TY - JOUR

T1 - Invalidity of translational symmetry argument for the existence of a stark ladder in finite crystals

AU - Rabinovitch, A.

N1 - Funding Information:
There had recently been a dispute over the theoretical existence or non-existence of a " Stark Ladder" in solids \[1-3\]. Although there is no experimental evidence to show such an effect, several theoretical proofs \[4,5\] have appeared in the literature and the negative experimental result was attributed to difficulties of measurement. The inconsistency of most of the existing proofs was demonstrated by Zak \[1,3\]. But one basic idea which is the origin of the whole notion of a Stark Ladder in solids still remained undisputed. This idea is the translational symmetry of the SchrSdinger equation. In this paper we show that the symmetry argument is not true for a finite crystal. It is usually stated in the literature \[4\] and commonly believed that results obtained for infinite crystals should hold for finite ones as well, provided the appropriate boundary conditions are chosen. The boundary conditions most frequently quoted are the "Born-von-Karman" or "periodic" ones. We discuss this point for the case where the crystal is put in an external electric field, and show that for this case the finite and infinite cases cannot be reconciled by the Born-von-Karman boundary conditions. Now, as was pointed out previously \[1\], for the infinite crystal this translational symmetry argument does not lead to the so called "Stark Ladder". In this work we show that for the finite crystal this argument is not valid at all and thus does not indicate an existence of a "Stark Ladder". Furthermore. if one tries to * Supported by Adv3nced Research Projects Agency through the Northwestern University Materials Re-search Center, and by the Air Force Office of Scien-tific Research.

PY - 1970/11/30

Y1 - 1970/11/30

N2 - The usual translational symmetry argument in finite solids does not indicate the existence of a Stark Ladder. The (usually implied) use of "periodic boundary conditions", which could have indicated a Stark Ladder, has a two fold interpretation. The Born-von Karman one is incompatible with Schrödinger's equation, while the second is incompatible with the symmetry argument.

AB - The usual translational symmetry argument in finite solids does not indicate the existence of a Stark Ladder. The (usually implied) use of "periodic boundary conditions", which could have indicated a Stark Ladder, has a two fold interpretation. The Born-von Karman one is incompatible with Schrödinger's equation, while the second is incompatible with the symmetry argument.

UR - http://www.scopus.com/inward/record.url?scp=0042321781&partnerID=8YFLogxK

U2 - 10.1016/0375-9601(70)90855-8

DO - 10.1016/0375-9601(70)90855-8

M3 - Article

AN - SCOPUS:0042321781

SN - 0375-9601

VL - 33

SP - 403

EP - 404

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 6

ER -