rashba and Dresselhaus spin-orbit couplings. At the classical level, new forms of forces from conservative and Lorentz-type to (anti-)friction-like forces emerge from the effective spacetime structure in these materials. The velocity-dependent forces are odd with respect to tilt and therefore have opposite signs in the two valleys when the system is inversion symmetric. Furthermore, toggling the chemical potential between the valence and conduction bands by a gate voltage reverses the sign of the all these classical forces, which indicates these forces couple to the electric charge of the carriers. As such, these “gravitomagnetic” forces are natural extensions of the electric and magnetic forces that appear in the particular geometry of the tilted Dirac cone systems.

中文翻译：

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倾斜的狄拉克锥系统中的非阿贝尔规范场和重力效应

在平面倾斜的狄拉克锥系统中，可以通过垂直位移场或在某些系统中通过化学取代使倾斜参数与空间有关。我们表明，倾斜参数的对称偏导数在这些系统中生成非阿贝尔合成量规场。这些标尺力的较小速度极限对应于Rashba和Dresselhaus自旋轨道耦合。在古典水平上，从这些材料的有效时空结构中出现了新形式的力量，从保守的和洛伦兹型的到（反）摩擦型的力量。与速度有关的力相对于倾斜是奇数的，因此当系统反对称时，在两个谷中具有相反的符号。此外，通过栅极电压在价带和导带之间切换化学势会颠倒所有这些经典力的符号，这表明这些力耦合到载流子的电荷。这样，这些“重力”力是在倾斜的狄拉克锥系统的特定几何形状中出现的电磁力的自然延伸。