Nieh-Yan anomaly: Torsional Landau levels, central charge, and anomalous thermal Hall effect

Abstract

The Nieh-Yan anomaly is the anomalous breakdown of the chiral U(1) symmetry caused by the interaction between torsion and fermions. We study this anomaly from the point of view of torsional Landau levels. It was found that the torsional Landau levels are gapless, while their contributions to the chiral anomaly are canceled, except those from the lowest torsional Landau levels. Hence, the dimension is effectively reduced from (3+1)d to (1+1)d. We further show that the coefficient of the Nieh-Yan anomaly is the free energy density in (1+1)d. Especially, at finite temperature, the thermal Nieh-Yan anomaly is proportional to the central charge. The anomalous thermal Hall conductance in Weyl semimetals is then shown to be proportional to the central charge, which is the experimental fingerprint of the thermal Nieh-Yan anomaly. * zeminh2@illinois.edu[1] F. W. Hehl, P. von der Heyde, G. D. Kerlick, and J. M. Nester, Rev. Mod. Phys. 48, 393 (1976).

Topological magnetotorsional effect in Weyl semimetals

“…Due to the flexibility of condensed matter systems, there are no fundamental limitations to realize predictions that have remained hypothetical in the high-energy context. A fascinating example of such predictions is the Nieh-Yan anomaly [2][3][4][5][6][7][8] of chiral fermions in torsional spacetimes which has recently been proposed as a source of universal effects in condensed matter systems.…”

“…Until recently, physical consequences of the Nieh-Yan anomaly [2,3] have remained controversial due to the explicit appearance of the non-universal high-energy cutoff in physical predictions. However, several recent studies [4][5][6][7] have confirmed its universal character by identifying temperature as the appropriate substitute for the high-energy cutoff.…”

“…(4) has far-reaching physical consequences. Here we focus on the torsion-induced effects which have attracted significant attention recently [3,[5][6][7][8][24][25][26][27][28][29][30][31][32][33][34]. It has been shown that the torsion gives a contribution to the chiral anomaly [2] through the Nieh-Yan term [35], which in the absence of spin connection reads…”

“…This result has been verified by a direct calculation of the chiral charge density induced by torsional Landau levels, establishing the Nieh-Yan anomaly as a universal Fermi-surface effect at finite-temperatures. Furthermore, it has been argued that in addition to temperature, coefficient contains dimensionless central charge of (1+1)-d Dirac fermions [7]. Since the central charge is also related to the (1+1)-d gravitational anomaly [38], there could be a connection between the thermal Nieh-Yan anomaly in (3+1)-d and the gravitational anomaly in (1+1)-d which is yet to be revealed, moreover, temperature dependent torsional anomalies may also appear in other dimensions [8].…”

“…The second term on the right-hand side of the above equation is omitted in [7], but in our case it is of the same order as the first term since the frame fields and axial gauge potential have the same physical origin. It can also be understood as the 0th chiral pseudo-Landau level contribution to the energy current [39].…”