4 the quantum wire. In equilibrium, this measured electric field is just the transverse electric field derived in Eq.(8). Usually it is the Hall resistance R$_{H}$ that is directly mea- sured. Taking account all the factors concerned before, in the realistic case ℓ ≪ R ≪ d , we have to this layer directly. In this case, one can have a system with coexistence of AHE and UAHE. When the layer is thin, the effective current-surface separation is small, so that anomalous electric field is large. Meanwhile, the phonon scattering greatly suppresses AHE. As a result, UAHE is overwhelming, and the net Hall conductance decreases if the layer thinkness increases. However, in the thick layer limit, UAHE is vanishingly small, and AHE is dominant. The Hall conductance would approach to a constant value. This cross-over between AHE and UAHE help us to distinguish these two effect not only conceptually, but also experimentally. In conclusion, we have proposed an unconventional anomalous Hall effect in this work. In the laboratory frame, the upward magnetic field induced by a charged current leads to an unconventional Hall response. This effect can be explained as a monopole current in the co- moving frame. This UAHE survives even when the chem- ical potential is away from the gap opened by chirality fixing ferromagnetic layer on top of TI. Two experiments are proposed in this paper, which hopefully provide the smoking-guns of TI. This result shows that the Hall resistance decays in- versely proportional to R , which serves as a quantitative characteristic for this monopole-induced Hall effect. If R = 1 µ m, and the longitude current I = 1mA, we have the rough estimation that R$_{H}$ ≈ 0 . 01Ω, and V$_{H}$ ≈ 10 µ V. This Hall voltage can be easily measured by usual volt- meters. Actually these conditions can be further opti- mized. The most effective way is to drive Fermi surface closer to the Dirac point, as the Hall voltage increases with ∝ 1 /ε 2 $_{F}$. Consequently this effect is quite promising to be detected in the near future. Conventional anomalous Hall effect (AHE) in ferro- magnetic metals has been well studied in the past[7]. In that case, the magnetization alone is not sufficient to support the giant Hall effect. Its role is to break the time reversal only, while it is the spin-orbit interaction that provides the driving force. The situation is similar in our setup. The ferromagnetic layer on top of TI sur- face only breaks the time reversal symmetry and fixes the chirality. The real driving force is the transverse electric field given by the monopole current. In this sense we name our new effect as unconventional anomalous Hall effect (UAHE). Actually the magnetic field provided by the magnetic layer is vanishingly small in the Hall bar measured, and the conventional Hall effect is negligible here. This magnetic field is restricted on the TI surface only. In addition, UAHE is fundamentally different from the conventional Hall effect. For the conventional one, the Hall voltage satisfies V$_{H}$ = vBd ∝ I/ρ , where ρ is the charge density. While in the present situation, V$_{H}$ ∝ ρv ∝ I . It means that the Hall voltage here is un- changed as long as the current is fixed. On the contrary, in the conventional Hall effect, the charge density mat- ters. If the gate changes sign, charge density and conse- quently Hall voltage acquire a sign change as well. From this point of view, we can easily distinguish UAHE from conventional Hall effect. Actually, even when the chiral- ity is fixed by an external magnetic field, where UAHE coexists with conventional Hall effect, one can also sepa- rate UAHE from the conventional one effectively. In this case, we may adjust the gate voltage to vary the carrier density, and plot the Hall voltage versus inverse of the carrier density. The intercept gives the UAHE. On the other hand, we may also vary the magnetic field. The zero field limit gives the desired result as well. It’s a revealing issue when the ferromagnetic layer on TI surface is metallic, and Hall measurement is applied It’s also an interesting issue when the chirality of TI surface is fixed by the spin of the charge carrier itself. When the current-surface separation is quite small, the local magnetic field is provided by the local spin only. Opposite spins would lead to opposite chiralities, and the direction of local monopole current is therefore op- posite. As the charge here is the same for both spin, the transverse force would be opposite. Consequently, the conventional spin Hall effect emerges and the trans- verse spin voltage is expected. The issue can be simpli- fied when the incident current is spin polarized, where UAHE induced spin Hall effect would lead to a Hall volt- age built between the two edges. However it should be pointed out that the gap opened by a single spin is pretty small ( T (K) ∝ R (m) − $^{3}$, and T ∼ 1K when R = 1 ˚ A ), and ultra-low temperature is called for. We thank M. Kawasaki, P. A. Lee, Y. Tokura and D. Vanderbilt for insightful discussions. This work is supported by Grant-in-Aids from under the Grant No. 21244053 No. 17105002, No. 19048015 and No. 19048008 from MEXT, Japan and Grand in Ministry of Education of China under the Grant No. B06011. R$_{H}$ = h e $_{2}$α 2 m ε$_{F}$ ℓ R (9) [5] X. L. Qi, T. L. Hughes, and S. C. Zhang, Phys. Rev. B 78 , 195424 (2008). [4] D. Hsieh, et. al , Nature 452 , 970 (2008). [3] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95 , 146802 (2005). [2] L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 98 , 106803 (2007). [1] B. A. Bernevig, T. L. Hughes, and S. C. Zhang, Science 314 , 1757 (2006).