It has recently been shown that electronic states in bulk gapless HgCdTe offer another realization of pseudo-relativistic three-dimensional particles in condensed matter systems. These single valley ...relativistic states, massless Kane fermions, cannot be described by any other relativistic particles. Furthermore, the HgCdTe band structure can be continuously tailored by modifying cadmium content or temperature. At critical concentration or temperature, the bandgap collapses as the system undergoes a semimetal-to-semiconductor topological phase transition between the inverted and normal alignments. Here, using far-infrared magneto-spectroscopy we explore the continuous evolution of band structure of bulk HgCdTe as temperature is tuned across the topological phase transition. We demonstrate that the rest mass of Kane fermions changes sign at critical temperature, whereas their velocity remains constant. The velocity universal value of (1.07±0.05) × 10(6) m s(-1) remains valid in a broad range of temperatures and Cd concentrations, indicating a striking universality of the pseudo-relativistic description of the Kane fermions in HgCdTe.
The universal value of the Faraday rotation angle close to the fine structure constant (α≈1/137) is experimentally observed in thin HgTe quantum wells with a thickness on the border between trivial ...insulating and the topologically nontrivial Dirac phases. The quantized value of the Faraday angle remains robust in the broad range of magnetic fields and gate voltages. Dynamic Hall conductivity of the holelike carriers extracted from the analysis of the transmission data shows a theoretically predicted universal value of σ_{xy}=e^{2}/h, which is consistent with the doubly degenerate Dirac state. On shifting the Fermi level by the gate voltage, the effective sign of the charge carriers changes from positive (holes) to negative (electrons). The electronlike part of the dynamic response does not show quantum plateaus and is well described within the classical Drude model.
A
bstract
We consider the most general two-loop massless correlator
I
(
n
1
, n
2
, n
3
, n
4
, n
5
;
x, y
;
D
) of two composite vertices with the Bjorken fractions
x
and
y
for arbitrary indices {
n
...i
} and space-time dimension
D
; this correlator is represented by a “kite” diagram. The correlator
I
({
n
i
};
x, y
;
D
) is the generating function for any scalar Feynman integrals related to this kind of diagrams. We calculate
I
({
n
i
};
x, y
;
D
) and its Mellin moments in a direct way by evaluating hypergeometric integrals in the α representation. The result for
I
({
n
i
};
x, y
;
D
) is given in terms of a double hypergeometric series — the Kampé de Férriet function. In some particular but still quite general cases it reduces to a sum of generalized hypergeometric functions
3
F
2
. The Mellin moments can be expressed through generalized Lauricella functions, which reduce to the Kampé de Férriet functions in several physically interesting situations. A number of Feynman integrals involved and relations for them are obtained.
We consider the calculation of the pion-photon transition form factor F super(gamma*gammapi0)(Q super(2)) within light-cone sum rules focusing attention to the low-mid region of momenta. The central ...aim is to estimate the theoretical uncertainties which originate from a wide variety of sources related to (i) the relevance of next-to-next-to-leading order radiative corrections (ii) the influence of the twist-four and the twist-six term (iii) the sensitivity of the results on auxiliary parameters, like the Borel scale M super(2), (iv) the role of the phenomenological description of resonances, and (v) the significance of a small but finite virtuality of the quasireal photon. Predictions for F super(gamma*gammapi0)(Q super(2)) are presented which include all these uncertainties and found to comply within the margin of experimental error with the existing data in the Q super(2) range between 1 and 5GeV super(2), thus justifying the reliability of the applied calculational scheme. This provides a solid basis for confronting theoretical predictions with forthcoming data bearing small statistical errors.
A two-dimensional semimetal is discovered in the (013) HgTe quantum well with a thickness of
d
= 14 nm, which is much smaller than those previously studied. It is found that such semimetal is ...characterized by the same band overlap as the wells with
d
=18−22 nm having the same orientation, but here the impurity scattering of both electrons and holes is much more pronounced. The electron cyclotron photoresistance is measured as a function of the electron density (
N
s
) and it is shown that the amplitude of the electron cyclotron photoresistance decreases with decreasing density, and the electron cyclotron photoresistance is not detected at
N
s
< 5 × 10
9
cm
−2
. Thus, the two-dimensional semimetal under study does not exhibit the
N
s
-independent electron cyclotron photoresistance, which was earlier observed in the two-dimensional semimetal arising near the (100) surface. This is assumingly due to a significantly lower (by more than an order of magnitude) electron mobility in the system under study.
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